Nonlinear model predictive control of processes

Abstract

Provided herein is a chemical system for exhibiting an operation of steady-state gain reversal, and the chemical system includes a reactor configured to receive a feed stream and produce an outlet stream to form a process, and a control device configured to control the process. The control device receives inputs indicative of operating parameters and receives output variables, and provides steady-state manipulation inputs configured to control or optimize the process in response to the inputs and the output variables. The control device includes an input disturbance model, a state estimator, a nonlinear steady-state target calculator, and a regulator configured to provide signals for adjusting one or more inputs based on the steady-state manipulation inputs and associated output variables.

Description

Background Art

[0001] The production of alkylene oxides can be accomplished via a chemical system that utilizes the catalytic epoxidation of olefins using silver-based catalysts in the presence of oxygen. Conventional silver-based catalysts used in such processes typically provide relatively low efficiency or "selectivity" (e.g., a lower percentage of reacted alkylene is converted to the desired alkylene oxide). In some processes, when conventional catalysts are used in the epoxidation of ethylene, the theoretical maximum efficiency towards ethylene oxide, expressed as the fraction of converted ethylene, does not reach values ​​above the 6 / 7 or 85.7% limit.

[0002] Certain such catalysts, such as so-called "high selectivity" or "high efficiency" catalysts, tend to exhibit relatively steep efficiency curves as a function of gas-phase promoter concentration as the concentration is moved away from a value that provides high efficiency (e.g., the change in efficiency relative to a change in gas-phase promoter concentration is at least 0.2% / ppmv when operating away from the efficiency that maximizes the promoter concentration). Thus, small changes in promoter concentration can result in significant changes in efficiency because the efficiency can exhibit a distinct maximum, such as an optimum, over time at a certain concentration (or feed rate) of the gas-phase promoter. The distinct maximum of a chemical process is due to multiphase flow and chemical reactions that are characterized by process nonlinearity and time delays due to mass transport and chemical reaction rates.

[0003] Because many variables in chemical processes have nonlinear relationships with other variables, such as inter-loop interactions of variables, it is necessary to develop process models that effectively characterize these multiple interdependent variable relationships, which can be nonlinear. In various implementations, linear model predictive control (LMPC), among other approaches, has been proposed for application in the field of process control. However, such approaches continue to lack robustness for processes with steady-state gain reversals. Summary of the Invention

[0004] In some embodiments, a chemical system for operating to exhibit steady-state gain inversion includes: a reactor configured to receive a feed stream and produce an outlet stream to form a process; and a control device configured to control the process. The control device receives an input indicative of an operating parameter and receives an output variable, and in response to the input and the output variable, provides a steady-state manipulative input configured to control or optimize the process. The control device includes: an input disturbance model that determines an unmeasured disturbance based on using the steady-state manipulative input as a custom output measurement; a state estimator configured to utilize the custom output measurement to estimate the unmeasured disturbance entering the process and thereby predict changes to the process based on a representation of the process by the model; a nonlinear steady-state target calculator configured to determine the steady-state manipulative input for the process based on the representation of the process as calculated by the model; and a regulator configured to provide a signal for regulating one or more inputs based on the steady-state manipulative input and associated output variable.

[0005] In some embodiments, a method for controlling a chemical system via a control device includes receiving an input indicating an operating parameter of a process and receiving a steady-state output variable. The method further includes implementing an input disturbance model based on using an optimal control steady-state input as a custom output measurement to determine an optimized control input in the presence of both a measured disturbance and an unmeasured disturbance. Additionally, the method includes estimating a state of the process to predict the process based on a characterization of the process by the model. The method further includes determining a directional control input for the process based on the characterization of the process by modeling and an estimate of one or more steady-state output variables of the chemical system. Finally, the method includes adjusting the process based on the directional control input. BRIEF DESCRIPTION OF THE DRAWINGS

[0006] Referring now to the drawings, illustrative embodiments are shown in detail. Although the drawings represent some embodiments, they are not necessarily drawn to scale, and certain features may be exaggerated, removed, or partially segmented to better illustrate and explain the present invention. Furthermore, the embodiments described herein are exemplary and are not intended to be exhaustive or otherwise limit or restrict the claims to the precise forms and configurations shown in the drawings and disclosed in the following detailed description.

[0007] Figure 1 is a process flow diagram depicting an embodiment of a process for producing an alkylene oxide by epoxidizing an olefin according to an embodiment of the present disclosure.

[0008] Figure 2 Schematic diagram of a nonlinear model predictive control (NMPC) apparatus for a process with steady-state gain inversion according to an embodiment of the present disclosure.

[0009] Figure 3 Graph depicting steady-state changes in output based on manipulation input according to an embodiment of the present disclosure.

[0010] Figure 4 is a graph depicting steady-state ethylene oxide (EO) selectivity according to an embodiment of the present disclosure.

[0011] Figure 5 Graph depicting EO selectivity based on baseline data according to an embodiment of the present disclosure.

[0012] Figure 6 A pair of graphs depicting the chlorination effectiveness parameter Z and EO production rate over time based on baseline data according to an embodiment of the present disclosure.

[0013] Figure 7 Graph depicting EO selectivity at high production rates based on utilization of an NMPC unit according to an embodiment of the present disclosure.

[0014] Figure 8 Graphs depicting a pair of graphs depicting the chlorination effectiveness parameter Z and EO production rate over time at high production rates based on utilization of an NMPC unit according to an embodiment of the present disclosure.

[0015] Figure 9 Graphs depicting a pair of graphs depicting the chlorination effectiveness parameter Z and EO production rate over time at increasing production rates based on utilization of an NMPC unit according to an embodiment of the present disclosure.

[0016] Figure 10 Graph depicting EO selectivity at increasing production rates based on utilization of an NMPC unit according to an embodiment of the present disclosure.

[0017] Figure 11 Graphs depicting a pair of graphs depicting the chlorination effectiveness parameter Z and EO production rate over time based on the utilization of the NMPC unit with no measured disturbances, according to an embodiment of the present disclosure.

[0018] Figure 12 Graph depicting EO selectivity under unmeasured disturbances based on utilization of an NMPC device according to an embodiment of the present disclosure.

[0019] definition

[0020] All references to the Periodic Table of the Elements herein shall refer to the Periodic Table of the Elements published and copyrighted by CRC Press, Inc. in 2003. In addition, any reference to one or more families shall be to the family or families reflected in this Periodic Table of the Elements using the IUPAC system for numbering families. Unless otherwise stated, implied from the context, or customary in the art, all parts and percentages are by weight. For the purposes of U.S. patent practice, the contents of any patent, patent application, or publication cited herein are incorporated by reference in their entirety (or their equivalent US versions are so incorporated by reference), particularly with respect to disclosure of synthesis techniques, definitions (to the extent consistent with any definitions provided herein), and common knowledge in the art.

