Robust adaptive model predictive controller with tuning to compensate for model mismatch

Abstract

The invention relates to a method for tuning a tunable model-based process controller used to control a process plant. The method comprises the steps of obtaining an error signal associated with the operation of the process controller, performing an autocorrelation analysis on the error signal to determine an indication of the presence of a model mismatch between the process controller as currently tuned and the process plant; and implementing a tuning cycle to retune the process controller based on the results of the autocorrelation analysis.

Description

RELATED APPLICATIONS

[0001] This application is a properly filed application and claims priority to and the filing date of U.S. Provisional Patent Application No. 61 / 025,190, entitled "Robust Adaptive Model Predictive Controller with Automatic Correction for Model Mismatch," filed January 31, 2008, the entire disclosure of which is hereby expressly incorporated by reference. TECHNICAL FIELD

[0002] The present application relates to process control performed, for example, in an industrial process plant, and more particularly to an improved method for performing control of a process plant using a model predictive controller in the presence of a model mismatch. GENERAL STATE OF THE ART

[0003] Process control hardware and software are essential components of virtually all facilities in the chemical, pharmaceutical, and refining industries and represent a multi-billion dollar business worldwide. Although in the past the focus was not always on achieving the best possible control in every specific case, new facilities, such as industrial process plants, are increasingly being designed with controllability and optimizability in mind. Furthermore, many existing process plants are being refurbished with this goal in mind. Such refurbishment includes not only redesigning the geometry of the installed hardware, such as the locations of reactors, reservoirs, piping, etc., but also redesigning the locations and types of control, monitoring, and measurement elements used to implement process control.With the rising cost of natural resources and the effective costs associated with emissions, energy consumption has also become a key factor in plant design.

[0004] Monitoring control performance, along with controller retuning or model planning, can dramatically improve the efficiency of industrial plants, thereby saving millions of dollars annually. Another technique that has gained popularity in recent years is abnormal situation monitoring and prevention (ASP). In some cases, the designs of modern equipment and control systems incorporate innovative sensors and integrated statistical algorithms capable of predicting potential failures or upcoming maintenance cycles. Such predictive maintenance systems can dramatically increase plant uptime and prevent costly and dangerous indicators of unexpected shutdowns. Furthermore, the reliability of these techniques has increased significantly over the past decade, leading to improvements in plant efficiency.

[0005] As part of these efforts, a group of predictive control techniques, commonly referred to as model predictive control (MPC) techniques, has gained significant industry acceptance since it was first developed and applied approximately 25 years ago. In general, MPC refers to a group of control algorithms that calculate a manipulated variable profile using a process model (which is typically linear) to optimize a linear or quadratic open-loop performance objective, subject to constraints, for some future time horizon. The first action of this optimal open-loop manipulated variable profile is then implemented within the process, and the process is repeated at each control interval or controller cycle to execute process control. Process measurements are used to update the optimization problem during ongoing control.This group of control algorithms is also called receding horizon control or moving horizon control.

[0006] However, due to its complexity, MPC has primarily been used in advanced control applications, and thus, MPC configurations are typically developed and commissioned by control experts. Therefore, it has traditionally only been worthwhile to apply MPC implementations to processes that promised significant profit increases in return for the high implementation costs. The scale of MPC applications has typically been large in terms of the number of inputs and outputs, which is one reason why MPC has typically not been used for simple control loops, such as single-controlled variable loops.

[0007] In particular, the commissioning costs of a control system are significant, and it is rarely practical to consider the detailed configuration of each control loop in a specific process plant. Therefore, approximately 90 percent of all control loops are controlled by conventional linear feedback controllers, such as proportional, integral, derivative (PID) controllers or proportional, integral (PI) controllers. Furthermore, where MPC controllers are used, these controllers are also typically linear in nature. Although linear controllers are predominantly used in the process control industry, most real-world processes unfortunately exhibit nonlinear behavior. The consequence of this mismatch is that model mismatch is inevitable. Unaddressed model mismatch not only leads to suboptimal control performance but also negates many of the benefits of technologies developed to improve control performance and uptime.Model mismatch is therefore not only costly in terms of control hardware and software, but actually reduces the savings of other related plant technologies.

[0008] In general, the performance of industrial controllers can be measured in a variety of ways, and different processes can have very different quality and safety requirements. Plant engineers can use one or many different performance criteria, such as overflow, lock-up time (integration processes), oscillation characteristics, integrated error, and integrated absolute error (IAE), to evaluate the performance of a particular control loop. However, for PID controllers, the measured control performance for a given controller typically results from a trade-off between setpoint tracking and disturbance rejection behavior, with better setpoint tracking performance leading to poorer disturbance rejection performance, and vice versa. For example, it is known that long-term constants (i.e.Load disturbances (e.g., those present in lag-predominant processes) can lead to poor disturbance rejection performance in PID controllers tuned for setpoint tracking performance. This trade-off, inherent in the design of PID controllers, can be explained by the fact that a PID controller ideally tuned for load disturbance rejection must have a relatively strong integral action (i.e., a relatively small integral time constant), and that strong integral action is detrimental to the controller's setpoint change performance. In particular, during a setpoint change, the process error (e) remains large for a time, even while the controlled variable (y) approaches the setpoint (SP). With a very large integral gain, the integral term increases rapidly, more than necessary, causing setpoint overflow.Consequently, PID tuning focused on setpoint variation performance results in lower integral response and poorer load variation or disturbance rejection performance. Since conventional PID control, which, as mentioned above, is still the most popular controller choice across all industries, suffers from this problem, numerous solutions have been proposed in an attempt to reduce the impact of this problem, including structural changes to the PID controller and setpoint filtering.

[0009] Even with these changes, tuning PID controllers still presents a challenge when it comes to determining the trade-off between setpoint tracking and disturbance rejection performance. Different PID tuning techniques typically favor either setpoint tracking performance or disturbance rejection performance. Furthermore, many model-based tuning techniques match the internal parameters of a PID controller to the internal parameters of a model for the controlled process, resulting in this very trade-off. For example, PID tuning techniques such as pole rejection and lambda tuning match the controller's integral time to the prevailing process time constant. This involves adjusting the controller's gain to achieve a specific closed-loop time constant and setpoint change response (e.g., no overshoot).Because the resulting integral action of such controllers is relatively small, this technique exhibits very good setpoint change performance but poor disturbance rejection performance. On the other hand, empirical PID tuning techniques, such as Ziegler-Nichols methods, are specifically designed for disturbance rejection performance. However, because the integral action of such controllers is strong enough to bring the process variable back to the setpoint very quickly, it leads to undesirable setpoint overflow in response to setpoint changes.

[0010] In a few cases, the purpose of a control loop is solely disturbance rejection (e.g., a buffer reservoir level with no setpoint changes) or solely setpoint tracking (e.g., a secondary control loop in a cascade strategy with no disturbances). Although it may be easy to choose a tuning configuration in such cases, the aforementioned trade-off is often completely overlooked, and instead a standard tuning technique is typically chosen, resulting in less than optimal tuning for a given process situation. Although, as previously mentioned, numerous tuning techniques have been developed to address this limitation of PID tuning, including setpoint filtering and two-degree-of-freedom structures, these tuning techniques typically favor disturbance rejection performance, and thus the controller response to setpoint changes is artificially reduced.For example, if setpoint filtering is selected, setpoint changes by the operator are filtered to prevent overflow, resulting in a slower response to setpoint changes.

[0011] In any case, it is a direct result of the performance trade-off discussed above that different tuning techniques must be chosen for different control objectives, which is one of the reasons why so many tuning techniques have been proposed for PID tuning. Another reason for the availability of so many PID tuning techniques is that different tuning rules or techniques use different inputs, perhaps only some of which are available in any particular process. For example, although many tuning techniques calculate tuning based on a process model, other techniques calculate tuning based on other process characteristics.As an example of the latter method, Ziegler-Nichols tuning rules use a critical gain and a critical frequency that may be easy to determine for some mechanical processes, but cannot be determined in a practical way for many industrial chemical processes.

[0012] On the other hand, a predictive controller, such as an MPC controller, should be able to perform similarly under setpoint changes and load changes because the integral part of an MPC controller does not allow the same trade-off seen in PID controllers. In particular, MPC controllers generally do not exhibit a performance trade-off between setpoint tracking and disturbance rejection because the error and action loss terms are inherently separate, theoretically making the MPC controller a desirable replacement for PID controllers. Likewise, in a predictive controller, the error (e) does not increase as the controlled variable or process output (y) approaches the setpoint. In fact, the error can theoretically be zero after the first execution cycle, thereby reducing or eliminating the integral gain problems inherent in PID control.Unfortunately, the performance of an MPC controller can degrade rapidly when there is a process model mismatch, that is, when the process model used by the MPC controller does not accurately match the actual process characteristics.

[0013] Furthermore, it is known that the disturbance rejection performance of industrial MPC controllers lags behind that of PID controllers when the PID controllers are specifically tuned for disturbance rejection. Recent MPC improvements in the area of ​​state update have somewhat closed this performance gap, assuming that an observer model used in the MPC technique is perfectly known. However, in the presence of a model mismatch, the control performance of a PID controller, as measured by the integrated absolute error (IAE), is still better than that of a best-tuned MPC controller.

[0014] Nevertheless, MPC has been considered one of the primary control technologies to be used to replace PID controllers, as it is believed that MPC controllers are able to combine the advantages of predictive control performance with the convenience of only a few more or less intuitive tuning parameters. To date, MPC controllers have generally only been successful in industrial environments where PID control performs poorly or is too difficult to implement or maintain, despite the fact that academia and control system vendors have recently made significant efforts to expand the range of MPC applications. Fundamentally, because PID control still performs better than MPC for a significant number of processes, and because PID controllers are cheaper and faster to deploy than MPC-type controllers, MPC controllers have actually replaced only a fraction of PID controllers in real process plant configurations.

[0015] One of the main reasons why MPC controllers tend to perform worse than PID controllers is that, as stated above, MPC controllers are more susceptible to performance degradation due to process model mismatch than PID controllers (except perhaps in processes with prevalent delay). Although there are practical ways to address model mismatch resulting from nonlinearities (or other sources) in processes, such as linearizing the control elements and transmitters and using controller gain scheduling, the most common technique for addressing model mismatch is controller tuning. However, due to the difficulties in tuning controllers, process operators or engineers often tune a controller for the worst-case scenario (e.g., for the largest process gain) and accept suboptimal tuning for other areas of the process.The default tuning parameters of an industrial PID or MPC controller are thus typically conservative, so that these tuning parameters may initially work for various process applications. However, the controllers are typically left at their default settings indefinitely, resulting in poorer overall performance. Even if this were not the case, model mismatch resulting from an identification error or from a plant deviation is more difficult to handle with tuning. Indeed, such model mismatch is difficult to capture because sufficient process disturbance is required to implement model identification, which typically contradicts the goal of process control (i.e., to maintain the process in a steady state in response to process disturbances). Furthermore, it is difficult to distinguish a process disturbance from unmeasured disturbances.

[0016] One method for "tuning" an MPC controller in response to a model mismatch is to regenerate the process model for process changes and then use this new model in the MPC controller. Unfortunately, there are many practical obstacles to developing an accurate process model for use with model-based controllers. For example, although many industrial processes are minimum-phase, most closed loops are not. Time delay, also called dead time, and higher-order delays create right-hand poles that make developing an accurate process model very difficult.In most cases, the dead time of a closed loop is created by material transport delays in pipes and discrete sampling mechanisms, which are unavoidable in computer control systems, whereas higher-order delays usually arise from filter time constants in measurement and control devices. Other challenges commonly encountered when defining process models for industrial plants include resolution and deadband, which are created by the mechanical behavior of valves and seals.

[0017] These and other factors present numerous challenges for industrial plant control engineers when developing process models for controllers. For example, even if one assumes that a certain process behaves as a first-order filter, with a specific gain and time constant depending on the vessel geometry, the control engineer must consider additional time constants of transmitters, control elements, computer sampling, and jitter. In particular, every digital control system has constraints on a central processing unit (CPU) and communications, meaning that extensive oversampling is not practical for all types of control loops in a plant.For example, while a sampling rate of three times the largest time constant plus dead time, or five times the dead time, whichever is greater, is often considered quite sufficient, this sampling rate is usually unattainable for many control loops in a plant (such as flow loops or pressure loops). As a result, the engineer usually cannot rely solely on the first-principles models that may be available for some of the responses. Furthermore, process model identification is ideally performed by integrated automated tools. However, the first-principles modeling and universal third-party solutions typically used in a real plant to identify a process model do so by interfacing directly with the field instruments.These solutions are therefore not integrated because they do not consider (or at best only approximate) the effect of the computer control system itself on control loop performance. All of these factors can lead to a significant mismatch between the process and the process model developed to control the process, making model-based control and tuning techniques less desirable in practical situations. SUMMARY OF THE INVENTION

[0018] It has been determined that deficiencies in the feedback control capabilities of MPC controllers are one reason for the performance gap between PID and MPC controllers, particularly in the presence of process model mismatch. Recognizing this fact, an MPC adaptation and tuning technique described here incorporates feedback control performance that is superior to the techniques commonly used in MPC-type controllers today, resulting in an MPC adaptation / tuning technique that performs better than conventional MPC techniques in the presence of process model mismatch.

[0019] In particular, the MPC controller performance is improved by adding an adaptation / tuning unit to an MPC controller, wherein the adaptation / tuning unit determines the best or most optimized combination of process model and MPC design and / or tuning parameters to be used during online process control to improve the disturbance rejection performance of the MPC controller in the presence of a specific degree or range of model mismatch. In particular, the adaptation / tuning unit implements an optimization routine that determines one or more tuning and design parameters of the MPC controller, including, for example,an MPC form, loss factors for an MPC controller or an observer, such as a Kalman filter, or both, and a controller model for use in the MPC controller based on a previously determined process model and either a known or expected process model mismatch or a known or expected process model mismatch range. This adaptation / tuning unit can be used to adapt and / or tune the MPC controller either periodically or continuously to develop an MPC controller with the best overall performance in the presence of a known or expected model mismatch or a model mismatch range, without the need to regenerate the original process model.This method of automatic adaptation / tuning of an MPC controller thus determines optimal tuning parameters based on a model mismatch or a model mismatch range to enable the MPC controller to function optimally in the presence of a model mismatch and can be advantageously used to perform adaptive closed-loop control, making it a better choice than PID control techniques in many cases.

