A dry-type electric dust removal control method and system for a thermal power unit based on integral time delay DOB

Abstract

The present application belongs to the field of energy saving and environmental protection operation of coal-fired units and industrial process control, and discloses a dry-type electric dust removal control method and system for thermal power units based on integral time delay DOB, wherein the secondary current set value of the first three electric fields is determined through static test, a step test is performed on the last-stage fourth and fifth electric fields, and an integral first-order plus pure lag transfer function model of the secondary current to the outlet smoke dust concentration is identified; a normalized model and an independent outer loop are constructed with the nominal time delay as the scale, the relationship between the phase margin, the normalized gain cross frequency and the scaling parameters of the PD controller is established according to the target relative time delay margin, and the optimal PD parameters are obtained in the stable feasible region; the allowable range of the low-pass filter time constant is determined based on the DOB closed-loop characteristic equation containing uncertain time delay, and the target filter parameters are determined in coordination. The present application improves the response performance, anti-disturbance ability and time delay robustness of the outlet smoke dust concentration control, and is suitable for the last-stage electric field control of the dry-type electric dust remover of thermal power units.

Description

Technical Field

[0001] This invention relates to the field of energy-saving and environmentally friendly operation and industrial process control technology of coal-fired power units, and to high-frequency power supply regulation of the final stage electric field of dry electrostatic precipitators, outlet dust concentration modeling, time-delay robust control and disturbance compensation, specifically a control method and system for dry electrostatic precipitators of thermal power units based on integral time-delay DOB (Disturbance Observer). Background Technology

[0002] In actual operation of coal-fired power plants, the concentration of flue gas dust at the outlet is mainly changed by adjusting the secondary voltage or current of the rectifier transformer in the dust collector. For dry electrostatic precipitators with a multi-field structure, each field is assigned a corresponding dust removal load. However, generally, there is only one turbidity meter at the main exhaust port of the dust collector, making it very difficult to achieve precise control of each field in the dry electrostatic precipitator. One solution is to treat multiple fields as a whole for control, that is, to control the outlet dust concentration by simultaneously adjusting the secondary current of the high-frequency power supply of all fields. However, due to the large structure of the electrostatic precipitator, the process of simultaneously changing the power supply parameters of all fields to adjust the outlet dust concentration will have significant inertia, bringing additional difficulties to the implementation of the controller. In addition, the dust removal load borne by each field is inconsistent. From an energy-saving perspective, most of the dust in the flue gas is generally removed in the front-stage field of the dust collector, that is, most of the dust removal capacity of the dust collector is placed in the front-stage field, while the final-stage field achieves precise regulation of the outlet dust through closed-loop feedback control. Therefore, most current dry electrostatic precipitator control systems in coal-fired power plants adopt a collaborative control framework consisting of load feedforward and closed-loop feedback.

[0003] However, from a control-oriented design perspective, the controlled objects in each stage of the dust removal process exhibit the following characteristics, making the establishment of an effective closed-loop automatic control system challenging. First, the controlled object model in each stage of the dust removal process is a typical process with significant time delays and high variability. Due to the material transport and signal transmission stages involved in dust removal, the dynamic response of the output variable exhibits a significant lag compared to the signal changes of the input variable. Furthermore, in most coal-fired power units, pollutant concentration measurements are only performed at the chimney outlet, meaning there is a considerable measurement lag between the implementation of control and the measurement of the corresponding pollutant concentration change. Second, the dynamic inertia time span of the controlled object model in each stage of the dust removal process is large. Because the dust removal process involves physical processes, when a fixed amount is changed in the input variable, the corresponding output variable will only reach steady state after a certain reaction time (inertia time). Finally, the internal dynamic model of each stage of the dust removal process exhibits significant uncertainties and external unknown disturbances. Numerous uncertainties exist in the flue gas parameters and physical processes, leading to significant parameter variations and nonlinearities in the dynamic characteristics of the controlled object in the dust removal process.

[0004] For the controlled processes exhibiting large inertia and pure time delay characteristics, proportional-integral-derivative (PID) control, load feedforward control, or current correction strategies based on empirical rules are commonly used in engineering. These methods have limited adaptability to model changes, nonlinear processes, and unknown external disturbances. Aggressive control parameter settings can easily lead to outlet concentration oscillations, frequent secondary current actions, and high-voltage power supply output fluctuations; while conservative settings result in slow regulation and difficulty in timely suppressing emission deviations caused by sudden changes in dust load. Although Data Obligation (DOB) can be used to estimate model mismatch and external disturbances, its design typically does not fully consider the interaction with the external loop controller in terms of time-delay robustness, making it difficult to balance tracking speed and disturbance rejection robustness.