[0021] For purposes of U.S. patent practice, the contents of any cited patent, patent application, or publication are incorporated by reference in their entirety (or their equivalent U.S. versions are so incorporated by reference), particularly with respect to definitions (to the extent consistent with any definitions specifically provided in this disclosure) and disclosure of common general knowledge in the art.

[0022] The numerical ranges disclosed herein include all values ​​from and including the lower limit and the upper limit. For ranges containing specific values ​​(e.g., a range from 1 or 2 or 3 to 5 or 6 or 7), any subrange between any two specific values ​​is included (e.g., the above range 1 to 7 includes subranges 1 to 2; 2 to 6; 5 to 7; 3 to 7; 5 to 6; etc.).

[0023] Unless stated to the contrary, implicit from the context, or customary in the art, all parts and percentages are by weight, and all test methods are current as of the filing date of this disclosure.

[0024] The term "composition" as used herein refers to a mixture including the materials of the composition, as well as reaction products and decomposition products formed from the materials of the composition.

[0025] The term "alkylene oxide" as used herein has the following structure A:

[0026]

[0027] wherein R1 and R2 are independently selected from the group consisting of hydrogen and an alkyl group having 1 to 6 carbon atoms. For example, the alkylene oxide may be propylene oxide (R1═CH3, R2═H) or ethylene oxide (R1═R2═H).

[0028] The terms "comprises," "comprising," "having," and their derivatives are not intended to exclude the presence of any additional components, steps, or processes, whether or not specifically disclosed. For the avoidance of any doubt, all compositions claimed through use of the term "comprising" may include any additional additives, adjuvants, or compounds, whether polymeric or otherwise, unless stated to the contrary. In contrast, the term "consisting essentially of excludes from the scope of any subsequently recited component, step, or process, except those that are not essential to operability. The term "consisting of excludes any component, step, or process not specifically recited or recited.

[0029] The term "operably connected" or "operably coupled" includes any two components that, in combination, achieve the desired functionality. Some examples of operable coupling include, but are not limited to, physically manufacturable components, physically interacting components, wirelessly interacting components, wirelessly interacting components, logically interacting components, and / or logically interacting components.

[0030] A "control device" includes any combination of software and / or processing circuitry suitable for controlling the various components described herein, including but not limited to processors, microcontrollers, application specific integrated circuits, programmable gate arrays, and any other digital and / or analog components, and combinations of the foregoing along with inputs and outputs for transmitting and receiving control signals, drive signals, power signals, sensor signals, etc. All such computing devices and environments are intended to fall within the meaning of the terms "control device," "controller," or "processor" as used herein, unless a different meaning is expressly provided or otherwise apparent from the context.

[0031] "Oxirane" is a cyclic ether (epoxide) having the formula C2H4O and structure B below.

[0032] DETAILED DESCRIPTION

[0033] The present disclosure provides a chemical system that utilizes a nonlinear model predictive control (NMPC) device enhanced with an appropriate disturbance model capable of substantially solving a nonlinear constrained optimization problem without formulating an unconstrained control law. The control device provided herein can ensure sufficient robustness for controlling a process at an optimal point (e.g., a "peak") or within a desired or optimal range where the steady-state gain process changes sign. In addition, the control device provided herein manipulates inputs to substantially maintain the process near the peak where steady-state gain reversals occur in the presence of disturbances, rather than operating away from that point to prevent instability.

[0034] Controlling a process with steady-state gain reversal at an optimum point in the presence of measured disturbances can result in frequent sign changes of the steady-state gain and requires appropriate estimation of the disturbance to take appropriate control actions that maximize the control output. Due to significant process disturbances and potential modeling errors, problems may arise in applications where gain reversal is used to control actual industrial processes, thereby increasing the importance of robust solutions. Therefore, the chemical system provided herein can be configured to maximize an output variable having a steady-state gain reversal relative to the manipulated input by using an observed optimized manipulated steady-state input as an occasionally available custom output measurement. The chemical system also implements an input disturbance model that utilizes infrequent custom output measurements to maximize the output variable having a steady-state gain reversal.

[0035] Now refer to Figure 1 , a chemical system 10 capable of producing alkylene oxide includes a reactor 12 according to an embodiment of the present disclosure. An olefin feed stream 14 containing saturated hydrocarbons such as ethane as impurities is combined with an oxygen feed 16 and a gas-phase promoter feed 18 to define a reactor feed stream 20 near the reactor inlet. The reactor product stream 22 comprises the alkylene oxide product plus by-products (such as CO2, H2O and a small amount of saturated hydrocarbons), unreacted olefins, oxygen and inerts. In some commercial processes, the alkylene oxide product, along with a certain water product, can be removed from the reactor product stream 22 in an alkylene oxide recovery unit. If desired, a recycle stream 24 can also be provided to recycle unreacted olefins and oxygen. However, if a recycle stream 24 is implemented, a vent line can be provided to reduce the accumulation of impurities and / or by-products such as argon and ethane. In addition, in some embodiments, the apparatus 10 further includes a carbon dioxide removal step, which is performed upstream of the point where the recycle stream 24 is combined with the fresh feed stream 20 before entering the reactor 12.

[0036] In one embodiment, the olefin provided by the feed stream 14 is ethylene. Additionally or alternatively, in one embodiment, the olefin feed stream 14 may comprise aromatic olefins, diolefins (whether conjugated or not), C2-C 12 α-olefins, and / or C2-C8 α-olefins. The oxygen feed 16 may comprise substantially pure oxygen or air. If pure oxygen is used, a ballast gas or diluent 26, such as nitrogen or methane, may also be included to maintain the oxygen concentration below the maximum level permitted by flammability considerations. The oxygen concentration in the reactor feed stream 20 varies over a wide range, and in practice, flammability is the limiting factor in oxygen concentration.

[0037] When present, the concentration of carbon dioxide in reactor feed stream 20 can adversely affect the efficiency, activity, and / or stability of the catalyst used in reactor 12. Carbon dioxide is produced as a reaction byproduct and is introduced as an impurity along with the other inlet reactant gases. In various commercial ethylene epoxidation processes, at least a portion of the carbon dioxide is continuously removed to control its concentration at an acceptable level during the cycle.