[0020] Additionally, one method that can be used, for example, in an MPC controller unit uses an autocorrelation function of a control error and / or a prediction error to determine an estimated magnitude or change in the model mismatch between the currently used process model in the MPC controller and the actual process. This estimate can be used to initiate a new adaptation / tuning cycle to update the design and tuning parameters of the MPC controller, thereby implementing better control in the presence of the new degree of model mismatch.This method of detecting model mismatch can be used to determine when a controller is tuned to be more responsive to process state changes, particularly when such state changes coincide with a change in the process model, and can therefore be used to modify or retune an MPC controller before a process change occurs that the currently tuned MPC controller may not be able to handle or handle well. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] They show: Fig. 1 a functional diagram of a process control system comprising a control module including an extended controller function block implementing an MPC controller. Fig. 2 a functional diagram of a typical MPC controller. Fig.3 a functional diagram of a typical MPC control unit comprising an MPC controller and a condition observer connected to control a process plant. Fig. 4 a schematic representation of an adaptation / tuning block coupled to an MPC controller unit to determine MPC design and tuning parameters based on a process model and a model mismatch in one or more process model parameters. Fig. 5 is an example plot of the minimum integrated absolute error associated with determining an optimal tuning in the presence of a model misfit in a process gain parameter of a process model. Fig.Figure 6 is an exemplary diagram of the minimum achievable integrated absolute error associated with determining an optimal tuning in the presence of a model misfit at a first-order time constant of a process model. Fig. Figure 7 is an exemplary diagram of the minimum achievable integrated absolute error associated with determining an optimal tuning in the presence of a model misfit at a second-order time constant of a process model. Fig. 8 a three-dimensional surface graphic of the best possible integrated absolute error as obtained from the adaptation / tuning block Fig. 4 for a model mismatch between two process model parameters of an MPC controller with a state update of the standard Kalman filter. Fig.9 a three-dimensional surface graphic of the best possible integrated absolute error as obtained from the adaptation / tuning block Fig. 4 for a model mismatch of two process model parameters of an MPC controller with a state update of the simplified Kalman filter. Fig. 10 an illustration of an area of ​​model misfit in a two-dimensional subspace. Fig. 11 an illustration of the two-dimensional subspace of model misfit from Fig. 10, which in the three-dimensional diagram from Fig. 8 is superimposed at the assumed process model center to define a two-dimensional subspace of the model misfit region. Fig. 12 an illustration of how the two-dimensional subspace of the model misfit region in Fig. 11 to another location in the three-dimensional diagram Fig.11 to determine a new set of controller model parameters as well as a new set of optimal MPC tuning and design parameters associated with the subspace of the model misfit region. Fig. 13 a functional diagram of an adaptation / tuning block that optimizes an MPC controller based on a process or plant model and a model mismatch region. Fig. 14 a functional diagram showing the application of the adaptation / tuning block from Fig. 13 illustrates an MPC control using open loop tuning. Fig. 15 a functional diagram showing the application of the adaptation / tuning block from Fig. 13 illustrates an MPC control in a closed-loop tuning configuration using a property estimation function block coupled to a process. Fig.16 a functional diagram showing the application of the adaptation / tuning block from Fig. 13 illustrates an MPC control in a closed-loop tuning configuration using an innovation analysis block coupled to an MPC controller. Fig. 17 a PID of a binary distillation column used for experimental trials of an adaptation / tuning procedure of an MPC controller described here. Fig. 18 a graph of the performance of three differently tuned MPC controllers and one PID controller in controlling a level within the binary distillation column from Fig. 17 at a first steam throughput. Fig. 19 a graph of the performance of the three differently tuned MPC controllers and the PID controller when a level within the binary distillation column consists of Fig.17 after introducing an artificial unmeasured disturbance in the steam flow rate, the steam flow rate is regulated from the first steam flow rate to a second steam flow rate. Fig. 20 a graph of the performance of the two differently tuned MPC controllers and a PID controller when a level within the binary distillation column consists of Fig. 17 is regulated on the second steam flow rate. Fig. 21 is a diagram of an autocorrelation of a prediction error in the MPC controller at the three different MPC tuning settings when operated at the first steam flow rate, which is consistent with the diagram from Fig. 18 is linked. Fig. 22 is a diagram of an autocorrelation of a prediction error in the MPC controller for two of the three different MPC tuning settings when operated at the second steam flow rate compared to the diagram in Fig. 20 is linked. Fig.23 is a diagram of an autocorrelation of a prediction error in the MPC controller for the three different MPC tuning settings when operated during the rejection of the unmeasured disturbance, which is comparable to the diagram in Fig. 19 is linked. Fig. 24 is a diagram of an autocorrelation of a control error in the MPC controller at the three different MPC tuning settings (and a PID controller) when operated at the first steam flow rate, which is consistent with the diagram from Fig. 18 is linked. Fig. 25 is a diagram of an autocorrelation of a control error in the MPC controller at the three different MPC tuning settings (and a PID controller) when operated during the suppression of an unmeasured disturbance associated with the change of the steam flow rate from the first steam flow rate to the second steam flow rate. Fig.26 a functional diagram showing an application of the adaptation / tuning block from Fig. 13 illustrates an MPC controller in a closed-loop tuning configuration that includes an estimator based on either a process estimate or an innovation analysis estimate, or both, to initiate adaptive tuning of an MPC controller. DETAILED DESCRIPTION

[0022] In general, a new technique for adapting, designing, and tuning a controller is discussed here, which can be applied to various different types of model predictive control (MPC) controllers for use in any desired or suitable controller setting. However, this new technique for adapting, designing, and tuning a controller is particularly useful for control systems used in process plants, such as industrial process plants, such as pharmaceutical and chemical manufacturing plants, refineries, etc. Although the new technique for adapting, designing, and tuning an MPC controller is described here as implemented as part of a distributed process control network, it could also be implemented in other types of control environments, e.g.also as part of a centralized control system, as part of a programmable logic control (PLC) system, as part of an independent control system, etc.

[0023] With reference to Fig.1 now comprises a process control system 10 in which the technique described here for adaptation, design, and tuning of an MPC controller can be implemented, comprising a process controller 11 communicatively connected to a data archive 12 and to one or more host workstations or computers 13 (which may be any type of PC, workstation, etc.), each having a display screen 14. The controller 11 is also connected to field devices 15 to 22 via input / output (I / O) cards 26 and 28. The data archive 12 may be any desired type of data collection unit having any desired type of memory and any desired or known software, hardware, or firmware for storing data, and may be separate from the workstations 13 (as in Fig.1) or a portion thereof. The controller 11, which may be, purely by way of example, the DeltaV™ controller marketed by Emerson Process Management, is communicatively connected to the host computers 13 and the data archive 12, for example, via an Ethernet connection or other desired communications network 29. The communications network 29 may be in the form of a local area network (LAN), a wide area network (WAN), a telecommunications network, etc., and may be implemented using wired or wireless technology. The controller 11 is communicatively connected to the field devices 15 through 22 using any desired hardware and software, e.g., linked to standard 4-20 mA devices and / or any intelligent communications protocol, such as the FOUNDATION® Fieldbus (Fieldbus) protocol, the HART® protocol, the WirelessHART™ protocol, etc.

[0024] The field devices 15 to 22 can be any devices, such as sensors, valves, transmitters, positioners, etc., while the I / O cards 26 and 28 can be any type of I / O device that corresponds to any desired communication or control protocol. Fig.1, field devices 15 through 18 are standard 4-20 mA devices or HART® devices that communicate with I / O card 26 via analog lines or combined analog / digital lines, while field devices 19 through 22 are intelligent devices, such as Fieldbus field devices, that communicate with I / O card 28 via a digital bus using communications according to the Fieldbus protocol. Of course, field devices 15 through 22 could conform to any other desired standards or protocols, including any standards or protocols currently in existence or developed in the future. Likewise, communications between field devices 15 through 22 could be implemented using wired technology, wireless technology, or a combination of wired and wireless technology, as desired.

[0025] The controller 11, which may be one of many distributed controllers within the plant 10, has at least one processor therein that implements or directs one or more process control routines, which may include control loops stored therein or otherwise associated therewith. The controller 11 also communicates with the devices 15 through 22, the host computers 13, and the data archive 12 to control a process in a desired manner. It should be noted that any of the control routines or elements described herein may have portions implemented or executed by various controllers or other devices, as desired. Likewise, the control routines or elements described herein for implementation in the process control system 10 may take any form, including software, firmware, hardware, etc.For the purpose of this discussion, a process control element may be any part or section of a process control system, including, for example, a routine, block, or module stored on any computer-readable medium to be executable by a processor, such as a central processing unit of a computing device. Control routines, which may be modules or part of a control procedure, such as a subroutine, portions of a subroutine (such as lines of code), etc., may be implemented in any desired software format, such as using ladder logic, sequential function charts, functional diagrams, object-oriented programming, or another software programming language or design paradigm. Likewise, the control routines may, for example,be permanently embedded in one or more EPROMs, EEPROMs, application-specific integrated circuits (ASICs), or any other hardware or firmware elements. Furthermore, the control routines may be designed using any design tools, including graphical design tools or any other type of software, hardware, or firmware programming or design tools. Thus, the controller 11 can generally be configured to implement a control strategy or control routine in any desired manner.

[0026] In one embodiment, controller 11 implements a control strategy using so-called function blocks, where each function block is a part or object of an overall control routine and works in conjunction with other function blocks (via communications called links) to implement process control loops within process control system 10. Function blocks typically perform either an input function, such as that associated with a transmitter, sensor, or other process parameter measuring device; a control function, such as that associated with a control routine that performs PID, MPC, fuzzy logic, etc., control; or an output function that controls the operation of a device, such as a valve, to perform a physical function within process control system 10. Of course, hybrid and other types of function blocks exist.Function blocks may be stored and executed within the controller 11, which is typically the case when these function blocks are used for or associated with standard 4-20 mA devices and some types of intelligent field devices, such as HART devices, or may be stored within and implemented by the field devices themselves, which may be the case with FOUNDATION® Fieldbus devices. Furthermore, function blocks implementing controller routines, such as the controller adaptation and tuning routines or techniques described herein, may be implemented in whole or in part in the host workstations or computers 13 or in any other computing device.Although the description of the control system is provided here using a functional block control strategy that employs an object-oriented programming paradigm, the control strategy or the control loops or control modules could also be implemented or designed using other conventions and using any desired programming language or paradigm.

[0027] As the enlarged Block 30 from Fig.1, the controller 11 may include a series of single-loop control routines, depicted as routines 32 and 34, and may implement one or more extended control loops, depicted as control loop 36. Each of these loops is typically referred to as a control module. The single-loop control routines 32 and 34 are depicted as implementing single-loop control using, respectively, a single-input / single-output fuzzy logic control block and a single-input / single-output PID control block connected to suitable analog input (AI) and analog output (AO) function blocks, which may be linked to process control devices, such as valves, to measuring devices, such as temperature and pressure transmitters, or to any other device within the process control system 10.The extended control loop 36 is depicted as including an extended control block 38 having inputs communicatively connected to numerous AI function blocks and outputs communicatively connected to numerous AO function blocks. However, the inputs and outputs of the extended control block 38 may be communicatively connected to any desired function blocks or control elements to receive other types of inputs and provide other types of control outputs. While the extended control block 38 is depicted as implementing multi-variable control (e.g., multiple input / multiple output), it could also be used to implement single-variable control (e.g., single input / single output).As described below, the extended control block 38 may be a control block that integrates a model predictive control (MPC) routine with a controller adaptation / tuning block that provides the MPC controller routine with controller design and tuning parameters to perform control of the process or a portion of the process. Although the extended control block 38 is described herein as generally comprising a model predictive control (MPC) block, the extended control block 38 could actually implement any of many different types of MPC techniques, and may even, in some cases, switch between these techniques, as described in more detail herein. It should be understood that the MPC adaptation / tuning block described in . Fig.1 or subcomponents of those modules, including the extended control block 38 or its components, may be executed by the controller 11 or, alternatively, may be located in and executed by any other processing device, such as one of the workstations 13 or even one of the field devices 19 to 22. In one embodiment, for example, an MPC controller adaptation / tuning block 42 may be stored in and executed on the computer 13 to provide MPC controller tuning parameters, design parameters, and process model parameters to an MPC controller stored in the extended control block 38 executing in the controller 11.

[0028] As in Fig.1, one of the workstations 13 includes an extended control block generation routine 44 used to create, download, and implement the extended control block 38. While the extended control block generation routine 44 may be stored in memory within the workstation 13 and executed therein by a processor, this routine (or any portion thereof) may additionally or alternatively be stored in and executed by any other device within the process control system 10, as desired. Further, a user interface routine 46 may be provided to a user, such as a process operator, a control engineer, etc.enable to specify or change tuning, design, or control parameters associated with the extended control block 38, change setpoints, start an adaptation / tuning procedure executed by the adaptation / tuning block 42, to provide new model parameters, to provide model mismatch values ​​or model mismatch range values, etc.

[0029] For informational purposes, many industrial implementations of MPC techniques include model-algorithmic control (MAC) techniques and dynamic matrix control (DMC) techniques. DMC technology uses linear step-response or impulse-response models of the process, and in this case, the optimal control path is pre-calculated offline and stored in a large matrix. This controller matrix is ​​then used to calculate the online actions of the manipulated variables through superposition. This drastically reduces computational costs compared to MPC methods that solve optimal equations online.Another advantage of DMC technology is that a state variable used in it is intuitively calculated by the process model and represents the explicit future output prediction, meaning that future predictions of process outputs, such as quantities associated with boundary conditions, are readily available and can be displayed to the user.

[0030] Other MPC implementations include IDCOM and linear dynamic matrix control (LDMC), which uses a linear objective function and explicitly incorporates constraints; quadratic dynamic matrix control (QDMC), which is an extension of DMC and incorporates a quadratic power function and is explicit in incorporating constraints; IDCOM-M, which is an extension of IDCOM that uses a quadratic programming algorithm to replace the iterative solution technique of the original implementation; and Shell's multi-size optimization control (SMOC), which is a state-space implementation. Another group of MPC techniques uses a state observer to provide better MPC performance.

[0031] Fig. Figure 2 depicts a detailed functional diagram of one embodiment of a multivariable MPC controller unit 52 (communicatively coupled to the process 50) that is controlled by the extended control block 38 of Fig. 1 can be implemented to perform multi-variable process control. In this case, the MPC controller unit 52 can be used to implement a DMC control technique. However, this discussion provides a good basis for a generalized understanding of MPC control. As in Fig. 2, the extended control block 38 generates a set of manipulated variables (MV) that are provided to other function blocks, which in turn are connected to control inputs of the process 50. As shown in Fig.2, the extended control block 38 includes the MPC controller block 52, which may include or implement any standard MPC routine or method, typically having as many inputs as outputs, although this requirement is not mandatory. The MPC controller 52 receives as inputs a set of N controlled variables (CV) and auxiliary variables (AV), which are typically vectors of values ​​as measured within the process 50, a set of disturbance variables (DV), which are known or expected changes or disturbances provided to the process 50 at some time in the future, and a set of controlled and auxiliary variables of a target steady state (CV T ) and (AV T), provided, for example, by an optimizer (not shown), a user, or another source. The MPC controller 52 uses these inputs to create the set of M manipulated variable (MV) signals in the form of control signals and provides the MV manipulated variable signals to the control inputs of the process 50, which may be valve actuators, burners, pumps, etc.

[0032] Furthermore, the MPC controller 52 calculates and generates a set of controlled variables (CV SS ) and auxiliary quantities (AV SS ) of a predicted steady state together with a set of manipulated variables (MV SS ) of a predicted steady state, which respectively represent the predicted values ​​of the controlled variables (CV S ), auxiliary variables (AV S ) and manipulated variables (MV S ) at a control horizon. These variables can be used in one or more MPC optimization routines to determine the target control and target auxiliary variables CV T and AVT to develop in order to control process 50 into an optimal operating state.

[0033] Regardless of how they are developed, the target control and target auxiliary variables CV T and AV T provided as inputs to the MPC controller 52, which, as previously mentioned, sets these target values ​​CV T and AV T used to create a new set of steady-state manipulated variables MV SS (over the control horizon) which adjusts the current control and manipulated variables CV and AV to the target values ​​CV T and AV T at the end of the control horizon. It is, of course, known that the MPC controller 52 changes the manipulated variables abruptly in an attempt to achieve the steady-state values ​​for the steady-state manipulated variables MV SS which theoretically leads to the process reaching the target control and target auxiliary variables CV T and AV Tachieved. Since the MPC controller 52 operates as described above during each process sample, the target values ​​of the manipulated variables may change from one sample to another, and therefore the MPC controller 52 may never reach a particular one of these sets of target manipulated variables MV, particularly in the presence of noise, unexpected disturbances, changes in the process 50, etc.