[0005] In summary, existing dry electrostatic precipitator (ESP) control methods struggle to simultaneously address factors such as outlet dust concentration tracking speed, unknown disturbance suppression capability, measurement noise attenuation capability, and stability under time-delay conditions. Therefore, constructing a closed-loop control system that combines high-performance tracking with robust disturbance rejection for the controlled process of the final-stage electric field in dry ESPs, which exhibits significant time-delay characteristics, is a pressing technical challenge. Summary of the Invention

[0006] (a) Purpose of the invention To address the shortcomings of existing technologies, this invention provides a dry electrostatic precipitator control method and system for thermal power units based on integral time-delay (DOB). By identifying the dynamic response between the secondary current of the final-stage electric field and the outlet dust concentration, an integral first-order plus time-delay product model is established, and the external controller parameters are determined based on the time-delay robustness index. Simultaneously, based on the closed-loop stability boundary under uncertain time-delay conditions, low-pass filter parameters for the disturbance observer are designed to estimate and compensate for lumped disturbances caused by changes in flue gas operating conditions, model mismatch, and unknown external disturbances. This achieves stable regulation of the secondary current of the high-frequency power supply in the final-stage electric field, improves the tracking performance, disturbance rejection capability, and time-delay robustness of the outlet dust concentration control, and reduces the impact of measurement noise and frequent control actions on system operation.

[0007] (II) Technical Solution To achieve the objective of this invention and solve its technical problems, the present invention adopts the following technical solution: In a first aspect, the present invention provides a control method for dry electrostatic precipitators in thermal power units based on integral time-delay (DOB), used to control the secondary current of the final stage electric field of the dry electrostatic precipitator to achieve closed-loop control of the outlet dust concentration, comprising at least the following steps: SS1. Modeling and Identification: The setpoints of the secondary currents of the first three electric fields are determined through static experiments. A step experiment is conducted on the secondary currents of the fourth and fifth electric fields of the final stage to obtain the step response data of the outlet dust concentration. The integral first-order plus pure time delay transfer function model from the secondary current to the outlet dust concentration is identified. SS2. Control Structure and Model Scaling: Based on the transfer function model, a two-degree-of-freedom control structure including an external PD controller and an internal DOB low-pass filter is constructed. The transfer function model is scaled with nominal time delay as the scale to obtain a normalized model. The independent outer loops that do not include DOB compensation are extracted. SS3. External Loop Controller Design: Set the target relative time delay margin for the external loop, establish the relationship between phase margin, normalized gain crossover frequency and PD controller scaling parameters, determine the stable feasible region, and obtain the optimal normalized gain crossover frequency by maximizing the generalized proportional gain to obtain the PD controller parameters; SS4. Inner Loop Stability Boundary Design: Based on Transfer Function Model G p The relative order of (s) determines the structure of the DOB low-pass filter. Based on the PD controller parameters, the closed-loop characteristic equation of DOB with uncertain time delay is established. The minimum critical time delay is obtained, and the allowable range of the time constant of the DOB low-pass filter is determined according to the condition that the minimum critical time delay is greater than the nominal time delay. SS5. Coordination and parameter setting of internal and external loops: Keep the PD controller parameters unchanged, adjust the DOB low-pass filter time constant within the allowable range, and determine the target DOB low-pass filter time constant based on the relationship between the relative time delay margin of the closed-loop system after adding DOB compensation and the target relative time delay margin.

[0008] Preferably, in step SS1, static calibration of the first three electric fields, step test of the final electric field, and identification of the transfer function model are performed under multiple typical unit loads to obtain the combination of secondary currents of the first three electric fields and the integral first-order plus pure time-delay transfer function model corresponding to each typical unit load, and to establish the multi-condition correspondence between the unit load, the combination of secondary currents of the first three electric fields, and the transfer function model; during the operation of the thermal power unit, the corresponding combination of secondary currents of the first three electric fields and the transfer function model are called according to the load range to which the current unit load belongs, wherein the combination of secondary currents of the first three electric fields is used for feedforward power supply control of the front-stage electric field, and the transfer function model is used for closed-loop control of the final electric field.