[0038] A vapor-phase promoter is a compound that enhances the efficiency and / or activity of the chemical system 10 for producing the desired alkylene oxide. In one embodiment, the vapor-phase promoter comprises an organic chloride. For example, the vapor-phase promoter is at least one selected from the group consisting of methyl chloride, ethyl chloride, ethylene dichloride, vinyl chloride, and mixtures thereof. In various embodiments, ethyl chloride and ethylene dichloride may be the vapor-phase promoter feed stream 18. Using a chlorocarbon vapor-phase promoter as an example, it is believed that the ability of the promoter to enhance the performance (e.g., efficiency and / or activity) of the chemical system 10 for producing the desired alkylene oxide depends on the extent to which the vapor-phase promoter chlorinates the surface of the catalyst in the reactor 12, for example, by depositing a specific chlorine species, such as atomic chlorine or chloride ions, on the catalyst. However, it is believed that hydrocarbons lacking chlorine atoms strip chlorides from the catalyst and, therefore, detract from the overall performance enhancement provided by the vapor-phase promoter. It is believed that paraffinic compounds, such as ethane or propane, are particularly effective for stripping chlorides from the catalyst. However, it is believed that olefins, such as ethylene and propylene, also serve to strip chlorides from the catalyst. Some of these hydrocarbons may also be introduced as impurities in the ethylene feed stream 12, or may be present for other reasons, such as the use of recycle stream 24. In some embodiments, when present, the ethane concentration in the reactor feed stream 20 is from 0 mole percent to about 2 mole percent. In view of the competing effects of the vapor-phase promoter and the dechlorinated hydrocarbons in the reactor feed stream 20, it is convenient to define an "overall catalyst chlorination effectiveness value," which represents the net effect of the vapor-phase species in chlorinating the catalyst. In the case of an organic chloride vapor-phase promoter, the total catalyst chlorination effectiveness can be defined as a dimensionless quantity, Z, and is represented by the following formula:

[0039]

[0040] wherein the ethyl chloride equivalent is the concentration of ethyl chloride in ppmv (which is equivalent to ppm molar) that provides approximately the same catalyst chlorination effectiveness of the organic chloride present in reactor feed stream 20 at the concentration of the organic chloride in feed stream 20; and the ethane equivalent is the concentration of ethane in mole percent that provides approximately the same catalyst dechlorination effectiveness of the chloride-free hydrocarbons in reactor feed stream 20 at the concentration of the chloride-free hydrocarbons in reactor feed stream 20.

[0041] Although the gaseous chlorine-containing promoter may be supplied as a single species, upon contact with the catalyst, other species may be formed, thereby producing a gaseous mixture. Thus, if the reaction gas is recycled, for example, via recycle stream 24, a mixture of species will be found at the inlet of reactor 12. Specifically, even if only ethyl chloride or ethylene dichloride is supplied to fresh feed stream 20, the recycled reaction gas at the inlet may contain ethyl chloride, vinyl chloride, ethylene dichloride, and / or methyl chloride.

[0042] The order in which the inlet gases (alkylene, oxygen, and ballast gas) are mixed with the gaseous-phase promoter can vary, and the mixing can occur simultaneously or sequentially. The order in which the gaseous components of the process are mixed is selected for reasons of convenience, safety, and / or any other reason. For example, oxygen may be added after the ballast gas for safety reasons. However, in some embodiments, the gaseous-phase promoter should be present in the reactor feed stream 20 because it is introduced into the solid catalyst in the reactor 12.

[0043] Non-limiting examples of suitable reactors for reactor 12 include fixed bed tubular reactors, continuously stirred tank reactors (CSTRs), and fluidized bed reactors. The particular operating mode selected may be dictated by process economics. The epoxidation reaction is exothermic. Therefore, a coolant system 26 (e.g., a cooling water jacket or hydraulic circuit having a coolant fluid such as a heat transfer fluid or boiling water) is provided to regulate the temperature of reactor 12. The reaction temperature is selected to provide the desired yield of ethylene oxide. In one embodiment, the epoxidation reaction is carried out at a temperature of at least 200°C, or at least 210°C, or at least 220°C. In various embodiments, a reaction temperature of no more than 300°C or a reaction temperature of no more than 290°C is implemented. The reactor pressure is selected based on the desired mass velocity and productivity and is in the range of 5 atm (506 kPa) to 30 atm (3.0 MPa). The gas hourly space velocity (GHSV) is greater than 3000 hr -1 , more than 4,000hr -1 or more than 5,000hr -1 .

[0044] Catalysts for the production of alkylene oxides, such as ethylene oxide or propylene oxide, can be prepared by impregnating a suitable support material with a solution of one or more silver compounds, followed by treatment to reduce the silver and deposit it throughout the pores of the support. Typically, the support is impregnated with a catalytic amount of silver, which is any amount of silver capable of catalyzing the oxidation of an alkylene group to the corresponding alkylene oxide with oxygen or an oxygen-containing gas.

[0045] In one embodiment, a plurality of promoters, i.e., materials that, when present, combine with a particular catalytic material such as silver to benefit one or more aspects of catalyst performance or otherwise serve to promote the ability of the catalyst to produce a desired product such as ethylene oxide or propylene oxide. The presence of such promoters in a catalyst has been shown to contribute to one or more beneficial effects on catalyst performance, such as enhancing the rate or amount of production of the desired product, lowering the temperature required to achieve a suitable reaction rate, reducing the rate or amount of undesirable reactions, and the like. Competing reactions occur simultaneously in reactor 12, and a critical factor in determining the effectiveness of the overall process is the control of these competing reactions. A material that is a promoter for the desired reaction can be an inhibitor of another reaction, such as a combustion reaction. Importantly, the effect of the promoter on the overall reaction is beneficial for the efficient production of the desired product, such as ethylene oxide. The concentration of the one or more promoters present in the catalyst varies over a wide range depending on the desired effect on catalyst performance, the other components of the particular catalyst, the physical and chemical properties of the support, and the epoxidation reaction conditions.

[0046] There are at least two types of promoters— solid promoters and gaseous promoters. Solid and / or gaseous promoters are provided in a promoting amount. A "promoting amount" of a component of a catalyst refers to the amount of the component that is effective to provide one or more improvements in catalytic properties to the catalyst as compared to the catalyst without the component. Examples of catalytic properties include operability (resistance to runaway), efficiency, activity, conversion, stability, and yield. One skilled in the art will appreciate that one or more individual catalytic properties can be enhanced by a "promoting amount," while other catalytic properties can or can not be enhanced or can even be reduced. It will be further appreciated that different catalytic properties can be enhanced under different operating conditions. For example, a catalyst that is enhanced in efficiency under one set of operating conditions can be operated under a different set of conditions that show an improvement in activity rather than an improvement in efficiency, and an operator of an ethylene oxide plant will intentionally vary the operating conditions in order to take advantage of certain catalytic properties even at the expense of other catalytic properties in order to maximize benefits by taking into account feedstock costs, energy costs, byproduct removal costs, and the like.

[0047] The promoting effect provided by a promoter can be influenced by several variables, such as reaction conditions, catalyst preparation techniques, surface area and pore structure of the support, and surface chemical properties, silver and co-promoter content of the catalyst, the presence of other cations, and the anions present on the catalyst. The presence of other activators, stabilizers, promoters, enhancers, or other catalyst promoters can also influence the promoting effect.