[0034] In a known manner, the MPC controller 52 includes a process model 70 for control prediction (also called a "controller model"), which may be any type of model used in any of the various different MPC control techniques. For example, the model 70 may be an N times M+D step response matrix (where N is the number of controlled variables CV plus the number of auxiliary variables AV, M is the number of manipulated variables MV, and D is the number of disturbance variables DV). However, the model 70 may be a predictive or first-principles model of first order, second order, third order, etc., a state-space model, a convolutional process model, or any other type of process model.The controller model 70 may be determined from process failure tests using time series analysis techniques that do not require significant fundamental modeling effort, or may be determined using any other known process modeling techniques, including those that overlay one or more sets of linear models or nonlinear models. In any event, the control prediction process model 70 generates an output 72 defining a previously calculated prediction for each of the controlled and auxiliary variables CV and AV, and a vector summer 74 subtracts these predicted values ​​for the current time from the actually measured values ​​of the controlled and auxiliary variables CV and AV to generate an error or correction vector for the input 76. This error is typically referred to as the prediction error.

[0035] The control prediction process model 70 then predicts a future control parameter for each of the controlled and auxiliary variables CV and AV over the control horizon based on the disturbances and manipulated variables provided to other inputs of the control prediction process model 70. The control prediction process model 70 also generates the predicted steady-state values ​​of the controlled and auxiliary variables CV discussed above. SS and AV SS .

[0036] A control target block 80 determines a control target vector for each of the N target control and target auxiliary variables CV T and AV T, which are provided to it by the target conversion block 55 using a trajectory filter 82 previously created for block 38. In particular, the trajectory filter provides a unit vector that defines how the controlled and auxiliary variables are to be controlled to their target values ​​over time. The control target block 80 uses this unit vector and the target variables CV T and AV T to generate a dynamic control target vector for each of the control and auxiliary variables, which represents the changes in the target variables CV T and AV Tover the period defined by the control horizon time. A vector summer 84 then subtracts the future control parameter vector for each of the controlled and auxiliary variables CV and AV from the dynamic control vectors to define a future error vector for each of the controlled and auxiliary variables CV and AV. The future error vector for each of the controlled and auxiliary variables CV and AV is then provided to the MPC algorithm 86, which functions to select the steps of the manipulated variables MV that minimize, for example, the least squares error or the integrated absolute error (IAE) over the control horizon. In some embodiments, the MPC algorithm 86 may use an MxM control matrix developed, as desired, from ratios between the N controlled and auxiliary variables input to the MPC controller 52 and the M manipulated variables output from the MPC controller 52. In particular, the MPC algorithm 86 has two main objectives.First, the MPC algorithm 86 attempts to minimize the CV control error with minimal MV measures within the operating constraints, and second, attempts to achieve optimal steady-state MV values ​​and the target CV values ​​calculated directly from the optimal steady-state MV values.

[0037] The state equations for a typical model predictive controller can be formulated as follows: x^k+1=Axk+Buk k=0,1,2, ... y^k=Cx^k minuN∑j=0∞(yk+jTQyk+j+uk+jTRuk+j+Δuk+jTSΔUk+j) where Q, R, S are the loss weights for error, controller action and incremental action respectively, x k is the model state matrix, y k the process output and u kthe controller output. Because the Q, R, and S loss vectors are inherently separate, MPC controllers generally do not have a performance trade-off between setpoint tracking and disturbance rejection. However, MPC controllers must still be tuned to a specific multi-variable process control objective. While the process model is always adapted to the internal structure of an MPC controller (e.g., the process state space of the state-space MPC formulation), additional tuning parameters determine the behavior with respect to setpoint change and disturbance rejection.

[0038] In particular, the loss vectors can be used to emphasize one quantity over others depending on the control objective for the specific process, as defined by the end user. If a model mismatch is suspected, the loss vectors Q and R can also be used to make the controller more robust (i.e., detune the controller). Techniques such as funnel control or a reference trajectory have a more obvious impact on robustness, as they effectively filter the error vector, which is why these techniques are the preferred means for engineers and operators to tune model-predictive controllers in industrial process applications. Because a model-predictive controller inherently "adapts" to the process, the control actions are always optimal for the specific process model.This fact means that the controller can only be detuned (according to the physical constraints on the final control elements) and can never be tuned very aggressively. For example, a valve opening speed can never be infinite, and therefore the value of R can never realistically be zero. It is known that the disturbance rejection of industrial MPC controllers cannot match that of PID controllers when PID controllers are specifically tuned for disturbance rejection. Recent MPC improvements in the area of ​​state updating have closed this performance gap if an observer model used in the MPC routine is assumed to be perfectly known. In the presence of a model mismatch, the control performance (e.g., measured in IAE) of a PID controller is still better than that of an MPC controller with the best possible tuning.Nevertheless, single-observer MPC techniques can be used to improve feedback control performance and typically perform better than DMC techniques in this regard.

[0039] An example of an observer-based MPC control system 88 is given in Fig. 3. Here, the MPC controller system 88 comprises an MPC controller 90 and an observer 92, which in this case is assumed to be a Kalman filter. The MPC controller 90 provides control signals u to a process plant 94 and the Kalman filter 92. In addition, the MPC controller and the Kalman filter 92 receive disturbance inputs d, which are also provided to or present in the process plant 94, and receive feedback from the plant 94 in the form of measured controlled variables y. The process plant 94 is in Fig.3, where the system 94 comprises a system transfer function 96, which receives the control signals u and the disturbance signals d, and various sources of unexpected errors or disturbances. In particular, a disturbance and noise model 98 (transfer function G w ) the noise w (which may be, for example, white noise), and the output of the noise model 98 is added (in a purely theoretical summer 100) to the output of the plant transfer function 96. The output of the summer 100 is added to measurement errors or noise z in another theoretical summer 102 to produce the measured process outputs y.

[0040] In this model, the update of the state variable x of a process characterized by a stochastic state-space model can be expressed as follows: xk+1=Axk+Buk+wk yk=Cxk+nk for a process noise w kwith Gaussian distribution and a measurement noise n k .

[0041] The general goal of state observers, such as observer 92 from Fig. 3, is to provide an estimate of the internal states of a system based on all measurable system inputs and outputs. In particular, if one of the assumptions of equations (4) and (5) states that the vectors A, B, and C (which model the process) are precisely known, then the observer gains can be calculated. The filter formulation developed in the 1960s, known as the Kalman filter, was the most popular method in process control for estimating internal process states based on noisy or incomplete measurements. For a discrete sampling system using the MPC formulation given in equations (1) to (3), the Kalman filter equation for estimating the next state x is k+1 following: x^k+1=Ax^k+Bu^k+J(yk−y^k) y^k=Cx^k where J is the Kalman filter gain, x̂ k the state vector with k state variables, y k the predicted process output and ŷ k is the actual value of the process output. If covariances for unmeasured disturbances and measurement noise are known, the standard Kalman filter structure can be modified by adding G w (disturbance and noise model) to the plant model and then by recalculating the MPC controller gain for the extended model (in Fig. 3). The filter gain J can be determined by solving the Riccati equation numerically, where Q KF is the positive semidefinite matrix representing the covariances of the disturbances at w, and R KFis the positive definite matrix representing the covariances of the measurement noise z. If the covariances are unknown, a simplified version of the Kalman filter can be used. This formulation assumes that the disturbances w are independent and thus each element of the disturbances w affects one (and only one) element of the process outputs y. From this assumption, Q KF and R KF , the covariances of the input and the measurement noise, are not necessary. Instead, this simplification uses a filter time constant τ i and an estimate of the signal-to-noise ratio SNR i per fault to create the fault model as follows: Gwi(q)=1q−ai where a i = e -T / ti , 0 ≤ τ i ≤ ∞ and T is the sampling period. If τ i → 0, approaches Gw i (q) a unity gain, whereas if τ i → ∞, Gw ibecomes an integrator. The element i of Δw is a stationary white noise signal with a mean of zero and a standard deviation σ wi (where w i (k) = w i (k) - w i (k-1)). The element i of z is a stationary white noise signal with a mean of zero and a standard deviation σ zi .

[0042] The goal of state updating is to find the best possible estimate of the current state variable at each time instant (i.e., at each sampling period of a discrete controller). However, using the best possible state estimate in a well-tuned MPC controller does not necessarily result in the best possible control performance. In particular, the dynamic behavior of the closed-loop feedback path of the state updating model depends on the observer gain J. However, since the observer gain J depends on the noise covariance (or the signal-to-noise ratio in a simplified Kalman filter formulation), there is no tuning parameter or generic quantity that takes the observer transfer function into account. Therefore, the closed-loop control performance may be affected in an undesirable (suboptimal) way.However, it was determined that the closed-loop responses are very similar for a wide range of J for a given controller situation. Thus, it appears that the value of J has only a very small effect on control performance. Surprisingly, this observation holds both for a perfect model and in the case of model mismatch. Indeed, it was determined that the tuning of action losses and error losses within the observer has a much larger effect on control performance both with and without model mismatch, and thus, these tuning parameters are used in the tuning discussions provided below.

[0043] Although observers improve MPC feedback performance, they still have constraints that empirically tuned controllers, such as PID controllers, lack. Furthermore, any model-based predictive controller, with or without a model-based observer, assumes that the model is perfectly known, which is almost never the case in actual process plants. Unfortunately, even small model errors can cause large prediction and state update errors, leading to poorer controller performance.

[0044] As discussed above, tuning parameters for model-predictive controllers are typically used to adjust the controller behavior in a manner desirable for a particular plant application. For example, a particular desired response speed can be achieved by setting the action losses R to a specific value. However, the expected behavior designed by the commissioning engineer only occurs when the model mismatch is negligible, which is rarely the case for industrial plants. To account for the apparent model mismatch, practitioners often resort to iterative tuning until the desired behavior is observed. This process is costly because it is very time-consuming and may be suboptimal because it is difficult to cover all possible control and boundary condition scenarios on a running plant.Even if this procedure leads to the desired plant behavior for the given model misfit, one can assume that the behavior will change if the magnitude of the model misfit changes. Furthermore, even if the magnitude of the model misfit and its variation are known, there is no method to derive tuning information from this information.

[0045] The MPC adaptation and tuning technique described below uses knowledge of the process model mismatch to adjust the tuning for optimal control performance in the presence of a constant or varying model mismatch. In general, this MPC adaptation and tuning technique implements an optimization criterion based on a specific process model (e.g., the process or plant model determined during plant commissioning) and an indication of a process model mismatch to develop an optimal set of MPC controller design and tuning parameters, which, when used in the MPC controller with the original process model, provides better or more optimized control. This MPC controller adaptation and tuning technique can be used with many different types of MPC controllers, including:MPC controllers with observers (such as Kalman filters), DMC controllers, or one of the other MPC controller types mentioned above. However, for illustrative purposes, the MPC controller adaptation and tuning technique will be described as applied to determine various design and tuning criteria for an MPC controller with an observer in the form of a Kalman filter. As will be seen below, the adaptation and tuning technique in this case is capable of selecting the type of Kalman filter to be used, the tuning parameters to be used for this type of Kalman filter, and the tuning parameters to be used in the MPC controller itself.Furthermore, in some embodiments, the adaptation and tuning technique of the MPC controller will develop a new controller model to be used as a predictive model in the MPC controller instead of the originally developed plant model, without the need to reshape or redefine the process model.

[0046] Although two types of Kalman filter techniques (including a standard Kalman filter and a simplified Kalman filter) are discussed as alternative controller forms in the adaptation / tuning technique disclosed herein, other types of MPC controller forms could, of course, be considered in this technique in addition to or instead of the techniques specifically described below. Furthermore, while specific controller design and tuning parameters are described as available for use with the Kalman filters and the MPC controllers, other design and tuning parameters may be used in other embodiments, where these design and tuning parameters are based on the particular MPC controller forms contemplated by the tuning technique.

[0047] The first main principle underlying the new MPC controller adaptation and tuning technique is that the manner in which the tuning parameters affect the behavior of the MPC controller, and thus the closed-loop control performance, depends on the degree of model mismatch present at any given time. In some cases, these relationships can be very significant and / or may even be nonlinear. The new MPC controller adaptation and tuning system described here, which works well in the presence of model mismatch, involves the eventual selection of several different possible MPC design and tuning parameters to determine the shape and / or design and tuning settings of the MPC controller that provide the most optimized control scheme in the presence of the model mismatch.In one embodiment, the following adaptation and tuning technique of the MPC controller may select from various forms of an observer-based MPC controller, discussed here in the form of an MPC controller with Kalman filtering. However, selection from other MPC controller forms could be used in addition to or instead. In the particular embodiment described below, the Kalman filter type (TKF) may be standard (i.e., the standard Kalman filter) or simplified (the simplified Kalman filter). In this case, design and tuning parameters for both the MPC controller may be determined in the form of a selection of a prediction horizon (P), a control horizon (M), an action loss (Q), and an error loss (R). Likewise, tuning parameters for the Kalman filter may be determined that are suitable for a standard Kalman filter, a covariance of the disturbances at w (Q). KF ) and a covariance of the measurement noise (RKF ), and in the case of a simplified Kalman filter, a vector of filter time constants τ i (T) and a signal-to-noise ratio (SNR) for each disturbance. The design and tuning parameters are summarized below, with an indication of the type of data that can be used in a computer implementation to specify these parameters. • Tuning the MPC controller: ◯ P (forecast horizon), integer ◯ M (control horizon), integer ◯ Q (measure loss), flow vector ◯ R (error loss), flow vector • Type of Kalman filter (TKF): standard or simplified, Boolean • Tuning the Kalman filter ◯ By default • Q KF (covariance of the disturbances at w), flow matrix • R KF (covariance of the measurement noise, z), flow matrix ◯ Simplified • T (filter time constant τi ), flow vector • SNR (signal-to-noise ratio for each disturbance), flow vector

[0048] Different MPC implementations may use additional or different tuning parameters, such as a maximum action rate or a reference trajectory. However, such parameters are typically intended for specific operator needs, and the resulting effects may overlap with the parameters identified above. Thus, although there are other means of influencing the dynamic behavior of an MPC controller, many of the desired process behavior types can be addressed with the parameters described above. Further, the design / tuning parameters described here include a controller shape parameter (i.e., TFK), which in this case is specifically a form of the MPC controller as one of two different types of observer-based MPC controllers (i.e., either a standard Kalman filter or a simplified Kalman filter form).However, the controller shape parameter could specify controllers in different shapes, such as either an observer-based controller shape or a non-observer-based controller shape, either a DMC controller or a MAC controller, etc.

[0049] Since the model mismatch and the tuning parameters are highly correlated with respect to the closed-loop control performance, the MPC controller adaptation and tuning technique can be characterized as a constraint optimization problem that can be solved to determine an optimal set of design and tuning parameters of the MPC controller in the presence of a model mismatch. Fig. Figure 4 depicts a configuration that implements and solves this optimization problem to develop and provide either design or tuning parameters, or both, for an MPC controller. In particular, an optimization block 110 of Fig.4 ideal or optimal design and tuning parameters for use in an MPC controller unit 112 having an MPC controller 114 coupled to an observer in the form of a Kalman filter 106, based on knowledge of the process model used in the MPC controller 114 and the extent of the model mismatch. The MPC controller 114 and the Kalman filter 116 may be the controller 90 and the observer 92, respectively, described above with reference to Fig. 3 were discussed.