[0009] Furthermore, in step SS1, when using DOB to estimate and compensate for the disturbance of model parameter changes under different unit loads, a representative unit load is selected from multiple typical unit loads. Under the representative unit load, a final-stage electric field step test is performed, and the nominal transfer function model G is identified. p,0(s) The nominal transfer function model is used for the final-stage electric field closed-loop control under the load of the remaining units; for the qth actual unit load, the actual controlled object G is... p,q (s) relative to the nominal transfer function model G p,0 (s) dynamic deviation The lumped disturbance observed by DOB is included, where U(s) is the control input corresponding to the equivalent secondary current of the final stage electric field.

[0010] Preferably, in step SS3, let α1 be... The solution in the interval (π / 2, π) is the generalized differential gain. satisfy For the selected generalized differential gain Let α2 be The solution lies within the interval (0, α1); then the generalized proportional gain... satisfy α1 is the normalized angular frequency corresponding to the stability boundary of the generalized differential gain, and α2 is the normalized angular frequency corresponding to the stability boundary of the generalized proportional gain under the given generalized differential gain condition.

[0011] Preferably, in step SS3, when the high-frequency noise in the outlet dust concentration detection signal exceeds a preset noise level or the differential action causes frequent changes in the secondary current of the final-stage electric field, the generalized differential gain is set to... Maintain relative time lag margin r dm Unchanged, with optimal normalized gain crossover frequency Initial value solution for numerical solution The normalized gain crossover frequency corresponding to the pure proportional control form is obtained, and the proportional gain of the pure proportional controller is determined according to the generalized proportional gain expression.

[0012] Preferably, the method further includes step SS6 for implementing lumped disturbance estimation and control quantity synthesis, obtaining the outlet dust concentration setpoint R(s) and the measured outlet dust concentration Y(s), calculating the concentration deviation; inputting the concentration deviation into an external PD controller, and according to... Generate the fundamental control quantity U of the final stage electric field c (s); nominal transfer function model Decomposed into P n + (s), These represent the stable invertible minimum-phase and non-minimum-phase components of the nominal model, respectively; and the lumped perturbation estimate after processing with a DOB low-pass filter. according to Obtain, and in accordance with Will As a disturbance compensation, it is superimposed on the basic control quantity U in the opposite direction to the lumped disturbance. c (s) forms a secondary current control quantity applied to the controlled object in the final electric field.

[0013] Preferably, it further includes step SS7 for implementing the final-stage electric field execution and feedback update, distributing the secondary current control increment ΔI(t) of the final-stage electric field according to the fourth electric field distribution coefficient λ4 and the fifth electric field distribution coefficient λ5, where λ4≥0, λ5≥0 and λ4+λ5=1; according to , Generate secondary current commands I for the fourth and fifth electric fields respectively. 4,cmd I 5,cmd I 4,0 and I 5,0 These are the reference secondary currents I and I corresponding to the electric field. 4,min I 4,max I 5,min and I 5,max These represent the lower and upper limits of the secondary current allowed by the corresponding high-frequency power supply, respectively, with sat indicating the amplitude limiting operation; the corresponding high-frequency power supply is controlled to adjust the actual secondary current, and the concentration deviation calculation, lumped disturbance estimation, disturbance compensation, and secondary current adjustment are repeatedly performed based on the updated measured value of the outlet dust concentration.

[0014] The second objective of this invention is to provide a dry electrostatic precipitator control system for thermal power units based on integral time-delay (DOB), comprising at least: The data acquisition and model identification module is used to collect the unit load, secondary current of each electric field and outlet dust concentration, determine the set value of the secondary current of the first three electric fields, and identify the integral first-order plus pure time delay transfer function model with the average value of the secondary current of the fourth and fifth electric fields as input and the outlet dust concentration as output. The control structure and model scaling module is used to construct a two-degree-of-freedom control structure containing an external PD controller and an internal DOB low-pass filter based on the transfer function model, obtain a normalized model using the nominal time delay as the scale, and extract the independent outer loop that does not include DOB compensation. The external loop controller design module is used to set the target relative time delay margin for the independent external loop, establish the relationship between phase margin, normalized gain cross frequency and PD controller scaling parameters, determine the stable feasible region, and obtain the optimal normalized gain cross frequency and PD controller parameters by maximizing the generalized proportional gain. The inner loop stability boundary design module is used to determine the DOB low-pass filter structure based on the relative order of the transfer function model, establish the DOB closed-loop characteristic equation with uncertain time delay, obtain the minimum critical time delay ratio, and determine the allowable range of the DOB low-pass filter time constant. The coordination parameter setting module is used to keep the PD controller parameters unchanged, adjust the DOB low-pass filter time constant within the allowable range, determine the target DOB low-pass filter time constant based on the relationship between the relative time delay margin of the closed-loop system after adding DOB compensation and the target relative time delay margin, and configure the PD controller parameters and the target DOB low-pass filter time constant in the final stage electric field controller.