[0048] The performance of the epoxidation process is evaluated during the process based on the activity of the selectivity, catalyst and / or the stability of the operation. Selectivity is the mole fraction of converted olefins that produces the desired olefin oxide. In some cases, in the production of ethylene oxide, the operator of the chemical system 10 will believe that, in the absence of constraints, in order to maximize selectivity, it will have to utilize higher ethylene, higher oxygen and lower CO2 content. However, due to the steady-state gain reversal characteristics of some processes, if the catalyst is operated at high temperatures and the temperature is reduced, a selectivity gain will be observed. But as the temperature further decreases, the degree of the selectivity gain becomes smaller, and then eventually reaches the selectivity maximum. As the temperature further decreases, the selectivity also decreases.

[0049] In one embodiment, the chemical system 10 described herein can be used in an open-loop or closed-loop process that maintains the process at or near an optimal point during operation of the apparatus 10. In both processes, a control device 28 is used to adjust one or more inputs. For example, a control device 28 is provided that receives inputs from an effluent concentration analyzer 30 operably coupled to the reactor outlet stream 22, a reactor feed concentration analyzer 32 operably coupled to the feed stream 20, an olefin feed flowmeter 34 downstream of the olefin feed stream 14, a vapor-phase promoter feed flowmeter 36 downstream of the vapor-phase promoter feed stream 18, and a flowmeter 38 operably coupled to the coolant system 26. The control device 28 is implemented in a computerized control system and also includes a central processing unit and memory, as well as outputs for ultimately adjusting control valves that adjust the inputs. Based on the received inputs, the control device 28 determines the mole percentage of alkylene oxide in the reactor effluent in the reactor stream 22 and a vapor-phase promoter effectiveness parameter (e.g., Z) for the reactor feed stream 20.

[0050] For ethylene oxide production, the vapor-phase promoter is one or more chlorinated hydrocarbons. Therefore, the control unit 28 also receives concentration data for chlorinated hydrocarbons, such as ethyl chloride, vinyl chloride, and ethylene dichloride, as well as the concentrations of ethylene, ethane, and other non-chlorinated hydrocarbons in the reactor feed stream 20 from the analyzer 32. The concentration data is then used to calculate the total chlorination effectiveness (e.g., Z). The control unit 28 also receives a user-input set point for the mole percentage of alkylene oxide in the reactor effluent in the reactor outlet stream 22 and / or the yield of alkylene oxide. Based on the user-input set point and the data from the analyzer 30, the control unit 28 determines whether the concentration of alkylene oxide and / or the yield of alkylene oxide in the reactor outlet stream 22 is within a predetermined range of the user-input set point. When the alkylene oxide concentration and / or yield is outside the predetermined range, the control unit 28 adjusts the reaction temperature or flow rate of the vapor-phase promoter (to change the value of the vapor-phase promoter effectiveness parameter) and / or any other variable inputs.

[0051] A control device 28 is provided to regulate the olefin concentration in the reactor feed stream 20. In the illustrated embodiment, the control device 28 receives composition data indicating the amount of olefins in the reactor feed stream 20 from an analyzer 32. The control device 28, which has a user-input set point for the olefin concentration in the reactor feed stream 20, receives flow data from a flow meter 34 and manipulates a control valve fluidly coupled to the olefin feed stream 12 to control its flow. The control device 28 can be analog or digital and implemented in a computerized distributed control system. The control scheme illustrated is merely exemplary and is not intended to limit the scope of the present disclosure.

[0052] refer to Figure 2 In order to achieve the goals of stability and maximum profitability for the chemical system, the control device 28 has various modules, including a model 42 of the chemical system 10, a state estimator 44 configured to simulate the operation of the chemical system 10 to predict the operation of the chemical system 10, a steady-state calculator 46 that operates to determine the optimal control input for operating the chemical system 10, and / or a regulator 48 configured to regulate the chemical system 10 based on the optimal control input. The "model," "state estimator," "calculator," and / or "regulator" described in this specification have been labeled as modules to more specifically emphasize their implementation independence. For example, a module can be implemented as a hardware circuit comprising a custom VLSI circuit or gate array, an off-the-shelf semiconductor such as a logic chip, a transistor, or other discrete components. A module can also be implemented as a programmable hardware device, such as a field programmable gate array, programmable array logic, a programmable logic device, or the like.

[0053] Modules may also be implemented in software for execution by various types of processors. An identified module of executable code may, for example, comprise one or more physical or logical blocks of computer instructions, which may, for example, be organized as objects, procedures, or functions. However, the executable code of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations that, when logically joined together, comprise the module and achieve the module's stated purpose.

[0054] A module of executable code may be a single instruction or many instructions, and may even be distributed across several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and described herein within a module, and may be implemented in a suitable form and organized within a suitable type of data structure. The operational data may be collected as a single data set, or may be distributed across different locations, including across different memory devices, and may exist, at least in part, solely as electronic signals on a system or network.

[0055] In one embodiment, a control device 28 of the chemical system 10 is configured to control the operation of the chemical system, wherein the control device receives inputs indicating operating parameters of the chemical system and receives output variables, and provides control inputs to the chemical system in response to the inputs and output variables for controlling and optimizing the operation of the chemical system. In various embodiments, the control device 28 is configured as an NMPC device 28 and provides values ​​for control inputs u (or input variables) of the device 10 capable of implementing a controllable chemical process. In one embodiment, an external unmeasured input disturbance d and / or a measured disturbance m are provided to the device. In response to receiving the control input u, the input disturbance d, and / or the measured disturbance m, the device 10 generates an output Y, which includes various output disturbances P1 and P2. The output Y is fed to a state estimator 44.

[0056] Model 42 may be defined by nonlinear and / or linear equations between at least one input and at least one output and operates in parallel with device 10. Nonlinear model 42 is a mathematical model of various processes of device 10 that provides predictive outputs similar to device 10 when each is supplied with the same input u. In various embodiments, model 42 includes at least one of a steady-state model, a dynamic model, an adaptive model, a fuzzy model, and / or a neural network model.

[0057] In one embodiment, the model 42 characterizes the dynamic and steady-state responses of the outputs in the chemical system 10 to the inputs received by the chemical system. In various embodiments, the nonlinear model 42 receives the manipulated input u and the estimated input disturbance In response, the model 42 generates a predicted output At the same time, the output interference estimation factored. Thus, the model 42 of the chemical system 10 can be designed to accurately depict the operation of the chemical system 10 and its control structure. To this end, the model 42 solves nonlinear problems and, therefore, can be computationally demanding due to the large number of calculations required for each output calculation. However, in practice, the model 42 should quickly obtain estimated outputs while taking into account the operating costs of the chemical system 10. Therefore, one of the control objectives may include optimizing (i.e., minimizing) operating costs, rather than simply optimizing operations.