[0050] The optimization block 110 from Fig. 4 takes as inputs the process model originally developed for the plant and likely used by the MPC controller (referred to as the "plant model") and an indication of the existing model mismatch. The extent of the existing model mismatch can be input by a user, e.g., via the user input routine 46. Fig.1, or can be otherwise determined, such as described below. Based on these inputs, the optimization block 110 determines the ideal or most suitable type or form of MPC controller to be used (from the available types under consideration), as well as the specific design parameters and controller and filter tuning parameters to be used for the particular MPC controller type in light of the particular process model and the existing model mismatch. As illustrated by the upper line representing the optimization block 110 from Fig. 4, the optimization block 110 determines the type of Kalman filter technique to be used in the MPC controller unit 112 (identified as TKF) and the tuning parameters to be used for this type of MPC controller (identified as Q KF and R KFidentified if TKF is a standard Kalman filter, or T and SNR if TKF is a simplified Kalman filter). Block 110 provides these design and tuning parameters to the Kalman filter 116. In addition, as part of the optimization, the optimization block 110 determines a set of design and tuning parameters to be used by the MPC controller 114, which parameters are Fig.4 as M and P (design parameters) and Q and R (tuning parameters). These parameters are shown as output by the optimization block 110 on the lower two lines exiting block 110. Generally speaking, the design and tuning parameters determined by the optimization block 110 are those that minimize an objective function stored in and executed by the optimization block 110 (within constraints provided to the objective function) that identifies the best controller performance given the process or plant model and the present model mismatch. Importantly, the optimization block 110 consists of Fig.4 based on its objective function, values ​​of a set of MPC design and tuning parameters are developed for use in the MPC controller unit 112, which design and tuning parameters result in the best possible or ideal control, given the current process or plant model and the model mismatch, without requiring any modification or regeneration of the plant model itself.

[0051] In one embodiment, optimization block 110 uses an objective function that attempts to minimize the integrated absolute error (IAE) of a function f(x) (the objective function) over the stabilization time. This optimization could be determined over a moving horizon, such as the control horizon or the prediction horizon of the MPC controller, or other time periods, as desired. Of course, any number of different objective functions could be used, and these objective functions could be implemented to determine the minimum IAE or another measurement, such as minimum square error, integrated error, variability, standard deviation, etc., to evaluate optimal control performance.Furthermore, constraints can be added to the optimization algorithm to handle physical and logical limits in an arbitrary manner, preventing the optimization block 110 from specifying a design parameter or set of controller tuning parameters that would cause a violation of a certain process or control constraint. Typically, however, the exact value of the constraints only affects the scope of the calculations and not the overall result.

[0052] In a particular embodiment, the optimization calculation performed by the optimization block 110 Fig. 4 is executed, implement the following objective function: min IAE(Γ,Ξ,ΞΞ) according to: g(Γ) ≥ 0 where Γ is the set of design and tuning parameters (which in this example is [P, M, Q, R, TKF, Q KF , R KF , T, SNR] Tcan be), Ξ is the process or plant model (which in this example =[G, τ1, τ2] T can be), ΞΞ is the process model mismatch for one or more process model parameters, and g(Γ) defines the computational boundary conditions that describe, for example, computational limits of the control algorithm, process limits, etc. Here, G is the gain parameter of the process model, and τ1, τ2 are the first- and second-order time constant parameters of the process model. IAE is, of course, the integrated absolute error, which is used as a measure of control performance and can be calculated as follows: IAE=∫10|y(t)−SP(t)|dt where y(t) is the process output control variable and SP(t) is the operator setpoint for this output control variable.

[0053] Basically, the optimization block 110 simulates Fig.4 the operation of the MPC controller when the controller is designed using the original process model, but operated in the presence of the process model mismatch, and performs this simulation for each of a plurality of different sets of controller design / tuning parameters (for a particular model mismatch) to determine a measure of controller performance (e.g., IAE) for each of the plurality of different sets of controller design / tuning parameters at the particular model mismatch. In one example, the optimization block 110 calculates the expected process error (as IAE) resulting from using each combination of a set of diverse possible combinations of different values ​​of the tuning parameters (for both the MPC controller and the Kalman filter) for the various possible MPC controller shapes (e.g.,the possible Kalman filter types) based on the process model and the expected or observed model mismatch. The optimization block 110 then determines the particular set of design and / or tuning parameters that results in the lowest IAE (i.e., the best performance) given the process model mismatch, and thereby determines an optimal set of the controller's design / tuning parameters for use in the model-predictive controller based on the controller performance measurements. These design and tuning parameters can then be used in the MPC controller unit 112 of FIG. Fig. 4 can be used to perform better or more optimized control in the presence of this degree of model mismatch without changing the controller model used by the MPC controller 114 and certainly without having to reshape or regenerate the plant model itself.

[0054] To illustrate the functionality of the optimization block 110 in more detail, Fig.Figure 5 provides a graph showing the best possible IAE (i.e., the minimum IAE) for a given degree of model misfit in the process model gain. This graph was obtained by solving the optimization of equation (9) for different values ​​of model misfit for both an MPC controller with a standard Kalman filter and one with a simplified Kalman filter. The detailed optimization results are shown in Table 1 below, where IAE values ​​associated with active constraints, i.e., where a tuning parameter was satisfied under a constraint, are shown with a prominent asterisk. In addition, the model misfit is expressed as a ratio between the actual process gain K and the modeled or expected process gain K̃ (i.e., K / K̃).Because this implementation is such that the MPC controller unit 112 used is a single-input / single-output controller instead of a multivariable controller, the tuning parameter Q of the MPC controller was set to 1, and only the tuning parameter R of the MPC controller was allowed to change. This mathematical operation can be performed because, in a single-loop MPC implementation, only the ratio of Q to R is relevant for tuning.

[0055] From Table 1, it can be seen that the optimization block 110 utilizes all possible tuning parameters to achieve the optimal control performance, as defined by the minimum IAE found for any particular model mismatch. Interestingly, the optimizer 110 determines different tuning parameters for different values ​​of the model mismatch, which result in fairly similar control performance as long as a constraint is not met. When a constraint is met, control performance typically suffers because the optimizer block 110 no longer has sufficient degrees of freedom (i.e., tuning parameters) to compensate for the model mismatch.As can be seen from Table 1, MPC with standard Kalman filtering also outperforms MPC with simplified Kalman filtering when the process gain mismatch K is such that K>K̃, where K is the actual process gain and K̃ is the modeled or expected process gain. However, MPC with simplified Kalman filtering outperforms MPC with standard Kalman filtering when the process gain mismatch K <K̃. Natürlich ist die Standard-Kalman-Filterungsformulierung strikter als die vereinfachte Kalman-Filterungstechnik, die eine Filterung mit exponentiell gewichtetem gleitendem Mittelwert (EWMA) verwendet, um die Zustandsgröße zu aktualisieren. Somit kann die vereinfachte Kalman-Filterungstechnik nicht abgestimmt werden, um sehr gut mit einer Verstärkung umzugehen, die größer als erwartet ist, kommt aber ausgezeichnet mit einer Verstärkung zurecht, die kleiner als erwartet ist.In other words, since the MPC with simplified Kalman filtering is based on filtering, it is more robust than the MPC with standard Kalman filtering when the process response is smaller than an expected quantity (i.e., when K<K̃). Bei K> However, K̃, the MPC with simplified Kalman filtering results in a slightly larger integrated absolute error than the MPC with standard Kalman filtering.

[0056] If the model misfit is attributed to or is present in the first-order time constant (τ1), the difference in the integrated absolute error between the two Kalman filtering methods becomes more apparent. As shown in Fig.As shown in Figure 6 and Table 2 below, when the process responds more rapidly than expected (i.e., τ1<τ̃1 1, where τ1 is the actual first-order time constant and τ̃1 is the first-order time constant associated with the process model), the IAE increases with a very steep slope because of oscillation. The two Kalman filtering methods are similarly affected by oscillation, and an automatic optimal control method in the presence of a constant or varying model mismatch should try to avoid oscillation if possible. However, when the process responds more slowly than expected (i.e., τ1 > τ̃1), MPC with simplified Kalman filtering performs considerably better, meaning that standard Kalman filtering, even if stable, should not be used in this scenario.Because the simplified Kalman filter formulation uses a filter time constant as one of the tuning parameters, an optimization procedure can easily use this tuning parameter to compensate for the time constant mismatch between the plant model and the actual plant characteristics. This compensation is easily observed in the values ​​of Table 2 (where, again, values ​​associated with active boundary conditions are shown with a protruding asterisk). While the tuning parameters of the standard Kalman filter are fixed at the boundary conditions, and only the tuning parameters of the MPC controller are allowed to change, the T parameter of the simplified Kalman filter moves over a wide range and compensates for the model mismatch, thus keeping the IAE at a very low level. Of course, the nature of the Kalman filter, as stated above, is specifically defined as a Boolean output of the [context missing] parameter defined in [context missing]. Fig.4 described optimization procedure, and this output causes the Kalman filter 116 from Fig. 4 to switch between using simplified Kalman filtering and standard Kalman filtering.

[0057] As can also be seen from Table 2 and Fig. 6, the minimum possible IAE for the standard Kalman filter is on the left (in the diagram from Fig.6) of τ1=τ̃1 (i.e., where the model mismatch ratio = 1). When the first-order time constant of the actual process changes to approximately half the value for which the MPC controller and the standard Kalman filter were designed for (τ1~0.5 τ̃1), the IAE decreases, meaning that the recommended tuning for the Kalman filter gain J does not provide the best possible control performance. This situation occurs because the controller optimization problem performed within the MPC controller is designed to minimize a static error while minimizing actions, whereas the adaptation / tuning optimization problem is designed to minimize the IAE of the controlled variable error, thereby directly maximizing control performance.

[0058] The effect of the model mismatch in the second-order time constant (τ2) is Fig.7 and is provided in Table 3 below, and is very similar to that of the model misfit in the first-order time constant (τ1) shown above. Although the magnitude of the differences between standard and simplified Kalman filters is smaller, the trend is basically the same.

[0059] Although the optimal tuning parameters for MPC control and state update are determined above from knowledge of the plant model and the model mismatch using optimization, the impact of the model mismatch and the optimal controller design and tuning used to compensate for this mismatch were analyzed separately for each model parameter in the above examples. In a real plant scenario, all process model parameters that conform to a prescribed model (and others that are not modeled for various reasons) can and likely will change simultaneously. Which model parameter is most affected depends primarily on the process type and the reason for the model mismatch (e.g., tube fouling, varying fuel heat coefficient, etc.).Furthermore, depending on the model identification method used, a model misfit in the lead time constant, for example, can be interpreted as a model misfit in the model dead time or time constant. Thus, one or two model parameters often contribute significantly to the model misfit simultaneously. It is then advantageous to analyze the model misfit in a multidimensional space to determine the best set of model parameters to be used in any particular case, rather than a one-dimensional space as performed in the examples above. This means that instead of determining an optimal set of design and tuning parameters for a misfit in one process model parameter, it is advantageous to determine an optimal set of design and tuning parameters for the situation in which there are simultaneous misfits in several process model parameters (e.g.with two or more elements of process gain, first-order time constant and second-order time constant).

[0060] Fig. Figure 8 shows a surface plot of the best possible IAE for a simulated MPC controller using a standard Kalman filter state update technique as used by the optimization procedure of Fig.4 is calculated when a process model mismatch is allowed in two dimensions, i.e., where both the process gain K and the first-order time constant τ1 were allowed to have a model mismatch at the same time. In this case, the optimal tunings for the model mismatch of the first-order time constant and the second-order time constant are very similar, with the first-order time constant being of greater importance. Since a three-dimensional visualization is preferred over a four-dimensional visualization, the effects of the model mismatch at the second-order time constant τ2 were shown in the diagram from Fig.8 was neglected, and the second-order time constant τ2 was not allowed to change at all, but was assumed to be free of mismatch. Table 4 below provides the values ​​of the minimum IAE for each combination of a set of various combinations of mismatch values ​​for the process gain K and the first-order time constant τ1 shown in the diagram from Fig. 8. The values ​​of the optimal tuning parameters for the MPC controller and the standard Kalman filter used with the MPC controller associated with each box in Table 4 are not shown, but were calculated using the optimization technique described above. Again, the model misfit is expressed as the ratio of the actual process parameter value to the modeled process parameter value (i.e., K / K̃ and τ1 / τ̃1).

[0061] For the sake of clarity, the values ​​of K / K̃=1 and τ1 / τ̃1=1 (i.e., where no model misfit occurs) are shown in Fig. 8. The point where these lines intersect represents the control power with a perfectly fitting process model. The cross section along each of these lines exactly represents the diagrams in Fig. 5 and Fig.6. As discussed previously, a model misfit in the first-order time constant leads to oscillations in the direction of τ1<τ̃1. However, it can be seen that this oscillation does not occur if a model misfit in the process gain also occurs, so that at the same time K<K̃. Bei einer Modellfehlanpassung, so dass K> K̃, the problem worsens, as expected. The fact that model mismatch can suppress or amplify the overall impact on control performance when inherently different model parameters are used shows that it is advantageous to evaluate all dimensions of model mismatch during the calculation of the optimal design and tuning parameters of the controller. Fig. 8 also shows that the best possible control performance is not necessarily achieved with a perfect model. For example, in the diagram from Fig.8, when K / K̃=2 and τ1 / τ̃1=1.5, the control power exhibits an IAE of 0.0545 instead of an IAE of 0.1226 at K / K̃=1 and τ1 / τ̃1=1. This difference corresponds to a 56 percent improvement, assuming that the tuning parameters are optimally calculated using the described optimization formulation.

[0062] Of course, if the assumed process model and the exact model mismatch were known, the process model used by the MPC controller and the observer (the Kalman filter) could be replaced by a perfect model to achieve even better performance. However, in actual control situations, it is difficult to measure model mismatch, and therefore the MPC design and tuning technique here is aimed at achieving better or optimal MPC controller operation without knowing an accurate or perfect process model. In fact, the design and tuning procedure described here adjusts the tuning parameters of the MPC controller unit (e.g., as in Fig. 4) and leaves the assumed plant model unchanged (since this would be the assessment of an engineer in the plant).

[0063] Fig.Figure 9 represents an equivalent three-dimensional optimal tuning map for an MPC with simplified Kalman filtering, i.e., a tuning map formulated like that of Fig. 8 for the MPC controller with standard Kalman filtering. Here, too, the model mismatch was allowed to occur both in the model parameter of the process gain K and in the model parameter τ1 of the first-order process time constant, but not in the model parameter of the second-order time constant τ2. Table 5 below shows the points for the mapping of Fig. 9 ready.

[0064] The upper left corner of the two optimal tuning images (from Fig. 8 and Fig.9) indicates an instability region. Furthermore, both diagrams are truncated at IAE = 2. In both cases, it is evident that this region is approximated with a very steep slope. Calculating and plotting three-dimensional tuning maps allows for the effortless evaluation of the size, position, and steepness of such unstable regions. Since such regions should be avoided whenever possible, boundary conditions for strongly penalized buffer sizes can be added to the optimization equation obtained in block 110. Fig.4, to avoid this region. When comparing the optimal tuning maps of the MPC with the different Kalman filter schemes, it is in any case evident that the two controllers in the region τ1>τ̃1 K <K̃ instabil werden. Jedoch wird nur die MPC mit einem Standard-Kalman-Filter im Gebiet τ1<τ̃1 K> K̃ is unstable. As previously suggested, the inherent filtering, which is only found in the simplified Kalman filter, serves as a stabilizing mechanism.