[0015] (III) Technical Effects Compared with the prior art, the dry electrostatic precipitator control method and system for thermal power units based on integral time delay (DOB) provided by the present invention has the following beneficial effects: (1) This invention establishes an integral first-order plus pure time delay model from the secondary current to the outlet dust concentration by static calibration of the first three electric fields and step identification of the fourth and fifth electric fields of the last stage. It also uses a nominal time delay unified model and controller parameter scale to obtain a quantifiable characterization of the long time delay, integral accumulation and operating condition change characteristics of the last stage electric field, providing a stable model basis for determining control parameters under wide load conditions.

[0016] (2) This invention uses relative time delay margin as the design constraint of the outer loop, establishes the correspondence between phase margin, normalized gain cross frequency and PD scaling parameters, and maximizes the generalized proportional gain within the stable feasible region, taking into account response speed, stability margin and noise suppression, and reducing concentration oscillation, control sluggishness and frequent operation of high frequency power supply caused by parameter empirical tuning.

[0017] (3) The present invention determines the allowable range of the low-pass filter time constant based on the DOB closed-loop characteristic equation with uncertain time delay, and coordinates the selection of target filter parameters while keeping the PD parameters unchanged, so that model mismatch, load change and external disturbance can be estimated and compensated, while maintaining the robustness of closed-loop time delay, thereby improving the control accuracy, anti-disturbance ability and operation stability of the outlet dust concentration. Attached Figure Description

[0018] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood in conjunction with the following description of the embodiments, in which: Figure 1 This is a flowchart of the dry electrostatic precipitator control method for thermal power units based on integral time delay (DOB) of the present invention. Figure 2 This is a diagram of the architecture of the dry electrostatic precipitator control system for thermal power units in this invention. Figure 3 This is a schematic diagram of the dry electrostatic precipitator structure in this invention; Figure 4 This is a schematic diagram of the front-stage feedforward power supply and the final-stage closed-loop regulation framework of a five-field dry electrostatic precipitator for a 1000MW coal-fired power unit. Figure 5A schematic diagram of a two-degree-of-freedom anti-interference control structure consisting of an external PD controller and an internal DOB; Figure 6 For the external PD controller with respect to the actual proportional gain k p and actual differential gain k d A schematic diagram of the stable region is drawn; Figure 7 For the external PD controller with respect to the normalized gain crossover frequency v c and phase margin A schematic diagram of the stable feasible region is shown. Figure 8 For function F l (A) and F r (A) A graph showing the change of intermediate variable A; Figure 9 For optimal generalized proportional gain Regarding the relative time lag margin r dm Distribution diagram; Figure 10 Maximum sensitivity function of independent external loop A schematic diagram illustrating the distribution of relative time delay margin; Figure 11 For the PD controller r dm Schematic diagram of minimum critical time delay distribution of DOB control at =2; Figure 12 For different normalized DOB filter time constants, the closed-loop transfer function from perturbation to outlet dust concentration Bode plot of amplitude characteristics.

[0019] Explanation of reference numerals in the attached diagram: #1, #2, #3, #4, and #5 represent the first, second, third, fourth, and fifth electric fields, respectively; C(s) represents the external PD controller; C f (s) represents the external PD controller after configuring the second-order filtering stage; Q(s) represents the DOB low-pass filter; G p (s) represents the actual controlled object; P n (s) represents the nominal transfer function model; P n + (s) represents the minimum phase component in the nominal transfer function model that can be stably inverted; The following modules are listed: 10 - Non-minimum phase part of the nominal transfer function model; 20 - Data acquisition and model identification module; 30 - Control structure and model scaling module; 40 - External loop controller design module; 50 - Internal loop stability boundary design module; 60 - Coordination parameter setting module; 61 - Final stage electric field controller; 62 - Lumped disturbance estimation and control quantity synthesis unit; 70 - Final stage electric field command allocation and feedback update unit; 80 - Fourth electric field high-frequency power supply; 90 - Fifth electric field high-frequency power supply; 100 - Outlet dust concentration detection device; 110 - Unit load signal interface; 110 - Electric field secondary current acquisition interface. Detailed Implementation