[0058] In one embodiment, an input disturbance model is used in conjunction with first-order dynamics for maximizing the output variable y1 that exhibits a steady-state gain reversal relative to the control input u. The input disturbance model is based on using the steady-state control input that can be the optimal steady-state control output as a custom output measure that can occasionally be used to determine the location of the optimized control input in the presence of measured and unmeasured disturbances. The steady-state nonlinear model equation can be expressed as:

[0059]

[0060] where u ss is the steady-state control input, m is the measured disturbance, and is the steady-state control output. The output variable with steady-state gain inversion is labeled y1, along with various operating limits y2 that occasionally become effective constraints. The steady-state nonlinear model 42 has a relative gain of y1 with respect to the control input u ss For output The quadratic change, which has relative to the maximization u at the peak ss Used for The sign of the steady-state gain changes, as Figure 3 . In other embodiments, any other mathematical function may be used to determine the defined target range for a chemical process or operation. First-order kinetics with different steady-state gains and time constants may be used to define the effects of inputs u and m on outputs y1 and y2. Thus, in one embodiment, the steady-state nonlinear model 42 (Equations (2) and (3)) together with the first-order kinetics may constitute the process model 42.

[0061] In embodiments incorporating NMPC, optimal control is not guaranteed, so the disturbance model may represent process disturbances along with plant model mismatch and also take into account the control objective. For processes with steady-state gain inversion where the control objective is to maximize the output variable y1 at a peak or within a desired range of the peak, it may be important to robustly locate the corresponding value of the control input in the presence of disturbances and potential modeling errors. In one embodiment, the control device 28 is configured to estimate unmeasured disturbances that shift the location of the optimal peak at which steady-state gain inversion occurs. In various embodiments, the unmeasured disturbances may include catalytic aging of the reactor or associated over / under performance. An output disturbance model for the output variable y1 may not give the location of the optimal steady-state control input u that depends on the input or state disturbance. An input disturbance model for the control input u that uses the error of the output variable y1 may also need to know whether the process is on the positive gain portion or the negative gain portion of the steady-state variation curve that is plotted at the control input u. Figure 3 50 and 52, respectively, separated by a peak 54. Identification of a positive or negative gain near peak 54 is problematic for maximizing the output variable y1 with noisy data, which is common in various industrial processes. The control output is maximized The best steady-state control input The position of depends on the measured disturbance m and the unmeasured disturbance, such that

[0062]

[0063] Optimal steady-state control input is introduced as a custom output measurement y3, which is occasionally available in the steady-state process model 42 (Equations (2) and (3)). The enhanced steady-state nonlinear model 42 equations can be expressed as:

[0064]

[0065] Under stable conditions, for The expected optimal value can be observed when the control device 28 settles during the time t s and for optimal steady-state control input The model 42 for the operating limit y2 that becomes effective occasionally is linear and independent of the optimal steady-state control input u is input towards the optimal steady-state control under the stable conditions for m The settling time t of the control device 28 s Movement within, such as Figure 4 As shown in the figure, it can cause the output variable y1 to increase unless the optimal steady-state control input The position of has changed and needs to be corrected by the input disturbance model 42. When a new peak 54 for the expected optimum value is observed under stable conditions for the measured disturbance m, as Figure 3 As shown in the figure, the input disturbance model is used to consider the optimal steady-state control input Various algorithms or models can be used to calculate the actual position of the data at the control device 28 during the settling time t s After meeting all the following criteria, the The optimal steady-state control input is updated based on the observation of the new peak value 54 Or the position mismatch of the steady-state output measurement y3:

[0066] 1. The control input u can be used to maximize the main output y1 instead of being constrained by the operating limit y2;

[0067] 2. The measured disturbance m is stable according to defined statistical criteria;

[0068] 3. The control input u is stable or moving towards the optimal steady-state control input Move; and

[0069] 4. Targeting optimal steady-state control input A new optimal position is observed, which is because the output variable y1 is within the settling time t of the control device. s Then decrease.

[0070] A steady-state statistical criterion is defined for the measured disturbance m by checking its standard deviation against appropriate limits during the settling time of the control device 28. For example, the standard deviation is calculated as follows:

[0071] σ m =δ (9)

[0072] In one embodiment, data filtering and screening is implemented for the noisy output measurement y. For example, a digital filter is implemented with the control device 28 to filter the noise and includes an amplitude filter to limit signal spikes and frequency jumps and / or a low-pass filter to remove high-order noise-related frequencies from the signal that can adversely affect the calculation speed of the control device 28.

[0073] In an embodiment implementing the state-space model 42, the discretized state-space model 42 (Equations (6), (7), and (8)) for the steady-state nonlinear model 42 with first-order dynamics at the control device frequency k can be expressed as:

[0074]

[0075] Where y1 is the maximized output variable with steady-state gain inversion, y2 is controlled within safe operating limits, and y3 denotes the optimal steady-state control input to maximize the output variable y1 For some device operations, the manipulated input u can be used to maximize the output variable y1 via a variable function, see Figure 1 Some of the variable functions are described. Thus, the reinforced state-space model can be written as:

[0076] X k+1 =F(X k ,u k ,m k ) (16),

[0077] Y k+1 =X k+1 17

[0078] Where X = [x1, x2, x3] denotes the state of the model 42 and Y = [y1, y2, y3] denotes the output measurement.

[0079] Further references Figure 3 In one embodiment, the control device 28 , along with instructions stored in a memory of the control device 28 , may be configured to optimize the output variable y 1 at a peak value 54 where a steady-state gain reversal occurs with respect to the control input u.

[0080] In some embodiments, the plant model mismatch may be attributable to a disturbance in the output measurement rather than an input or process in the NMPC of the control device 28. Instructions stored in the memory of the control device 28 are for implementing an input disturbance model based on a custom output measurement, such as the custom output measurement defined herein, to account for the position mismatch of the optimal control input u in the presence of measured disturbances and unmeasured disturbances. In order for the control device 28 to utilize the output measurement in the enhanced state space formulation (Equations (16) and (17)), the control device 28 includes a state estimator 44 configured to simulate the operation of the chemical system 10 to predict the operation of the chemical system 10 based on the characterization of the chemical system 10 by the model 42. For example, in one embodiment, the state estimator 44 is configured to utilize the custom output measurement to estimate the unmeasured disturbance entering the process and thereby predict the operation of the chemical system based on the characterization of the chemical system by the model 42.

[0081] In one embodiment, the state estimator 44 may include an input disturbance model that incorporates the input from the optimal steady-state control input. The optimal steady-state control input is denoted as the occasionally observed output measurement y3. In one embodiment, the optimal steady-state control input is calculated by assigning the difference between the observed and predicted values ​​as the input disturbance d for the control input u according to the following relationship Or make corrections by observing the output measurement y3:

[0082]

[0083] in is an estimate of the input disturbance based on the output prediction error in y3 at the sampling time or control device frequency k. The above correction (Equation (18)) can be made occasionally, for example only when the control device 28 settles during the time t s When all criteria for observing the new steady-state optimum y3 are met, as defined above. In embodiments where the estimate of the input disturbance remains the same, the new optimal steady-state control input Or the observed output measurement y3 is absent of correction, and therefore:

[0084]

[0085] To update the predictions of the state estimator 44, the fractional deviation α of the observed error in the output measurement y2 is used as a constant output disturbance p̂2 to update the model 42. The fractional deviation is calculated as:

[0086]

[0087] In operation, the output disturbance model is used to incorporate feedback from the maximized output variable y1 to obtain a state estimate at the control device frequency k. The state for the output variable y1 is and output interference The estimate of can then be obtained using an extended Kalman filter for the nonlinear model 42 together with an input disturbance estimate at the sampling time or control device frequency k. And obtain, as follows:

[0088]

[0089] The filters outlined above can then be used to provide feedback for updating the state estimates for X and p1. The entire filter is time-varying due to the infrequent availability of measurement updates for the output measurement y3. In one embodiment, the time-varying system can be reformulated as a time-invariant lifting system to obtain the filter gain.