[0065] In any case, the optimization-based voting procedure, which is based on Fig. 4, the determination of the best MPC controller form and design and tuning parameters given the process model mismatch for a particular process. The optimization block 110 then determines Fig.4 the optimal tuning for a given value of model mismatch, and this optimal tuning can be expressed as a tuning map, which is useful for determining the specific design and tuning of the MPC and the observer that ensure optimal control performance in the presence of this model mismatch. Fig. 4 linked technique can be used advantageously because industrial users of MPC controllers usually have to manually adjust tuning "knobs" until it appears as if a desired behavior is achieved. In this case, the user can view tuning visualization images, charts, and data, as shown in Fig.5 to 9 and in Tables 1 to 5 to determine the best controller shape and tuning parameters given a predetermined or expected value of process model mismatch in one or more process model parameters.

[0066] If desired, the optimization block 110 can thus be Fig.4 calculate the best design and / or tuning parameters for a particular degree of model mismatch (in one or more process model parameters) as input to block 110, e.g., by a user or by another semi-automatic or automatic method. After block 110 has determined the best set of design and tuning parameters to be used in the MPC controller unit 112 given these particular degrees of process model mismatch (in one or more process model parameters), these design and tuning parameters can be passed to the MPC controller unit 112 and used during online control to perform better control. Alternatively or additionally, block 110 can determine optimal IAE mappings, such as those from Fig. 8 and Fig.9, which illustrate the minimum possible IAE for each model mismatch of a certain number of combinations of process model parameter mismatches, and provide or display these maps to a user to enable the user to select the desired or appropriate tuning point in light of the map. Block 110 can then provide the values ​​of the design and tuning parameters to be used during online control based on the selected point to the controller 112. Since block 110 can operate independently of the controller unit 112, block 110 can be stored and executed in the same or a different device than the controller unit 112. Thus, block 110 can be executed, for example, on one of the computers 13 of Fig. 1 and communicate via the communication network 29 with the control unit 112, which is located in the controller 11 from Fig.1, in one or more of the field devices 15 to 22 Fig. 1 or in one or more other desired devices.

[0067] Of course, it is expected that the optimal set of design and tuning parameters for a given model misfit and process model will be suboptimal if there is no model misfit or if a different degree of model misfit is present. Furthermore, while it may be easier to determine the presence of model misfit than the correct model, it may still be difficult to determine the specific degree of model misfit for any particular model parameters in any particular situation.Although determining the extent of model misfit may be easier than determining the precise process model because determining the extent of model misfit requires less process disturbance, the extent of model misfit may still change over time, necessitating the development of new design and tuning parameters to account for this changing model misfit. For these reasons, in some cases, it may be desirable to define a model misfit range for each of the various process model parameters in the optimization block 110 of FIG. Fig. 4 to develop the appropriate set of design and tuning parameter values, rather than using a specific model misfit value for each process model parameter.

[0068] An example of a model misfit region in a two-dimensional subspace (which in this case ignores the second-order time constant) can be considered as the actual process gain K actual = 2 ±0.5 and as the actual first-order time constant t actual = 20s ± 5s. These areas are divided into a two-dimensional subspace in Fig. 10, where the gain range is 1 (i.e., ΔK = 1) and the range of the first-order time constant is 10 seconds (i.e., Δt = 10 s). If the model misfit is defined as a possible range, the model misfit range can be calculated with an optimal tuning map, as described above with reference to Fig. 8 and Fig. 9 to provide additional benefits in adapting and tuning the MPC controller. An example view of such an overlay is shown in Fig. 11 illustrates.

[0069] If desired, such an overlay can be implemented in a software package that displays this overlay for a process engineer, e.g. on an optimal tuning map such as one of those from Fig. 8 and Fig.9. This visualization can allow the engineer to see and determine the probability that the controller is moving into an undesirable operating region based on a possible model mismatch within the specified region. Such a region can be used additionally or alternatively for further design and tuning optimization of the MPC controller. In particular, such a display can be very useful for an engineer when commissioning the MPC controller because the engineer can easily visually evaluate the worst and best possible control performance as a function of the expected model mismatch region for a given tuning and make manual corrections as desired. This display software for displaying the optimization figures, such as those from Fig. 8, Fig. 9 and Fig.11 (with or without area overlay), may be generated by the block 110 or may be generated as part of the user display software 46 from Fig. 1. In this case, the user display software 46 may communicate with or include block 110 to generate these images.

[0070] In any case, in the example from Fig. 11 the worst control performance within the model mismatch range (centered around the point with no mismatch of either the gain or the time constant) when K actual = 1.5 and t actual= 25 s. However, the IAE at this point is 0.7, which the engineer might still consider acceptable, especially given that the probability of being in this region is relatively low because only a small portion of the model misfit area overlaps with IAE values ​​above 0.5. If one knew more about the model misfit (e.g., physical process boundaries), then the two-dimensional subspace of the model misfit could be calculated, as in Fig. 10, to take into account the probability of occurrence. Thus, for example, the subspace of model misfit could be Fig. 10 assume shapes other than the represented rectangle, including an oval, a circle, or any other desired shape, based on knowledge of the probability of model misfit.

[0071] As a further refinement of the voting procedure from Fig. 4, it may be advantageous to determine the ideal tuning point for a given plant model as a function of the extent of a possible or expected model mismatch range in the values ​​of one or more of the process model parameters. In particular, when considering Fig. 11 shows that the calculated tuning parameters do not necessarily represent the lowest possible IAE in the figure Fig. 11 at one of the points in the subspace of the model mismatch region, because the center of the subspace of the model mismatch region is fixed in the assumed "perfect" model. If this subspace, which in this two-dimensional example is represented as a surface, were allowed to move, a modified optimization technique compared to the one in Fig.4, it may be possible to find a lower value for the worst (largest) IAE within the area of ​​the model mismatch region, thereby increasing the overall performance of the controller. In other words, given a potential, expected, or possible model mismatch region (in any of the various dimensions defined by the process model parameters), it may be desirable to use a set of optimal tuning parameters calculated using the technique described above, which generally optimizes the operation of the MPC controller within a subspace defined by these regions, even if the best controller operation is not located at the center of the subspace or even within the subspace at all, and even if the center of the subspace of the model mismatch region does not correspond to the process model actually being developed for the plant.

[0072] While the design and tuning technique of the MPC controller described here uses the assumed process model (which is provided as input to block 110 of Fig. 4) is neither updated nor changed with the knowledge of the process mismatch (because the result may be as uncertain as the assumed model to begin with), this technique adapts and tunes the MPC controller in this case, given the known or assumed process model mismatch range, in order to perform better overall control given this model mismatch range. In particular, as in Fig.As shown in Figure 12, the center point of the model mismatch region subspace can be relocated or shifted within the modeled tuning region to find the best overall subspace of the tuning space in which to operate, given the expected process model mismatch. To operate within this subspace, the controller model (used in the MPC controller to calculate the MPC control actions) can be adjusted to center around a new center point in the tuning map, with this center point and model mismatch subspace resulting in the best overall operating region within the overall tuning map.In one case, the best overall subregion within the tuning map can be determined by calculating the possible minimum value of the worst (largest) IAE present within a given subregion when moving the model misfit subspace over the entire tuning map. Of course, other measures, including statistically based measures, could also be used to determine the best operating subregion, such as the lowest average IAE over the entire subspace of the misfit region, the lowest weighted average over the entire subspace of the misfit region, etc.

[0073] If desired, a particular best mismatch subregion can be found by solving a second optimization problem defined as follows: min(maxiψ IAE(ΞΞ^,Ψ)) according to: g Ψ (Γ) ≥ 0 where Ψ is the tuning map obtained by iterating equation (9) over arbitrary combinations of model misfits, g Ψ (Γ) defines the inequality boundary conditions that describe the dimensions of the voting map Ψ, and i Ψdefines the dimensions of the tuning map Ψ. The specific optimizations of equation (11) determine the subspace of the model misfit region that encompasses the lowest value of the IAE in the tuning map. Note that no additional knowledge of the process model is necessary for this process because the tuning map is still developed based on the process model originally provided by the engineer (the assumed process model). The result of the optimization of equation (11) is a modified controller model and a modified set of controller tuning parameters, which are subsequently used to develop the MPC controller to achieve better performance given the expected model misfit regions. The tuning map, for example, from Fig. 11 or Fig.12 is not recalculated based on the new process model because the sole purpose of determining the new controller model is to minimize the IAE within the current tuning map.

[0074] By adding this operation to the optimization block 110 of Fig.4, the design and tuning parameters of the MPC controller are changed to the newly determined ideal values ​​(of the new center point) to maximize control performance even further than is possible with the MPC and observer tuned at the original center point. In a sense, the process model parameters in this case have now also become design / tuning parameters of the controller because they are used to determine a new controller model used within the MPC controller. However, it is true that if there were no model mismatch, one would expect the control performance of a controller with a changed model to be worse than that of a controller with the original model. However, as discussed above, the prospect of no model mismatch is very remote.In a real plant scenario, the performance of the original controller may be worse than that of the modified controller for most model mismatch scenarios, because this is precisely the objective function of the optimization calculations of equation (11). Furthermore, the difference at the worst IAE point between the assumed and modified models is usually significant because slopes leading to instability on one side and poor performance on the other are typically very steep. Fig. 13 illustrates how the optimization block 110 of Fig. 4 can be modified to use a model mismatch region to determine a modified controller model and a set of controller design and tuning parameters for use in the MPC controller.

[0075] As in Fig.13, an optimization block 110A includes or executes two optimizations as specified by equation (11), including the optimization of equation (9), and the input to block 110A is changed from specifying a particular model misfit to a model misfit range (for one or more model parameters). Here, optimization block 110A also develops a new set of values ​​for the model parameters that are used to develop a new controller model (i.e., the modified controller model that is output at one of the outputs of block 110A in Fig.13). Essentially, the new center point of the model misfit subspace determined by optimization block 110A has a particular set of values ​​for the process model parameters associated with it, and these model parameter values ​​are different from the model parameter values ​​associated with the original center point (i.e., they are different from the model parameter values ​​associated with the original plant model). These new process model parameter values ​​are then used to generate a new controller model (without actually changing the plant model input to block 110A), and this controller model is provided as a controller design parameter to the MPC controller, along with the other design and tuning parameters (e.g., Q, R, M, P) associated with the new center point.

[0076] Extending the optimal tuning procedure from a specific model misfit to a model misfit range greatly increases its usefulness. This new range-based misfit technique is applicable to many industrial processes that have inherent process parameter variations that are known but difficult to measure accurately. As described below, the adaptation / tuning procedure can also use model misfit feedback to convert the presented dual optimization procedure from Fig. 13 to a varying model mismatch, thereby providing automatic or online determination of the optimal controller design and tuning parameters to be used at any particular time during online control.

[0077] In particular, it is possible to use the adaptation and tuning procedure of the MPC controller described above to perform closed-loop control with adaptive tuning (i.e., adaptive control). Most adaptive control techniques generally work by refining or rebuilding a process model either continuously (e.g., periodically) or spontaneously when triggered by a detectable event, such as a change in a process value, a change in an operator setpoint, etc. Once the new model has been determined, controller actions or tuning parameters are then calculated from the model. However, these models generally rely on process change, which can be introduced by disturbances or setpoint changes, and thus the efficiency, precision, and stability of these techniques increase proportionally with the amount of process variation.

[0078] However, it is generally easier to determine the statistical extent or variation of model misfit than to determine or create a precise process model. Although many methods, such as autocorrelation, have been proposed to determine the extent of model misfit during closed-loop plant operations, it is extremely difficult to determine a good process model during a closed-loop plant operation because the objective of the controller (minimizing the variation of a process output) conflicts with the requirement of model identification (operating the process through a process failure to maximize the variation of a process output).

[0079] A method described below for automatically performing adaptation and tuning of a controller uses the degree of model mismatch to determine when to adjust the design and tuning parameters of the MPC controller unit, ie when the optimization unit 110 or 110A of the Fig. 4 and Fig. 13. Although this adaptive tuning procedure depends on a certain degree of process variation, this adaptive tuning procedure does not need to maximize the process variation to derive the tuning parameters that maximize the control performance.

[0080] A concept that is considered an innovation in technology (I k ) and is known as deviation or prediction error, is defined as follows: Ik=(yk−y^k) where y k the predicted process output and ŷ kis the actual value of the process output. This term is used in the Kalman filter equation (6) to calculate the updated state variable. While researchers have proposed many methods that analyze innovation, the application of such methods typically occurs during the commissioning phase or the maintenance phase of a predictive control system or a virtual sensor project (e.g., a neural network). Autocorrelation, for example, is a method that researchers / engineers often use to analyze innovation because autocorrelation can distinguish between model errors and unmeasured disturbances during the commissioning phase of a plant. However, since unmeasured disturbances manifest themselves in the same way as the model error does for the operator, i.e.as the difference between the predicted process value and the actual or measured process value, it is difficult to distinguish between model error and unmeasured disturbances during online control operation, and thus the error that occurs can only be corrected using feedback control techniques.

[0081] Generally speaking, the autocorrelation of innovation (I k ) provides an indication of what proportion of an error signal is due to non-random contributions. The higher the value of the autocorrelation of the innovation, the greater the degree of process model mismatch. For a discrete time series of length n {e.g., y1, y2, ... y n} with known mean and known variance, an estimate of the autocorrelation can be obtained as follows: R(k)=1(n−k)σ2∑t=1n−k(yt−y¯)(yt+k−y¯) where R(k) is the autocorrelation, which lies in the range [-1, 1], σ2 where λ is the variance, y̅ is the mean, and k is the time lag. Since an optimally tuned controller can only remove correlated signals and cannot remove disturbances that are purely random (e.g., white noise), the ratio of white noise to the correlated signal is a good indication of the optimality of the controller tuning. Thus, for example, if the process output of a closed-loop control system exhibits high autocorrelation, then the tuning of the particular controller used in it is suboptimal.

[0082] Autocorrelation-based analysis techniques are often used during manual control loop tuning and retuning. If the autocorrelation analysis reveals a high degree of model mismatch, the engineer usually knows that the controller configuration is incomplete and needs to refine or re-identify the process model before commissioning the controller. Plant engineers often use a second criterion to verify tuning performance improvements. In particular, plant engineers may consider the amplitude spectrum to ensure that the amplitude ratio is acceptable at the most likely operating frequencies. Although this manual controller design procedure can be automated using innovator analysis, it cannot be applied continuously, for example, during online controller operation.In addition, this method only uses the degree of model misfit to trigger a process model improvement cycle in the form of developing or creating a new process model that reduces the model misfit.

[0083] The automatic adaptive tuning technique described below, using innovation or other fault analysis, can be executed continuously or otherwise during online controller operation and uses the degree of model mismatch not to trigger a process model regeneration cycle, but rather to trigger an adaptive tuning cycle for the controller (to retune the controller to optimally account for the new degree of model mismatch) without regenerating a new plant model. Thus, this technique does not require a new set of process measurements, process failure to determine a new set of process model parameters, etc. Specifically, for model-predictive controllers, the controller output calculation is derived directly from the process model, and therefore, the model mismatch can be assigned an autocorrelation.

[0084] Current practices used in industrial process control address the combination of model mismatch and unmeasured disturbance in the innovation in a very elementary manner. DMC controllers, for example, assume that a certain fraction of the innovation is contributed by unmeasured disturbances. Although attempts have been made to tune the Kalman filter gain based on an autocorrelation of the innovation, the present method strives to minimize the error covariance seen by the Kalman filter by matching the designed and actual signal-to-noise ratios. This technique essentially maximizes filter performance but does not unnecessarily maximize closed-loop performance. Furthermore, this adaptive method only calculates the error covariances and can only be used when the perfect model is already known.