[0020] This invention aims to provide a method and system for controlling dry electrostatic precipitators in thermal power units based on integral time-delay (DOB). To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below with reference to the accompanying drawings. The described embodiments are some, but not all, embodiments of this invention, and are exemplary, intended to explain the invention, and should not be construed as limiting the invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0021] It should be noted that the disturbance observer in this embodiment is abbreviated as DOB. Unless otherwise specified, the final electric field refers to the fourth and fifth electric fields; the first three electric fields refer to the first, second, and third electric fields; the secondary current refers to the secondary current on the output side of the high-frequency power supply corresponding to the electric field; and the outlet dust concentration refers to the dust mass concentration measured at the outlet of the main flue of the dry electrostatic precipitator.

[0022] Example 1: Control method for dry electrostatic precipitators in thermal power units like Figure 1 As shown, this embodiment of the invention provides a dry electrostatic precipitator control method for thermal power units based on integral time-delay (DOB). Generally, a dry electrostatic precipitator has multiple electric fields arranged sequentially along the flue gas flow direction; this embodiment uses a conventional five-field structure for illustration. The structure of the electrostatic precipitator in this embodiment is as follows: Figure 3 As shown, taking a 1000MW coal-fired power unit as an example, typical operating conditions generally include 980MW, 850MW, 750MW, and 650MW. The environmental emission requirements for the unit are... The flue gas flows sequentially through electric fields #1, #2, #3, #4, and #5. The first three electric fields are used to handle the main dust removal load, and their secondary current setpoints are obtained through static tests and adjusted according to the unit load. The fourth and fifth electric fields are used to implement closed-loop regulation of the outlet dust concentration to compensate for the effects caused by changes in unit load, inlet dust concentration, flue gas flow rate, dust resistivity, rapping status, and model parameters.

[0023] Taking the dry electrostatic precipitator of a 1000MW unit in a coal-fired power plant as an example, a control test was conducted. The overall control is as follows: Figure 4 As shown. To compensate for the inertia in the dry electrostatic precipitator process and remove most of the dust, a rough open-loop control of the first three electric fields is first established by creating an approximate relationship between the inlet flue gas dust concentration and the unit load, such as through neural network-based optimization. Based on this feedforward action, a closed-loop control system is then established using the two final electric fields to achieve precise control of the outlet flue gas dust concentration, while simultaneously compensating for the insufficient adjustment capability of a single electric field. Under this structure, external disturbances and uncertainties in the dry electrostatic precipitator process are mainly suppressed through closed-loop feedback; therefore, the design of the feedback controller is crucial for the precise adjustment of the outlet flue gas dust concentration of the dry electrostatic precipitator. Based on this composite control framework, the time-delay DOB closed-loop feedback control system studied in this invention is implemented. Based on this control system, the dry electrostatic precipitator control method for thermal power units of this invention mainly includes steps SS1~SS5, and preferably includes steps SS6~SS7.

[0024] Specifically, step SS1 is mainly used to obtain the integral first-order plus pure time delay transfer function model; SS2 is used to establish the two-degree-of-freedom control structure, normalization model, and the stable feasible region of the external PD controller; SS3 is used to obtain the optimal PD controller parameters under a given relative time delay margin constraint; SS4 is used to determine the stable parameter range of the DOB low-pass filter; and SS5 is used to coordinate the determination of the external PD controller parameters and the target DOB filter time constant. Furthermore, step SS6 is used to implement lumped disturbance estimation and control quantity synthesis, and SS7 is used to implement final-stage electric field execution and feedback update. The specific implementation process of each step is as follows: SS1. Dynamic modeling and identification of the final stage electric field: The setpoints of the secondary currents of the first three electric fields of the dry electrostatic precipitator for coal-fired power units were determined through static tests. A step test was then conducted on the secondary currents of the fourth and fifth electric fields of the final stage to obtain step response data for the outlet dust concentration. Subsequently, transfer function identification was performed, resulting in an integral first-order plus pure time-delay transfer function model representing the transition from the secondary current to the outlet dust concentration. The specific steps include the following: S1.1: Static calibration of the first three electric fields Before modeling the dynamic step response of the final-stage electric field, the secondary current setpoints for the first three electric fields need to be determined through static tests under typical unit loads. The general steps of the static test are as follows: The first step is to configure the initial power supply: adjust the secondary current of the high-frequency power supply of the last two electric fields to the minimum limit of the corresponding high-frequency power supply's allowable adjustment range, while setting the secondary current of the first three electric fields to an initial setting value that can handle the main dust removal load.