[0090] In one embodiment, the steady-state calculator 46 operates to determine an optimized control input for operating the chemical system 10 based on the characterization of the chemical system 10 by the model and one or more steady-state output variables of the chemical system 10. In some cases, the calculator 46 may be configured to output Y ss In one embodiment, the nonlinear steady-state target calculator 46 is configured to determine steady-state control inputs for operating the chemical system based on the characterization of the chemical system as calculated by the model. ss , enter u ss and state X ss The steady-state calculator 46 may use a nonlinear program to evaluate the output to minimize its corresponding set point The deviation of the input and its current value At high infeasibility values, the choice of The set point of the output variable to promote its maximization at the peak 54 where steady-state gain inversion occurs. The nonlinear target tracking optimization problem can then be written as follows:

[0091]

[0092] where Q S and S s is a positive definite weight matrix.

[0093] The reinforced output disturbance vector is denoted as P, and d is the input disturbance. The control constraints for model 42 can be expressed as follows:

[0094]

[0095] The above formulation considers the effects of the measured disturbance m and the constant disturbance on the input d and output p. During operation, in one embodiment, the input constraints are always satisfied, while the output constraints are ranked in terms of importance and satisfied based on the assigned relative priorities. Furthermore, in one embodiment, the new optimal steady-state control input is only satisfied when a new optimal steady-state control input is observed for the steady-state condition. The input interference estimate is updated only when the output measurement y3 is Instead, the output disturbance P may be estimated at each control device execution based on the deviation in the output measurements y1 and y2. However, it should be understood that the output disturbance P may be estimated at any other control device execution period or frequency without departing from the teachings provided herein.

[0096] Further references Figure 3 , the control device 28 also includes a regulator 48, which is configured to provide a signal for regulating one or more inputs of the chemical system 10 based on the optimized control input and the associated output target. The signal is configured to actuate a control valve to control the flow of fresh olefin feed, the set point of the oxygen feed, the set point of the gas phase promoter feed and / or the control device 28 for actuating any other variable input. In one embodiment, the control device 28 can be applied to the chemical system 10 as a supervisory control device 28, that is, the NMPC control device 28 does not directly control the process, but provides a set point to a slave control device such as a linear model predictive control device ("LMPC") or a proportional integral derivative ("PID") control device. In this control structure, the NMPC control device 28 is in supervisory mode and provides a set point to a lower-level LMPC or PID control device. In response, the chemical system 10 is adjusted directly by the PID control device according to the set point assigned by the NMPC control device 28. In other embodiments, a three-stage cascade control structure may be utilized, wherein the NMPC control unit 28 functions as a dynamic real-time optimizer (RTO). The NMPC control unit 28 calculates optimal values ​​for the independent variables at different operating points against a plurality of constraints. These values ​​are passed to the auxiliary control unit as external targets. The auxiliary control unit then determines how to move the set point relative to these external targets and provides the next set point movement to the PID control unit. The PID control unit directly controls the manipulated variable of the system and adjusts the system's manipulated variable to the set point assigned by the auxiliary control unit. In addition, the manipulated input may include at least one of a steady-state production rate, a steady-state chlorination effectiveness parameter (Z), or a steady-state ethylene oxide (EO) selectivity.

[0097] In one embodiment, the dynamic regulator 48 can be expressed as the following open-loop nonlinear objective function:

[0098]

[0099] where Q and S are positive definite weighting matrices, N is the output range, and M is the input range. Thus, the control constraints for optimization of the process are defined using the output measurements up to time k by the predictions of the states and outputs, where the constraints are defined as follows:

[0100]

[0101] For the processes described herein, consider the input and output constraints of the following form:

[0102]

[0103] In one embodiment, the input constraints are satisfied all the time for dynamic adjustment. On the other hand, the output constraints can be ordered in terms of importance and satisfied based on priority. The vector of future open loop control moves (u k ...u k+M ) is computed from equation (27), and the first input value is injected into the plant via control of one or more variable inputs. This process can be repeated at any desired subsequent time interval, with feedback using plant measurements to update the state estimates.

[0104] The control device 28 utilizes the optimal steady state manipulated input as an additional infrequent output measurement for updating the input disturbance estimate. The control output is maximized The location of the optimal steady state manipulated input (equation (4)) depends on the measured disturbance m and can be used to update the input disturbance estimate. Due to the associated input multiplicity, accurate identification of the input disturbance is problematic in the case of direct use of y1. Thus, robust identification of the input multiplicity can be important for the control device 28, which has the goal of remaining at or near the peak 54 of the process with steady state gain inversion with noisy industrial data as measurements. It is also conceivable that the chemical system 10 and / or control device 28 described herein can also be used for a process that exhibits steady state gain inversion at a minimum, not a maximum, with a control objective of minimizing, for example, operating costs at the valley.

[0105] In one embodiment, the control device 28 described herein is used in an industrial ethylene epoxidation reactor 12 to maximize selectivity for ethylene oxide production in the reactor. Compared to manually optimizing selectivity, the closed loop control device 28 yields significant commercial value by achieving an average gain of 0.5% to 1% on EO selectivity.

[0106] Without limitation, by way of example, some embodiments of the present disclosure are described in detail in the following Examples.

[0107] Examples

[0108] A control device for a chemical system implementing a process with steady-state gain reversal is applied to maximize selectivity for the reaction of ethylene oxide (EO). Ethylene oxide is produced using a silver-based catalyst for the selective oxidation of ethylene to ethylene oxide, thereby minimizing secondary reactions that reduce ethylene oxide (EO) selectivity. With conventional catalysts, EO selectivity does not reach values ​​above 85.7%, which has long been considered the theoretical maximum selectivity for the following overall reaction:

[0109] 7C2H4 + 6O2 → 6C2H4O + 2CO2 + 2H2O (33).