[0085] Fig.Figure 14 illustrates how the optimizer-based tuning block 110A of Fig.13 can be combined with an existing MPC controller and observer (specified as a Kalman filter "KF") to create an MPC controller with gain management. Gain management techniques are known to be very popular in industrial plants for processes with changing process parameter values. Such techniques can manage controller tuning or can manage the updating of the process model and tuning parameters. As long as the process parameters change deterministically, satisfactory results can be achieved with such techniques. Indeed, in industrial plants, many properties of feedstock and equipment change continuously. Examples include changes in the fuel's burning coefficient and changes in the concentration of a reagent.If they are measurable, these property changes are often used by a feedforward control strategy to directly reduce variation or by a gain management strategy to counteract the modeling error and indirectly suppress the effect.

[0086] Voting block 110A from Fig.13 can be used to perform gain management, and in particular, if one or more process model parameters have changed and are known, the process model parameters can be updated in the optimal MPC adaptation / tuning block 110A (via the plant model input), which causes the adaptation / tuning block 110A to generate a new set of design and tuning parameters (given the new process model and the current model mismatch ranges) for the MPC controller and the Kalman filter. This update can be performed manually by a plant engineer or operator, or it can be performed automatically based on a process state change. The latter is comparable to the model-based gain management of a PID controller. In Fig.In Figure 14, the interactions between tuning block 110A and controller unit 112 are indicated by dashed lines, illustrating that the information flow from block 110A to controller unit 112 is strictly unidirectional. The assumed model mismatch range can be entered into the MPC adaptation / tuning block 110A by the designing engineer or can be left at a default setting. As with any gain-managed controller, the state variable can be hard-coded into a specific process measurement, if one exists, or can be estimated by a separate property estimator. Neural networks are often used as property estimators in the process industry when the process properties can be inferred from process measurements.External property estimators such as neural networks or dynamic linear estimators can also be used to directly estimate main model parameters.

[0087] An embodiment of the adaptation / tuning block 110A configured as a gain manager using a property estimator is shown in Fig.15. As noted here, a property estimator 120 is coupled to receive one or more input and / or output (e.g., measured) quantities or signals from the process 94 and uses these quantities to estimate the values ​​of one or more properties or parameters of the process model (e.g., A, B, C, D). Of course, in this example, any desired or suitable property estimator can be used to determine new process model parameter values. This technique closes the loop on the model parameters and can therefore be considered adaptive. However, to function appropriately, most methods that identify process model parameters require significant setpoint changes or a process disturbance. Unfortunately, such a process disturbance is undesirable in online control and does not meet the main prerequisites of the adaptation / tuning method described above, i.e.,that the plant model cannot be known exactly and that it should not be necessary to rebuild this plant model during an adaptation / tuning cycle.

[0088] Estimators can be associated with many quantities, including those not measured or manipulated by the control loop. Indeed, an estimator can only be associated with the inputs of the Kalman filter 116. Fig. Figure 16 illustrates an adaptive tuning system 125 that uses the adaptation / tuning block 110A as part of a gain-managed controller system to perform adaptive control. Fig.16, an estimator 126 (which may implement innovation analysis or other error analysis) is coupled to the observer, i.e., the Kalman filter 116, and analyzes the innovation term associated with the Kalman filter to determine an estimate of the extent (e.g., range) of model misfit for one or more process model parameters. The estimator 126, which may additionally or instead be coupled to the controller 114, implements innovation analysis to determine the process model misfit or misfit range, and provides the determined process model misfit(s) or misfit range(s) to the adaptation / tuning block 110A to initiate a new adaptation / tuning cycle for the controller unit 112.In particular, the novelty analysis performed by the estimator 126 may be used to determine the model misfit region(s) in the system. Fig.16 automatically. If desired, the model misfit region(s) can be updated completely or only partially in this way at any particular time. Similarly, the model parameter(s) for which the misfit region(s) are considered can be changed completely or partially, depending on how comprehensive the innovation process is with respect to the number of model parameters. In other words, innovation analysis may sometimes only allow conclusions to be drawn about a subset of the model parameters in the actual process model. If this is the case, the range for the unknown parameters can be set conservatively to encompass all or most of the expected or possible model misfit scenarios.

[0089] The output of the optimal MPC adaptation / tuning block 110A functions like the on-demand update applications described above, but closes the adaptation loop by performing adaptation and tuning of the controller when a significant degree of model mismatch is detected, e.g., when the mismatch for one or more model parameters exceeds a predetermined or preset threshold, such as a user-supplied threshold, a mismatch range previously used in tuning block 110A, etc. The uniqueness of this adaptive approach is that the originally assumed process model is never changed by the adaptation / tuning mechanism, thus preventing runaway process identification, increasing robustness, and simplifying gain management.If desired, the assumed process model can be manually updated at any time without having to stop or reset the adaptation, which is yet another advantage over the current state of the art model update procedures.

[0090] As described in more detail below, a trigger for implementing a manual or automatic adaptation / tuning cycle can be readily derived from the value of the innovation or from a particular model mismatch region (i.e., either from the input or from the output of the innovation analysis performed by estimator 126). Of course, such a trigger could be based on comparisons of the innovation analysis or its outputs with predetermined thresholds to detect when to execute a new adaptation / tuning cycle of block 110A. In any event, it has been found that using the autocorrelation of the innovation calculation described above provides a model-free and interference-free alternative to other previously known methods for implementing controller adaptation.In particular, autocorrelation analysis can be used to determine whether or not the control performance of a loop can be improved without the need to identify or re-identify a process model. Specifically, the autocorrelation of control error (the difference between the measured process output and the setpoint for that variable) during steady-state operation has been found to be useful in determining whether a significant model mismatch exists, while the autocorrelation of prediction error (the difference between the measured process output and a previously predicted value for that variable) during process failure conditions can be useful in determining whether a significant process model mismatch exists, or in determining a magnitude or range of model mismatch.As used here, the innovation analysis could include the autocorrelation of a control error, a prediction error, or other errors within the MPC controller unit 112. These autocorrelations can be used as triggers to implement a new adaptation / tuning cycle, for example, if the autocorrelation analysis determines a significant degree of model misfit. Furthermore, comparisons of the autocorrelations of the control error or the prediction error for the same process variable at different times can be used to detect a change in model misfit, which can also be used as a trigger to implement a new adaptation / tuning cycle.

[0091] To verify the concepts presented above, some of the adaptation / tuning procedures described above were applied to an experimental binary distillation column. The results of the trial runs of the binary distillation column using a model predictive controller implementing the optimal tuning procedure developed with respect to Fig. 16 (using a practical approximation for estimating the model misfit from the autocorrelation of the innovation in the Kalman filter) are provided below. The distillation column used in these experiments was a smaller-than-average pilot plant, typically used to separate water and ethanol. The process and instrumentation diagram (PID) 200 for the pilot plant is shown in Fig.17. Since this PID is easily understandable to the skilled person, it will not be described further here than necessary for the discussion.

[0092] Since the flow from a pressure accumulator 202 can be measured, a cascade control strategy was chosen, which allows the fast flow to be separated from the slow integrating dynamics. This separation between a level controller 204 (LIC-091) and a flow controller 206 (FIC-100) generally increases robustness. However, the two controllers 204 and 206 must be fairly well matched to achieve this effect. This requirement is a difficult challenge in this plant because the process parameters change when the column energy input varies. Since the vapor flow rate is used to control the tray temperature to maintain purity, the process parameters of the level and flow control loops in the pressure accumulator 202 can change significantly during normal operation. A manual step test was performed to determine the process model at a vapor flow rate of 0.55 kg / min.The step test resulted in the following initial process model, which was used as the prerequisite model for the model-based MPC controllers and was used to provide initial tuning for the PID controllers at a steam flow rate of 0.55 kg / min: . G(S)FIC−100=0.613s+1e−0.6s; G(S)LIC−091=−0.9218s+1e−17.5s.

[0093] At a steam flow rate of 0.4 kg / min, the following system model was determined: G(S)LIC−091=−0.9160s+1e−14.5s.

[0094] For the experiment, the level controller (LIC-091) 204, which is normally a PID controller, was replaced with an MPC controller running in the well-known MATLAB® simulation program. This controller was implemented by leaving the PID controller in manual mode and sending OPC write commands from an OPC client on a laptop computer running the MATLAB® simulation to the PID controller outputs in a DeltaV™ control system deployed within the 200 plant. Because the output of the LIC-091 controller 204 was connected to a cascade input of the secondary FIC-100 flow controller 206, writing to the LIC-091 controller 204 indirectly manipulated the flow setpoint of the FIC-100 flow controller 206 and implemented a cascade control behavior that matched the original plant configuration.

[0095] Three different adjustments of action losses were used in the MPC controller 204 (specifically Q = 50, Q = 100 and Q = 1000) and the control performance at two different operating points was analyzed (specifically at a steam flow rate of 0.4 kg / min and at a steam flow rate of 0.55 kg / min). Fig.Figure 18 illustrates three different runs of the MPC controller 204 with the three different tuning settings at a steam flow rate of 0.5 kg / min. This data was recorded sequentially and then overlaid for comparison. A fourth run, performed using the original PID controller set to provide PI control, was carried out to allow comparisons between MPC and PID control. The PI tuning parameters (gain = 1.54 and reset = 141.68 s) were calculated from the final gain, final period, and dead time of the process with the modified Ziegler-Nichols tuning. Under this steady-state condition, the standard deviations for the four different controllers were determined as follows: σ Q=50 = 0.057, σ Q=100 = 0.066, σ Q=1000 = 0.052, σ PI = 0.036.

[0096] As in Fig.18, the time domain diagram of the level control with Q = 1000 appears to be the most stable. The MPC with Q = 1000 also achieves the lowest standard deviation (σ Q=1000 = 0.052). While in a real plant environment, a graph of current controlled variables is often the primary way to view the data, conclusions drawn solely from a real-time trend can be misleading. Fig.Figure 19 illustrates how the controllers responded to an unmeasured disturbance, which was chosen to be a change in steam flow, since such a disturbance presents greater difficulties for the controllers. First, such a disturbance changes the amount of condensate reaching the accumulator 202, which requires the controller 204 to change the accumulator's output flow. Second, such a disturbance changes the backflow time constants, thereby changing the degree of model mismatch. The change in steam flow is also a true input disturbance and is, in fact, common in industrial plants. Furthermore, a change in steam flow is also almost always unmeasured. For examples from various process industries,that have a similar effect to the artificial change in steam flow rate (used in the present experiment) include (1) the change in BTU output of fuel (which affects temperature and gain of a temperature loop), (2) the change in concentration and / or composition of the feed (which affects column loading, mass balance, and gain between energy input and product purity), (3) the fouling of tubes in a steam boiler (which changes both the heat transfer coefficient, which in turn changes the process gain, and affects the required flow rate for the same heat transfer, which therefore changes the dead time), and (4) the change in outside temperature and / or the occurrence of a thunderstorm (which changes the temperature and also changes the heat transfer coefficient to the atmosphere, which therefore changes the gain).

[0097] In any case, the performance of the controllers during this simulated “unmeasured” process disturbance (as in Fig. 19), in which the setpoint of the steam flow rate was changed from 0.55 kg / min to 0.4 kg / min, so that IAE Q=50 = 0.122, IAE Q=100 = 0.468, IAE Q=1000 = ∞ (in this case the control was not satisfactory and the system had to be stabilized by manual intervention) and IAE PI = 0.3. While, as in Fig. 19, the MPC controllers Q=50 and MPC Q=100 which suppressed the unmeasured disturbance quite well (with IAE Q=50 = 0.122, IAE Q=100 = 0.468), the same experiment could not be performed with MPC Q=1000because the large loss of action prevented this controller from reacting to the level drop in a timely manner, which triggered the accumulator pump lockout. After the pump activation, accumulator 202 filled too quickly for controller 204 to react, resulting in unacceptable control performance.

[0098] This example illustrates that overly cautious detuning of a controller (i.e., Q=1000) can be disruptive and dangerous. Without manual intervention by an operator, an overflow (accumulator overflow) would have occurred. At the other end of the spectrum, it was determined that the performance graph of MPC Q=50was close to the stability limit, which proved to be correct in further tests because when a faster tuning was applied (Q<50) or the plant was operated in an operating range with a higher steam throughput, these controllers became unstable (not shown).

[0099] A diagram for the case where the plant operated at 0.4 kg / min steam is shown in Fig. 20, where the controller performance is defined as σ Q=50 = 0.053, σ Q=100 = 0.028 was measured, the controller with Q=1000 did not control the system satisfactorily and σ PI = 0.032. Thus, the MPC controller with the same tuning as that used for 55 kg / min steam ( Fig. 18) has a lower standard deviation. The MPC with Q=1000 is Fig. 19 is not shown because it did not control the system satisfactorily and repeatedly triggered the accumulator pump lockout, as mentioned above.

[0100] In summary, the test runs of the distillation column from Fig.17 showed that values ​​of 50 and 100 of the MPC tuning parameter Q were suitable for a model mismatch spanning the desired operating ranges (here from 0.4 kg / min to 0.55 kg / min steam). Tuning below 50 and above 200 (tested but not shown) was not suitable. As suggested above with regard to optimal tuning, one could find a specific set of tuning parameters that would result in an ideal feedback control performance for the varying degree of model mismatch. This was experimentally possible, even without new knowledge regarding the plant model. No new model identification or model update was performed.In fact, the assumed plant model was used throughout the experiment, even though it was known to be quite inaccurate. Not only were the values ​​of the model parameters most likely incorrect, but the model form also did not match the underlying process characteristics of an integration process (i.e., a level control loop). An incorrect model formulation (first-order plus dead time) was deliberately chosen to ensure that model misfit would be present during the experiment, as it was not possible to determine the exact extent of model misfit that existed during the experiment.

[0101] A summary of the experimental performance of the four different controllers under four different process conditions for the process from Fig.17 is provided in Table 6 below, where all MPC controllers were tuned based on the same model assumptions. Here, the controllers were a PI controller and MPC controllers with Q values ​​of 50, 100, and 1000. As can be seen from Table 6, the MPC with a Q value of 50 performed with an even lower IAE than the PI controller in response to steam changes, while the MPC with the Q set to 100 performed worse, and the MPC with the Q value of 1000 performed very poorly (or was not tested) in response to steam change conditions, but performed best when controlled at the operating point of 0.55 kg / min. Table 6 PI MPC Q=50 MPC Q=100 MPC Q=1000 s Dampf =0,55kg / min 0,036 0,057 0,066 0,052 s Dampf=0,4kg / min 0,032 0,053 0,028 not tested IAE Dampfänderung 0,55 → 0,4 kg / min 0,302 0,122 0,468 ∞ IAE Dampfänderung 0,4 → 0,55 kg / min 0,281 0,136 0,424 not tested

[0102] However, in the actual control of a plant, it is important to be able to know, while the plant is running at one operating point, how a change to a different operating point affects performance for a particular tune. Thus, for the above example, it is important that the operator can know, before the steam flow changes from 0.55 kg / min to 0.4 kg / min, that although the loss tune of Q=1000 shows the best control at 0.55 kg / min, this tune is not sufficient for major upsets and may cause a plant shutdown. Manually going through all possible process regions and determining the tune that works in all of them is feasible and does not require model identification. However, this process creates a certain amount of scrap or bad product, may need to be repeated if the plant model changes, and is only possible if the parameter(s) being adjusted are not sufficient.that influence the model misfit are known and manipulable (like the steam in this example).