[0025] The second step is the stepped adjustment of the pre-stage current: Under relatively stable conditions of unit load, combustion status, and inlet flue gas conditions, the secondary current values ​​of the high-frequency power supplies of the first three electric fields are reduced in a stepped manner according to a preset gradient. This means the output reduction of the first three electric fields of the dry electrostatic precipitator follows a stepped pattern, maximizing the output of the pre-stage electric fields to achieve energy savings. A preset stabilization time is maintained after each adjustment, and the outlet dust concentration is recorded once the rate of change in outlet dust concentration enters the preset stable range.

[0026] The third step is to determine the critical current combination: when the dust concentration at the outlet of the dry electrostatic precipitator rises to near the limit by reducing the secondary current of the first three electric fields, stop reducing the secondary current of the first three electric fields and record the combination of the secondary currents of the first, second and third electric fields.

[0027] The fourth step is to repeat the above steps after the coal-fired unit changes load. The combination of secondary currents of the first three electric fields under wide load is statistically analyzed to obtain the correspondence between the set values ​​of the secondary currents of the first three electric fields and the unit load within the wide load range.

[0028] For a 1000MW coal-fired power unit, the outlet dust concentration limit for a dry electrostatic precipitator is typically 35 mg / Nm³. 3 Based on the above static tests, an approximate relationship between the unit load and the secondary currents of the first three electric fields can be obtained, and the feedforward regulation effect of the first three electric fields can be established accordingly. The focus of this invention is on the closed-loop feedback control studied in the design of the last two electric fields. The feedforward power supply control of the first three electric fields is mainly used to determine the stable power supply conditions of the first stage on which the dynamic test and closed-loop operation of the last stage electric field depend. The subsequent dynamic step response test of the last stage electric field is carried out on the basis of the above static tests.

[0029] S1.2: Step test of the final stage electric field When conducting a step response dynamic test on the final stage electric field, a typical unit load is selected as the dynamic test condition. During the step test, the unit load and the secondary current setpoints of the first three electric fields corresponding to this typical unit load are kept constant. The secondary currents of the fourth and fifth electric fields are respectively increased by a preset step amplitude from their pre-step steady-state values. The two electric fields can be changed synchronously at the same step moment so that their average secondary current forms a clear step input. The step amplitude should be determined within the allowable adjustment range of the high-frequency power supply and should be able to produce a identifiable response to the outlet dust concentration, while avoiding continuous spark discharge or significant back corona. The secondary currents of the fourth and fifth electric fields and the outlet dust concentration are synchronously collected according to a unified sampling sequence to form an input-output response sequence including pre-step steady-state data, step change data, and post-step response data. The sampling duration should cover the process of the outlet dust concentration starting to respond, major dynamic changes, and entering a new steady state. The collected data is time-aligned, and abnormal sampling points that are communication interrupted, instrument malfunctions, or significantly exceed reasonable ranges are removed. For noise in smoke and dust concentration measurement, low-pass processing or moving average processing that does not change the main step dynamic characteristics can be used.

[0030] This embodiment employs an Integrator First-Order Plus Time Delay (IFPTD) model to model the transfer function of the final-stage electric field dynamics. This model reflects the integral accumulation, dynamic inertia, and pure time delay characteristics caused by changes in the secondary current, including dust charging, migration, collection, flue gas transport, and outlet dust detection. The input to this transfer function is the average value of the secondary currents of the high-frequency power supply in electric fields 4 and 5, while the output is the outlet dust concentration of the dry electrostatic precipitator. When the control system has high model requirements, dynamic tests typically require obtaining transfer function models under various typical operating conditions of the unit, similar to the aforementioned static test process, and using these models to establish multimodal control logic to adapt to the wide-load operation of the unit.