[0110] Some industrial ethylene epoxidation reactors use a co-fed chlorination promoter that adsorbs onto the catalyst to modify the EO by promoting or moderating certain reaction pathways and thereby increasing the selective oxidation of ethylene oxide. Highly efficient industrial catalysts tend to exhibit a relatively steep parabolic curve for EO selectivity as a function of effective gas-phase chloride concentration, which can be measured as the dimensionless chlorination effectiveness parameter, Z. An empirical steady-state model gives EO selectivity EO sel It is related to the partial pressure dependent chlorination effectiveness parameter Z. The location of the peak or optimum EO selectivity is also a strong function of the reaction temperature used to control the EO production rate.

[0111] The goal of the feedback control device is to control the production rate EO by prod The chlorination effectiveness parameter Z is manipulated to maximize the EO selectivity under the interference of the inlet oxygen concentration iO2 sel As an example, for ethyl chloride flow EC flow The process operating limits are ranked to maximize EO selectivity over EO sel More importantly, the process operating limits can limit EO selectivity under extreme conditions. sel The EO selectivity relative to Z is maximized. sel The location of the peak where the maximum value is reached and the steady-state gain changes sign depends on the measured disturbances and the unmeasured disturbances. Unmeasured disturbances including over / under performance of the catalyst also affect the location of the peak compared to the prediction of catalyst age. Figure 4 The EO selectivity relative to Z at different production rates is shown in sel Before implementing the control apparatus provided herein, a steady-state nonlinear process model is used to calculate an open-loop target for Z, and based on the observed EO selectivity EO sel Perform the calibration manually.

[0112] A validated empirical steady-state model is used along with first-order dynamics to capture information from the process output measurements. First-order dynamics with varying steady-state gains (multipliers ranging from 1 to 10) and time constants (multipliers ranging from 1 to 2) are used to define the effects of the inputs u and m on the output y. The steady-state nonlinear model (Equations (6), (7), and (8)) has the following variables:

[0113] u=[Z] (34),

[0114] m=[EO prod ,iO2] (35),

[0115]

[0116] where u is the control input, m is the measured disturbance, and Y is the control output. is the optimal steady-state value of the control input Z that maximizes EO under stable conditions sel and used as the custom measurement y3. The steady-state nonlinear model for output Y is calculated as:

[0117]

[0118] Among them, EO prod The measured interference m is measured in lb / hr and iO2 is expressed as a percentage. sel With first-order kinetics, the EO production rate is prod The EC flow With first-order kinetics, the EO production rate is prod There is no dead time and a time constant of 2 hours. sel and EC flow The time constant of EO production rate EO prod And change. is the steady-state value of the optimal value Z and has no time-varying dynamics.

[0119] The discretized state space model is calculated at the frequencies provided in equations (16) and (17) together with the validated empirical steady state model and used by the control device 28 to maximize the EO selectivity EO sel or the maximized output variable y1. Hierarchical control is used as the primary control device in which NMPC is implemented, which maximizes EO selectivity by manipulating the chlorination effectiveness parameter Z, which is adjusted by a faster auxiliary PID control device.

[0120] The primary control device of the NMPC is used to maximize EO selectivity by manipulating the chlorination effectiveness parameter Z every 15 minutes.sel The slower execution time for the primary control device is sufficient because the model for EO selectivity has a long settling time and is also desirable due to the higher computational demands of the associated dynamic optimization problem. sel The NMPC model is nonlinear and has a long settling time of 6 to 12 hours depending on the EO production rate. The NMPC model is tuned appropriately to obtain the desired control action. The control objectives for the NMPC model are ordered so that the EC for ethyl chloride flow flow Or the operating limit of y2 is the most important, then maximize EO sel Or the output variable y1 is maximized, as summarized in Table 1.

[0121] Table 1

[0122]

[0123] These rankings are performed both during steady-state target optimization (Equation (23)) and during dynamic regulation (Equation (27)). Limitations on operating limits y2 or output measurements y3 have no effect on normal plant operation, thereby allowing maximization of EO selectivity EO sel Or by maximizing the output variable y1. EO Selectivity EO sel The maximization of is achieved by giving it an extremely high, infeasible target. Table 2 shows the operating limits of the manipulation inputs for the chlorination effectiveness parameter Z and the output y.

[0124] Table 2

[0125]

[0126] The limits on movement of the manipulated input to the chlorination effectiveness parameter Z used for dynamic adjustment (Equation (32)) are small enough to prevent it from moving faster than the underlying process and process control can respond.

[0127] For the control device, the input range M is set to three hours and the output range N is set to 12 hours (Equation (27)). Output Q, Q s and its expected value The quadratic loss of the deviation is set to its nominal value to obtain the same relative value for each output (Equations (23) and (27)), so that:

[0128]

[0129] After considering the upper and lower operating limits presented in Table 2 that can be calculated for the steady-state targets of the optimization function and dynamic regulation (Equations (23) and (27)), a quadratic penalty with respect to the rate of change of the control input for the chlorination effectiveness parameter Z(S) is set for the steady-state target calculation, such that

[0130] S=0.025 (40).

[0131] The movement is implemented by passing the movement for the chlorination effectiveness parameter Z as a target to the auxiliary LMPC or PID control device, which controls the ethyl chloride flow EC by manipulating the ethyl chloride flow EC per second. flow The chlorination effectiveness parameter Z is controlled by rejecting faster interferences.

[0132] Appropriate data screening and filtering is performed on the noisy EO selectivity measurement y. Erroneous analyzer data due to poor measurement analysis can provide inappropriate values ​​of calculated EO selectivity to the control device. sel The analyzer data was checked against validity limits prior to calculation to ensure appropriate feedback.

[0133] In operation, Figure 5 and Figure 6 Baseline plant data demonstrating the use of operating rules to manage EO selectivity prior to implementation of the NMPC control unit is shown in FIG. As shown, even though the production rate is reduced from time = 2400 minutes to time = 3500 minutes, selectivity does not consistently increase because the chlorination effectiveness parameter Z is not properly adjusted. Additionally, selectivity decreases around time = 3800 minutes due to the increase in production rate at time = 3600 minutes. The higher chlorination effectiveness parameter Z helps achieve higher selectivity at time = 5500 minutes due to the open-loop implementation. However, due to the delays and limitations associated with the open-loop implementation for targeting the chlorination effectiveness parameter Z, EO selectivity EO sel There are losses.

[0134] In contrast, the use of the NMPC control described herein is more effective in maximizing EO selectivity than the legacy control scheme that uses a steady-state nonlinear process model to calculate an open-loop target for the chlorination effectiveness parameter Z. sel , resulting in an average gain in selectivity of 0.5% to 1% for industrial processes. The NMPC application maximizes EO selectivity based on three scenarios: sel , the scenario includes:

[0135] 1. EO selectivity control at high EO production rates;

[0136] 2. EO selectivity control at increasing EO production rates; and

[0137] 3. EO selective control for large unmeasured disturbances.

[0138] In the above three scenarios, the EC for ethyl chloride flow flow The limit is wide and does not become an effective constraint, so the chlorination effectiveness parameter Z can be used to determine the EO selectivity. sel maximization.