[0103] However, it was determined that the use of a method described above with reference to Fig. The autocorrelation analysis discussed in Section 16 can be used as a trigger to initiate appropriate tuning adjustments in light of possible changes in operating parameters (and in light of changes in the plant model) and to select a set of tuning parameters that is appropriate or optimal in light of these changes. In particular, an error analysis of the prediction error or control error can be used to determine how well an MPC controller is matched to a plant and the extent and type of model mismatch present. Fig. 21 to 25 are provided to illustrate this point. Fig.Figure 21 provides a comparison of the autocorrelation of the prediction error in the MPC controller at the three different tuning settings of the exemplary plant discussed above, operating at a steady-state rate of 0.55 kg / min steam. From this graph, it is clear that no definitive statement can be made as to which MPC controller is better or worse. The amplitudes are different, but when considering the time lag axis, there is no indication that any of the graphs is significantly better autocorrelated for a given time lag, even though the tuning setting of the three controllers has significantly different feedback performance with respect to the IAE, as Fig. 19. The autocorrelation diagrams of the prediction error for steady-state operation at 0.4 kg / min are shown in Fig.22 and illustrate the same dilemma. This fact supports the finding that the best state update (the lowest prediction error) does not necessarily lead to the best feedback control performance. Here, the MPC with Q=50 shows the lowest prediction error but the worst integrated absolute error, and the MPC with Q=1000 shows the best IAE with the worst prediction error. However, the differences between the three controller settings can be observed when determining the autocorrelation of the prediction error during a large change in an unmeasured disturbance, as in Fig. 23, which shows the autocorrelation of the prediction error in the MPC controllers at the three different tuning settings during the suppression of an unmeasured disturbance in the form of a steam flow rate change from 0.55 kg / min to 0.4 kg / min.

[0104] Here, the large change in control error reveals a noticeable difference between the autocorrelation plots, which is otherwise obscured by noise. At this point, it is unfortunately too late to determine that the controller has been mistuned, because this information was needed to retune the controller before a large disturbance occurred. In any case, this plot illustrates why state-of-the-art methods that use autocorrelation analysis as a criterion for determining model misfit use process excitations to achieve insightful comparisons of autocorrelations. Although some methods can be considered "non-intrusive" because they wait for disturbance changes rather than injecting pulses that disturb the process, they do not work well during steady-state control, such as the steady-state operation at 0.55 kg / min steam in this experiment.

[0105] Although using prediction error autocorrelation to perform control performance evaluation during periods of disturbance suppression can be helpful in determining process model mismatch, using prediction error autocorrelation to perform control performance evaluation during periods of steady-state operation is not very useful. While using prediction error autocorrelation can be useful during times of process failure (e.g., unmeasured disturbances or setpoint changes) to trigger a controller adaptation / tuning cycle, this technique still requires some degree of process change or failure, which is generally less desirable.

[0106] However, it has been found that considering the autocorrelation of the control error during steady-state operation works well as a measure of process model mismatch, and that this type of error analysis can be used as a trigger for adaptation / retuning of an MPC controller. Fig. 24, for example, shows the autocorrelation of the controlled variable, which corresponds to the autocorrelation of the control error for a pure feedback control, ie, with a constant setpoint. The operation of the MPC controllers with the same three tuning settings is shown in Fig. 24 at a constant steam flow rate of 0.55 kg / min together with the operation of the original PI controller performance at this flow rate, which is added as a reference comparison.

[0107] Out of Fig. 24 it becomes clear that the MPC Q=1000significantly highlights and is easily identified as exhibiting inherent tuning problems (e.g., a high degree of process model mismatch). In particular, the autocorrelation of the controlled variable of the MPC with Q=1000 is quite different from all other controller tuning settings. In steady-state operation and without significant unmeasured disturbance, this tuning is easily identified as poor because it exhibits significantly higher autocorrelation for all values ​​of the time lag. The most obvious distinguishing feature of this curve is that it stays on only one side of the abscissa and never crosses zero.

[0108] Fig.Figure 25 presents the same error analysis calculations during an artificially introduced perturbation of the accumulator level, which is linked to the change in steam flow from 0.55 kg / min to 0.4 kg / min. Although one could argue for a difference in autocorrelation, it is by no means as clear as the autocorrelation performed without the unmeasured perturbation (which is shown in Fig.24). However, this fact does not pose a significant problem because the adaptation / tuning logic can automatically detect a disturbance and switch from analyzing the autocorrelation of a control error to analyzing the autocorrelation of a prediction error in these two different scenarios to provide better adaptation / tuning initiation. For example, switching between the two different calculation types can be performed when the control error exceeds a certain threshold, which typically occurs in response to an unmeasured disturbance or immediately after a change in a setpoint.

[0109] A simplified qualitative summary of the autocorrelation analysis discussed above is provided in Table 7 below. Here, the experimental data for the four different controllers are displayed as an overall indication of the results of the magnitude (i.e., small, medium, and large) of the autocorrelation analysis. The autocorrelation analyses that can be used to distinguish or identify model misfit can be found on the middle two rows due to the difference in the magnitudes of the autocorrelation analyses of the different controllers for these analyses. In particular, Table 7 provides a summary of qualitative estimates of various autocorrelation experimental data for the three different MPC controllers, with all controllers tuned based on the same model assumptions. In this table, R I (k) the autocorrelation of the prediction error and R y(k) the autocorrelation of the control error. The PI controller operation is added for comparison. Table 7 PI MPC Q=50 MPC Q=100 MPC Q=1000 R I (k) Dampf=0,55kg / min without specification small small Small R I (k) Dampf=0,4kg / min without specification small small not tested R I (k) Dampfänderung=0,55-0,4kg / min without specification small medium Large R y (k) Dampf=0,55kg / min small small medium Large R y (k) Dampf=0,4kg / min small medium medium not tested R y (k) Dampfänderung=0,55-0,4kg / min large large large Large

[0110] Generally, larger autocorrelation values ​​are assumed to indicate larger process model mismatches. In summary, closed-loop adaptive control of MPC design and tuning parameters can be initiated using a method that analyzes the autocorrelation of MPC controller information, such as the control error of the controlled variable(s) or the prediction error of the controlled variable(s). However, as discussed above, it can make a significant difference whether the autocorrelation is calculated from the prediction error or the control error. For example, the autocorrelation of a prediction error may only be meaningful during a setpoint change or a rejection of an unmeasured disturbance, whereas the autocorrelation of a control error may be most useful during steady-state operation.It is most useful (but also most difficult) to adapt the tuning to the process characteristics before an unmeasured disturbance occurs, rather than during or after the disturbance occurs, as required by most current state-of-the-art adaptive tuning techniques. Techniques that attempt to re-identify the process model usually rely on process changes and cannot capture model changes during steady-state operation. Such changes can be caused by a disturbance or setpoint changes and must be large enough to stand out from the noise band. Thus, based on the above discussion, the automatic adaptation / tuning technique should be... Fig.16 preferably include a prediction error analysis and a control error analysis in the manner described above. The result of this analysis is how well the current tuning is suited to the current process. Any degraded autocorrelation function (compared to expected or previous autocorrelation functions calculated for the same set of design / tuning parameters) must be the result of increased model misfit and can be accounted for or compensated for by a new adaptation / tuning.

[0111] The use of autocorrelation as a technique to develop useful feedback information about model misfit for use in the analysis of Fig.The adaptation / tuning technique described in Section 13 is useful for many different process and model types. While the results may vary depending on the particular type of model mismatch encountered, in general, the design and tuning parameter values ​​calculated by the optimal design / tuning procedure for a broader model mismatch range will be more conservative than the design / tuning parameter values ​​resulting from a narrower mismatch range. In other words, the automatic adaptation / tuning procedure presented above detunes the MPC controller to prevent oscillations and instability when a large process model mismatch (or an increase in the process model mismatch) is detected, acting as an automatic safety net that kicks in when necessary.On the other hand, if the autocorrelation analysis indicates a reduction in the process model mismatch, a new adaptation / tuning cycle can be implemented to tighten the controller shape and tuning parameters to provide better overall control. This automatic solution approach is clearly more desirable than proactively detuning the controller to be safe, as is common in industry, because this automatic solution approach applies faster tuning when the model mismatch is smaller and applies slower or looser tuning when the model mismatch is larger.

[0112] Importantly, the automatic adaptation / tuning procedure described here adapts the shape, controller model, and design and tuning parameters used by a model-based controller based on a controller model mismatch without performing a new plant model identification. This procedure is therefore very useful because plant model identification, especially closed-loop plant model identification, has proven to be significantly more intrusive or unreliable in industrial process applications.

[0113] Fig. Figure 26 illustrates another embodiment of an adaptive closed-loop voting system similar to that shown in Fig.16, but which includes an estimator 130 that uses one or both of the error analyses discussed above and a process estimate to determine one or more model mismatches or mismatch ranges for use in the tuning block 110A. Block 130 may thereby use either a fault analysis (e.g., of the innovation) of the controller or a process plant analysis, or both, to determine or acquire an estimate of a value or model mismatch range between the controller model and the plant, and may use this estimate to initiate a tuning cycle for the MPC controller 112.

[0114] It is thus understood that the adaptive tuning technique described here can be used to adjust the controller tuning in the following scenarios and various combinations thereof: (1) based on manual input of a new process model, (2) based on automatic property estimation or model identification developed from process plant inputs and outputs, (3) based on manual input of one or more new model mismatches or model mismatch ranges, or (4) based on an automatic estimate of a model mismatch (magnitude or range) developed from error analysis of a state estimation.

[0115] Although the invention has been described with reference to specific embodiments intended to teach and illustrate the invention, the disclosed adaptation / tuning apparatus and method are not limited to these embodiments. Various modifications, improvements, and additions may be employed by those skilled in the art, and such modifications, improvements, and additions do not depart from the scope of the invention.

[0116] For example, although the adaptation / tuning devices and methods described above have been described in conjunction with the use of process models in the form of first-order plus dead-time models, these techniques may include other types of process models, e.g., state-space process models, regressive models such as ARX models, finite impulse response (FIR) models, step response models, etc. Likewise, the adaptation / tuning devices and methods described herein may function to adapt an MPC controller using all or only some of the available MPC model, design, and tuning parameters based on a model mismatch or model mismatch range in any specific case.In particular, the adaptation / tuning devices or methods may focus on one or more "important" model, design, and / or tuning parameters present in any particular case or scenario, without adjusting or changing one or more of the other parameters during an adaptation / tuning process. Furthermore, although the description of the adaptive tuning techniques provided herein has been provided in the context of a single-loop MPC controller, these techniques are also, or instead, applicable or extensible to multi-variable MPC controller configurations.

[0117] Furthermore, those skilled in the art will understand that the allocation of the individual components of the adaptation / tuning blocks and controller units as described herein is reserved for those responsible for the implementation and operation of the controller. It is understood that all of these functions may be implemented in any desired manner in one or more desired devices. Moreover, although the adaptation / tuning technique described herein is preferably implemented in software, it, or any portion thereof, may be implemented in hardware, firmware, etc., and may be implemented by any other processor associated with a process control system. Thus, the elements described herein may be implemented in a standard general-purpose CPU or specifically designed hardware or firmware, such as an application-specific integrated circuit (ASIC) or other hard-wired device, as desired.When implemented as software, the software routine may be stored on any computer-readable storage, such as a magnetic disk, a laser disk (such as a CD, a DVD, etc.), a flash drive, or other storage medium, in a RAM or ROM of a computer or processor, in any database, etc. Likewise, such software may be delivered to a user or process equipment via any known or desired delivery method, including, for example, a computer-readable disk, smart card memory, flash drives, or other transportable computer storage mechanisms, or via a communications channel, such as a telephone line, the Internet, etc. (which is considered equivalent to or interchangeable with delivery of such software via a transportable storage medium).

[0118] It is also recognized that the specific approaches described herein represent only insignificant departures from the above-described embodiments of the invention. Accordingly, the claims provided herein should be properly interpreted to encompass all modifications, variations, and improvements that fall within the true spirit and scope of the invention, as well as substantial equivalents thereof. Accordingly, other embodiments of the invention, although not specifically described herein, are nevertheless included within the scope of the invention.

[0119] Further embodiments of the invention follow: Example 1

[0120] A method for tuning a model predictive controller for use in controlling a process, comprising the following steps: Obtaining a process model for the process, the process model comprising a value for each parameter of a set of process model parameters; Obtaining a process model mismatch indication that identifies a process model mismatch for at least one parameter of the set of process model parameters; and Performing controller optimization based on the process model and the indication of process model mismatch, comprising determining a control-based performance measure for the model-predictive controller when operated using each set of a plurality of different sets of design / tuning parameter values ​​of the controller and the process model in the presence of an amount of process model mismatch associated with the indication of process model mismatch, and determining an optimal value of the set of design / tuning parameter values ​​of the controller for use in the model-predictive controller based on the control-based performance measures. Example 2:

[0121] Method according to embodiment 1, wherein the control-based power measurement comprises an integrated absolute error. Example 3:

[0122] Method according to embodiment 1, wherein the design / tuning parameter values ​​of the controller comprise a controller shape parameter that specifies a controller shape. Example 4:

[0123] Method according to embodiment 3, wherein the controller form parameter specifies either an observer-based model-predictive controller form or a non-observer-based model-predictive controller form. Example 5:

[0124] Method according to embodiment 3, wherein the controller shape parameter comprises an indication of a model-predictive controller shape based on a standard Kalman filter observer or a model-predictive controller shape based on a simplified Kalman filter observer. Example 6:

[0125] Method according to embodiment 1, wherein the design / tuning parameters of the controller comprise one or more tuning parameters of an observer unit. Example 7:

[0126] Method according to embodiment 6, wherein the one or more tuning parameters of the observer unit comprise one or more loss quantities. Example 8:

[0127] The method of embodiment 6, wherein the one or more tuning parameters of the observer unit comprise a Kalman filter loss quantity comprising a time constant, a signal-to-noise ratio, a covariance in a disturbance function, or a covariance in a noise function. Example 9:

[0128] Method according to embodiment 1, wherein the design / tuning parameters of the controller comprise one or more tuning parameters of a model predictive control algorithm. Example 10:

[0129] The method of embodiment 9, wherein the one or more tuning parameters of a model predictive control algorithm comprise(s) a loss quantity or a control horizon or a prediction horizon. Example 11:

[0130] The method of embodiment 1, wherein obtaining the indication of the process model mismatch comprises obtaining a specific value of a process model mismatch in one of the process model parameters. Example 12:

[0131] The method of embodiment 1, wherein obtaining the indication of the process model mismatch comprises obtaining specific values ​​of the process model mismatch in two or more of the process model parameters. Example 13:

[0132] The method of embodiment 12, wherein the set of process model parameters comprises a process gain or a process time constant. Example 14:

[0133] The method of embodiment 1, wherein obtaining the indication of the process model mismatch comprises obtaining a range of process model mismatch in one or more of the process model parameters. Example 15:

[0134] The method of embodiment 1, wherein performing the controller optimization comprises determining a control-based performance measure for the model-predictive controller when operating using each parameter of a plurality of different sets of design / tuning parameter values ​​of the controller and the process model at each of a plurality of different sets of process model mismatch values ​​to yield a tuning map as a set of points, each point in the tuning map being associated with a particular optimal control-based performance measure achievable at a particular set of process model mismatch values ​​using the set of design / tuning parameter values ​​of the controller associated with the particular optimal control-based performance measure. Example 16:

[0135] The method of embodiment 15, comprising displaying the voting image on a display device so that it is visible to a user. Example 17:

[0136] The method of embodiment 16, comprising allowing a user to select a particular set of controller design / tuning parameter values ​​to be used in tuning the model predictive controller by selecting a particular point in the tuning map. Example 18:

[0137] The method of embodiment 16, wherein obtaining the indication of the process model mismatch comprises obtaining a model mismatch range for one or more parameters of the set of process model parameters, the model mismatch range defining a subspace in the tuning map, and wherein displaying the tuning map comprises displaying the subspace of the model mismatch range in the tuning map. Example 19:

[0138] The method of embodiment 18, further comprising allowing a user to move the subspace of the model mismatch region within the tuning map to determine an optimal adaptation / tuning point given the subspace of the model mismatch region. Example 20:

[0139] The method of embodiment 15, wherein obtaining the indication of the process model mismatch comprises obtaining a model mismatch range, the model mismatch range defining a subspace size in the tuning map, and performing a second optimization to find a particular subspace within the tuning map of the subspace size that results in an optimal value for a second performance measure. Example 21:

[0140] The method of embodiment 20, wherein the second performance measure determines the worst value of the control-based performance measure of the points in the tuning map within the determined subspace. Example 22:

[0141] The method of embodiment 20, comprising determining a new set of process model parameter values ​​for use in creating a new controller model for the model predictive controller and determining a set of controller design / tuning parameter values ​​to be used in the model predictive controller based on the second optimization. Example 23:

[0142] The method of embodiment 15, comprising determining a new set of controller design / tuning parameter values ​​as controller design / tuning parameter values ​​associated with one of the points in the tuning map. Example 24:

[0143] The method of embodiment 15, comprising selecting a new controller operating point as one of the points within the tuning map and providing the controller design / tuning parameter values ​​associated with the selected controller operating point to the model predictive controller for use in controlling the process, and providing a new controller model to the model predictive controller based on the process model mismatch values ​​associated with the selected controller operating point. Example 25:

[0144] The method of embodiment 1, wherein obtaining an indication of the process model mismatch comprises performing an autocorrelation procedure on an error signal. Example 26:

[0145] Method according to embodiment 25, wherein the error signal is a control error determined in the model predictive controller. Example 27:

[0146] The method of embodiment 26, wherein performing the autocorrelation method comprises performing the autocorrelation method on data collected during a period of time during which the process is in a steady state. Example 28:

[0147] The method of embodiment 25, wherein the error signal is a prediction error determined in the model predictive controller. Example 29:

[0148] The method of embodiment 28, wherein performing the autocorrelation method comprises performing the autocorrelation method on data collected during a period during which the process is regulated in response to a significant disturbance or failure. Example 30:

[0149] Adaptive model predictive controller for use in controlling a process plant, comprising: a model predictive controller unit comprising a controller model and one or more variable design / tuning parameters; and a voting unit comprising: a model memory storing a process model for the process plant, the process model specifying a value for each parameter of a set of process model parameters; and an optimization unit communicatively coupled to the model predictive controller, wherein the optimization unit simulates operation of the model predictive controller in the presence of a non-zero process model mismatch when the controller model is based on the process model, for each of a plurality of simulation cases, wherein during each simulation case the model predictive controller is configured with a different set of controller design / tuning parameter values, wherein the optimization unit determines a controller performance measurement for each of the simulation cases, wherein the optimization unit further determines an optimal value of the sets of controller design / tuning parameter values ​​for use in the model predictive controller based on the controller performance measurements. Example 31:

[0150] The adaptive model predictive controller of embodiment 30, wherein the design / tuning parameters of the controller comprise one or more of a controller shape parameter specifying a controller shape, one or more tuning parameters of an observer unit, or one or more loss quantities of a predictive controller algorithm. Example 32:

[0151] The adaptive model predictive controller of embodiment 30, wherein the design / tuning parameters of the controller comprise a controller shape parameter that specifies either (1) one of an observer-based model predictive controller shape or a non-observer-based model predictive controller shape, or (2) one of a first or a second type of observer-based model predictive controller shape. Example 33:

[0152] The adaptive model predictive controller of embodiment 30, wherein the optimization unit simulates operation of the model predictive controller in the presence of a plurality of different non-zero process model mismatches to develop a tuning map, the tuning map comprising a set of points, each point associated with (1) a particular optimal controller performance measurement possible at a particular one of the plurality of process model mismatches, and (2) the specific set of design / tuning parameter values ​​of the controller resulting from the optimal controller performance measurement at the particular one of the plurality of process model mismatches. Example 34:

[0153] The adaptive model predictive controller of embodiment 33, further comprising a display unit communicatively coupled to the optimization unit for displaying the tuning map to a user. Example 35:

[0154] The adaptive model predictive controller of embodiment 34, wherein the display unit enables a user to select a particular point in the tuning map, and wherein the optimization unit provides the design / tuning parameter values ​​associated with the selected point to the model predictive controller. Example 36:

[0155] The adaptive model predictive controller of embodiment 34, wherein the optimization unit stores a model mismatch range for one or more of the process model parameters, the model mismatch range defining a subspace of the model mismatch range in the tuning map, and the display unit displays the subspace of the model mismatch range in the tuning map. Example 37:

[0156] The adaptive model predictive controller of embodiment 36, wherein the display unit displays the subspace of the model mismatch region in the tuning map centered at a point that is not associated with any model mismatch. Example 38:

[0157] The adaptive model predictive controller of embodiment 37, wherein the display unit enables a user to move the subspace of the model mismatch region within the tuning map to determine an optimal adaptation / tuning point in the tuning map given the subspace of the model mismatch region. Example 39:

[0158] The adaptive model predictive controller of embodiment 33, wherein the optimization unit stores a model mismatch range, the model mismatch range defining a subspace size in the tuning map, and wherein the optimization unit performs a second optimization to determine a particular subspace within the tuning map of the subspace size that produces an optimal value for a second performance measurement. Example 40:

[0159] The adaptive model predictive controller of embodiment 39, wherein the optimization unit determines a new set of process model parameter values ​​for use in defining a new controller model for the model predictive controller and determines a set of controller design / tuning parameter values ​​for use in the model predictive controller based on the second optimization. Example 41:

[0160] The adaptive model predictive controller of embodiment 33, wherein the optimization unit determines a new set of controller design / tuning parameter values ​​as controller design / tuning parameter values ​​associated with one of the points in the tuning map. Example 42:

[0161] The adaptive model predictive controller of embodiment 33, further comprising an estimator unit that performs an autocorrelation method on an error function to implement a tuning cycle for the optimization unit. Example 43:

[0162] The adaptive model predictive controller of embodiment 42, wherein the estimator performs an autocorrelation process on the error function to estimate an amount of process model mismatch in one of the process model parameters. Example 44:

[0163] Adaptive model predictive controller according to embodiment 42, wherein the estimation function unit performs an autocorrelation method on a control error determined in the model predictive controller. Example 45:

[0164] The adaptive model predictive controller according to embodiment 42, wherein the estimation function unit performs an autocorrelation method on a control error determined in the model predictive controller during steady-state operation of the process. Example 46:

[0165] An adaptive model predictive controller tuning unit for implementation on a computer processor to tune a model predictive controller operative to control a process plant using a controller model, comprising: a computer-readable medium; a storage routine stored on the computer-readable medium for execution on a processor to store a process model for the process plant, the process model specifying a value for each parameter of a set of process model parameters; and an optimization routine stored on the computer-readable medium for execution on a processor to simulate the operation of the model-predictive controller in the presence of a process model mismatch when the controller model of the model-predictive controller is based on the process model, wherein the optimization routine simulates the model-predictive controller when the model-predictive controller is configured with each value of a plurality of different sets of design / tuning parameter values ​​of the controller, wherein the optimization routine determines a controller performance measurement for each value of the plurality of different sets of design / tuning parameter values ​​of the controller in the presence of the process model mismatch,and wherein the optimization routine further determines an optimal value of one of the various sets of controller design / tuning parameter values ​​for use in the model predictive controller based on the controller performance measurements. Example 47:

[0166] A tuning unit of an adaptive model-predictive controller according to embodiment 46, wherein the design / tuning parameters of the controller comprise a controller shape parameter that specifies a controller shape, or one or more tuning parameters of an observer unit of a model-predictive controller, or one or more loss variables of a model-predictive controller algorithm. Example 48:

[0167] The tuning unit of an adaptive model predictive controller according to embodiment 46, wherein the optimization routine is executed to simulate the operation of the model predictive controller in the presence of a plurality of different process model mismatches to develop a tuning map, the tuning map comprising a set of points, each point being associated with (1) a particular optimal controller performance measurement possible at a particular mismatch of the plurality of process model mismatches, and (2) the specific set of design / tuning parameter values ​​of the controller that resulted in the optimal controller performance measurement at the particular mismatch of the plurality of process model mismatches. Example 49:

[0168] The tuning unit of an adaptive model predictive controller according to embodiment 48, further comprising a display routine communicatively coupled to the optimization routine for displaying the tuning map to a user, and wherein the display routine enables a user to select a particular point in the tuning map to provide the design / tuning parameter values ​​associated with the selected point to the model predictive controller for tuning the model predictive controller. Example 50:

[0169] A tuning unit of an adaptive model predictive controller according to embodiment 49, wherein the optimization routine comprises a model mismatch region for one or more of the process model parameters, the model mismatch region defining a subspace in the tuning map, and the display unit displays the subspace of the model mismatch region in the tuning map. Example 51:

[0170] The tuning unit of an adaptive model predictive controller according to embodiment 48, wherein the optimization routine is executed to perform a second optimization to determine a particular model misfit subspace within the tuning map that yields an optimal value for a second performance measurement, the model misfit subspace defining a model misfit range in one or more of the process model parameters. Example 52:

[0171] The tuning unit of an adaptive model predictive controller according to embodiment 51, wherein the optimization routine is executed to determine a new set of process model parameter values ​​for use in defining a new controller model for the model predictive controller, and determines a set of controller design / tuning parameter values ​​for use in the model predictive controller based on the second optimization.

Claims

[1] A method for tuning a tunable model-based process controller used to control a process plant, comprising the following steps: Obtaining an error signal linked to the operation of the process controller; Performing an autocorrelation analysis on the error signal to determine an indication of the presence of a model mismatch between the process controller as currently tuned and the process plant; and Implement a tuning cycle to retune the process controller based on the results of the autocorrelation analysis. [2] The method of claim 1, wherein obtaining the error signal associated with the operation of the process controller comprises determining a control error signal associated with the process controller as a difference between a measured value of a process variable and a setpoint value for the process variable. [3] The method of claim 2, wherein performing the autocorrelation analysis comprises performing the autocorrelation analysis on a control error signal associated with a period of time during which the process variable is in a steady state. [4] The method of claim 1, wherein obtaining the error signal associated with the operation of the process controller comprises determining a prediction error signal associated with the process controller as a difference between a measured value of a process variable and a predicted value for the process variable produced by the process controller. [5] The method of claim 4, wherein the prediction error signal indicates a prediction error associated with the operation of a model predictive controller. [6] The method of claim 4, wherein performing the autocorrelation analysis comprises performing the autocorrelation analysis on a prediction error signal associated with a period during which the process variable is controlled in response to a disturbance or load failure. [7] The method of claim 1, wherein obtaining the error signal associated with operation of the process controller comprises obtaining an error signal for a first time period and obtaining an error signal for a second time period later than the first time period, and wherein performing the autocorrelation analysis on the error signal to determine an indication of a presence of a model mismatch comprises performing an autocorrelation analysis on the error signal for the first time period, performing an autocorrelation analysis on the error signal for the second time period, and comparing the results of the autocorrelation analyses for the first and second time periods to determine a change in the model mismatch between the first and second time periods. [8] An adaptive controller for use in controlling a process plant, the adaptive controller comprising: a control unit that generates control signals to control the process plant, the control unit comprising one or more variable tuning parameters; a tuning unit that determines one or more tuning parameter values ​​for use in the controller unit; an estimator unit configured to perform an estimator function and coupled between the controller unit and the tuning unit, wherein the estimator performs an autocorrelation analysis on an error signal associated with the controller unit to determine an indication of a model mismatch between the controller unit as currently tuned and the process plant, wherein the estimator unit triggers the tuning unit to perform a tuning cycle based on the indication of the model mismatch. [9] An adaptive controller according to claim 8, wherein the estimator performs the autocorrelation analysis on a control error signal associated with the controller unit, the control error signal indicating a difference between a measured value of a process variable and a setpoint value for the process variable. [10] The adaptive controller of claim 9, wherein the estimator performs the autocorrelation analysis on the control error signal associated with the controller unit based on control error data collected during a period during which the process variable is in a steady state. [11] An adaptive controller according to claim 8, wherein the estimator performs the autocorrelation analysis on a prediction error signal associated with the controller unit, the prediction error signal indicating a difference between a measured value of a process variable and a predicted value for the process variable. [12] The adaptive controller of claim 11, wherein the estimator performs the autocorrelation analysis on the prediction error signal associated with the controller unit based on prediction error data collected during a period during which the process variable experiences a disturbance or failure. [13] The adaptive controller of claim 8, wherein the estimator obtains the error signal for a first period and obtains the error signal for a second period later than the first period, and wherein the estimator performs an autocorrelation analysis on the error signal for the first period, performs an autocorrelation analysis on the error signal for the second period, and compares the results of the autocorrelation analyses for the first and second periods to determine a change in model misfit between the first and second periods. [14] Adaptive controller according to claim 8, wherein the controller unit is a model predictive controller. [15] Adaptive controller according to claim 8, wherein the controller unit is a model predictive controller with a Kalman filter. [16] A method for detecting a process model mismatch between a controller model used by a predictive process controller and a process plant, the method comprising the steps of: Determining an error signal associated with the control of the process plant; performing an autocorrelation analysis on the error signal; and Analyze the autocorrelation analysis to detect a process model mismatch between the controller model and the process plant. [17] The method of claim 16, wherein determining the error signal associated with the control of the process plant comprises determining a control error signal associated with the predictive process controller as a difference between a measured value of a process variable and a setpoint value for the process variable. [18] The method of claim 17, wherein performing the autocorrelation analysis on the error signal comprises performing the autocorrelation analysis on control error data collected during a period during which the process variable is in a steady state. [19] The method of claim 16, wherein determining the error signal associated with the control of the process plant comprises determining a prediction error signal associated with the predictive process controller as a difference between a predicted value of a process variable and a measured value of the process variable. [20] The method of claim 19, wherein performing the autocorrelation analysis on the error signal comprises performing the autocorrelation analysis on prediction error data collected during a period during which the process variable is controlled in response to a disturbance or failure. [21] The method of claim 20, wherein determining the error signal associated with the control of the process plant comprises obtaining a first control error signal for a first period of time as the difference between a measured value of a process variable and a setpoint value for the process variable during the first period of time, and obtaining a second control error signal for a second period of time later than the first period of time as the difference between a measured value of the process variable and a setpoint value for the process variable during the second period of time, and wherein performing an autocorrelation analysis on the error signal comprises performing an autocorrelation analysis on the first control error signal and performing an autocorrelation analysis on the second control error signal,and wherein analyzing the autocorrelation analysis to detect a process model mismatch comprises comparing the results of the autocorrelation analyses on the first and second control error signals to determine a change in the process model mismatch between the first and second time periods. [22] The method of claim 21, wherein obtaining the first control error signal and obtaining the second control error signal comprise obtaining the first and second control error signals during first and second time periods in which the process variable is in a steady state.

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