[0139] Figure 7 Demonstrates how to maximize EO selectivity by manipulating the chlorination effectiveness parameter Z at high EO production rates sel And make it fluctuate around the optimal value, such as Figure 8 The inlet oxygen concentration remains relatively constant during the time period. The final chlorination effectiveness parameter Z value is small because the optimal value is for maximizing EO selectivity. sel The fluctuation around the optimum value due to the input disturbance model ensures EO selectivity. sel maximization of effectiveness.

[0140] When the rate of the ethyl epoxidation reactor is increased from a low production rate to a higher production rate, the control device is still in use, such as Figure 9 The control input for the chlorination effectiveness parameter Z increases with the EO production rate over three days, as shown in Figure 10 As shown in , this is because it is used to selectively convert EO sel The optimum value which is kept maximized is gradually increased.In addition, the inlet oxygen concentration remains relatively constant during the time period.

[0141] exist Figure 11 and Figure 12 In the example shown in FIG, even though the actual chlorination effectiveness parameter Z has not changed, at time = 200 minutes one of the measuring analyzers is exchanged for the backup analyzer, resulting in a decrease in the measured chlorination effectiveness parameter Z. Therefore, the control device 28 increases the EC flow responds by increasing the measured chlorination effectiveness parameter Z, which can result in higher chlorination and selective EO sel When this is detected by the control device 28, the chlorination effectiveness parameter Z starts to decrease at time = 400 minutes to compensate for the overchlorination, thereby producing a higher EO selectivity EO sel The chlorination effectiveness parameter Z stops decreasing at around time = 1750 minutes, and stabilizes and swings around the optimal value to reduce the EO selectivity. selAppropriate data filtering criteria have been added to detect analyzer swapping and allow for recalibration to prevent associated unmeasured disturbances for various implementations of the control device.

[0142] It is specifically intended that the present disclosure is not limited to the embodiments and descriptions contained herein, but rather encompasses modifications of those embodiments including portions of the embodiments and combinations of elements of different embodiments occurring within the scope of the appended claims.

Claims

1. A chemical system for operation exhibiting steady-state gain inversion; the system comprising: a reactor feed stream comprising: an olefin feed stream comprising saturated hydrocarbons, oxygen feed, and Gas phase accelerator feed; a reactor configured to receive the reactor feed stream and produce an outlet stream to form a process, the outlet stream comprising alkylene oxide; as well as a control device configured to control the process, wherein the control device receives an input indicative of an operating parameter and receives an output variable and, in response to the input and the output variable, provides a steady-state manipulative input configured to control or optimize the process, the control device comprising: an input disturbance model based on using the steady-state control input as a custom output measurement to determine an unmeasured disturbance, a state estimator configured to utilize the custom output measurements to estimate the unmeasured disturbances entering the process and thereby predict changes to the process based on the characterization of the process by the input disturbance model, a nonlinear steady-state target calculator configured to determine the steady-state manipulative input for the process based on the representation of the process as calculated by the input disturbance model, and a regulator configured to provide a signal for regulating one or more inputs based on the steady-state manipulated input and the associated output variable, Wherein if the control input for maximizing the variable output is within an operating threshold, the regulator determines a change in the control input for optimizing the output variable based on observation of a gain reversal during a settling time of the control device, one or more measured disturbances are stable because the control input is stable or moving toward an optimal steady-state control input based on statistical criteria, and a new optimal optimized control input is observed after the settling time of the control device. 2 . The chemical system of claim 1 , wherein the calculator is configured to determine an optimal range for the steady-state maneuver input.

3. The chemical system of claim 1, wherein the input disturbance model comprises at least one of a basic first principles model, an empirical model, an adaptive model, a fuzzy model, or a neural network model with dynamics.

4. The chemical system of claim 1 , wherein the control device maximizes the output variable that exhibits a steady-state gain inversion with respect to the manipulated input (u) via the following relationship: where u ss is the steady-state control input, m is the measured disturbance, and is the output variable that exhibits steady-state gain inversion.

5. The chemical system of claim 1 , wherein the control device comprises a nonlinear model predictive control (NMPC) device as a primary controller to address real-time computational needs, and a linear model predictive controller (LMPC) or a proportional-integral-derivative (PID) controller for executing one or more moves of the nonlinear model predictive control (NMPC).

6. The chemical system of claim 1 , wherein the control device is configured to estimate the unmeasured disturbances that shift the position of the optimal peak where steady-state gain reversal occurs, the unmeasured disturbances comprising catalytic aging and associated over / under performance of the reactor.

7. The chemical system of claim 1, wherein the manipulation input comprises at least one of a steady-state production rate, a steady-state chlorination effectiveness parameter, or a steady-state ethylene oxide (EO) selectivity.

8. The chemical system of claim 1, wherein the output variable is intermittently maximized by using an output disturbance model in conjunction with a highly infeasible target for the calculator and the regulator.

9. The chemical system of claim 1, wherein the manipulation input comprises at least one of a chlorination effectiveness parameter (Z) or an ethylene oxide (EO) production rate to control ethylene oxide (EO) selectivity.

10. The chemical system of claim 1, wherein the control device is configured to optimize effluent ethylene oxide (EO) selectivity in the reactor.

11. A method for controlling a chemical system via a control device, the method comprising: combining an olefin feed stream comprising saturated hydrocarbons, an oxygen feed, and a vapor phase promoter feed to form a reactor feed stream; receiving the reactor feed stream in a reactor and producing an outlet stream to form a process, the outlet stream comprising alkylene oxide; receiving an input indicative of an operating parameter of the process and receiving a steady-state output variable; implementing an input disturbance model based on using an optimal maneuvering steady-state input as a customized output measure to determine an optimized maneuvering input in the presence of both a measured disturbance and an unmeasured disturbance; estimating a state of the process to predict the process based on the characterization of the process by the input disturbance model; determining a directed manipulative input for the process based on the characterization of the process and an estimate of one or more steady-state output variables of the chemical system through modeling; as well as The process is regulated based on the directional control input, wherein if the control input for maximizing the variable output is within an operating threshold, the regulator determines a change in the control input for optimizing the output variable based on observation of a gain reversal within a settling time of the control device, one or more measured disturbances are stable because the control input is stable or moving toward an optimal steady-state control input based on statistical criteria, and a new optimal optimized control input is observed after the settling time of the control device.

12. The method of claim 11, wherein adjusting the chemical system based on the optimization manipulation input comprises manipulating at least one of a chlorination effectiveness parameter (Z) or an ethylene oxide (EO) production rate to control ethylene oxide (EO) selectivity.

13. The method of claim 11, wherein adjusting the chemical system based on the optimized steering input comprises maximizing a steady-state gain reversal near a value where a sign change indicates a change from an increase in selectivity to a decrease in selectivity.

14. The method of claim 11, wherein adjusting the chemical system is configured to optimize effluent ethylene oxide (EO) selectivity in an epoxidation reactor.

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