[0031] When the control system requires high model accuracy, static calibration, step tests, and model identification can be performed under operating conditions of 980 MW, 850 MW, 750 MW, and 650 MW, respectively, and a multi-condition model group can be established. M i For the model group corresponding to the i-th typical working condition, P i For typical unit load, I 123,i For the corresponding combination of the secondary currents of the first three electric fields, K i and L 0,i These represent the object gain, time constant, and nominal time delay under this operating condition. During operation, the corresponding combination of the first three electric field secondary currents and the transfer function model are invoked based on the load range to which the current unit load belongs.

[0032] S1.3: Transfer Function Model Identification In this embodiment, the arithmetic mean of the secondary currents I4 and I5 of the fourth electric field is used as the equivalent secondary current u = (I4 + I5) / 2 of the final stage electric field. The equivalent secondary current u of the final stage electric field is used as the model input, and the outlet dust concentration y is used as the model output (for this embodiment, y(t) = ρ op (t). Based on the input-output response sequence obtained from the step test, the transfer function model is identified as shown in the following equation: (1-1) Among them, G p (s) is the integral first-order plus pure time delay transfer function model of the equivalent secondary current of the final stage electric field to the outlet dust concentration; K is the object gain of the controlled object under the nominal operating condition; T is the time constant; L0 is the nominal time delay; s is the Laplace complex frequency domain variable.

[0033] Under a representative 980 MW unit load, the secondary currents of the fourth and fifth electric fields were increased by a preset step amplitude to obtain step response data for the outlet dust concentration. K, T, and L0 were then estimated using a system identification toolbox or a numerical identification program with similar functionality. The identification results were verified by the response fit, residual distribution, and the deviation between the model output and the measured output.

[0034] When using a representative operating condition nominal model, the model identified under the 980 MW operating condition is denoted as G. p,0 (s), for the q-th actual unit load, the actual controlled object G p,q (s) relative to the nominal transfer function model G p,0 The dynamic deviation of (s) can be expressed as: U(s) is the control input corresponding to the equivalent secondary current of the final stage electric field. The dynamic deviation, along with changes in coal type, inlet dust concentration, flue gas parameters, and other external disturbances, serves as the lumped disturbance estimation object for the internal DOB.

[0035] SS2. Control structure, model normalization, and stable feasible region of the outer loop: Based on the transfer function model G p (s) A two-degree-of-freedom control structure including an external PD controller and an internal DOB low-pass filter is constructed. The transfer function model is scaled using the nominal time delay as the scale to obtain a normalized model, and the independent outer loop without considering DOB compensation is extracted. Specifically, in this embodiment, under the independent outer loop of the DOB control system, the gain design of the PD controller is carried out considering the time delay robustness index, and the index and the stability domain of the parameters are derived.

[0036] S2.1: Two-degree-of-freedom control structure and model normalization This invention studies a two-degree-of-freedom control structure for integral time-delay processes, as follows: Figure 5 As shown, the system includes an outlet dust concentration setpoint tracking channel and a lumped disturbance compensation channel. The external PD controller is located in the outlet dust concentration setpoint tracking channel, and the internal DOB is located in the lumped disturbance compensation channel. This represents the main controller, i.e., the PD controller for the external loop. The shaded area in the diagram is the DOB, which contains... Represented as The filter is typically a stable unity-gain low-pass filter with a DC gain of 1, and its type is usually selected using the binomial coefficient method. The controlled integral time delay process is denoted as... Its nominal model The minimum phase part is denoted as The non-minimum phase part is denoted as Nominal transfer function model It can be decomposed into: When designing an external PD controller, the lumped disturbance compensation channel is first excluded from the frequency domain analysis of the independent external loop, thus separating the setpoint tracking performance from the lumped disturbance suppression performance. For the transfer function (1-1), when time-delay robustness needs to be considered, the following normalized model with scaling parameters provides a more intuitive analysis: (2-1) in, , For normalized complex frequency domain variables with nominal time delay L0 as the time scale, Let τ be the normalized object gain and τ be the time scale ratio. Subsequent controller analysis and design will revolve around the regularized integral time delay process described in (2-1).

[0037] S2.2: PD controller parameter scaling and relative time delay margin The PD controller is used as the external loop controller of the control system, i.e., the feedback controller, according to the normalized complex frequency domain variables. Its form under parameter scaling conditions is: (2-2) in, , , For scaling gain, To scale the differential gain, k is the normalized differential time constant. p k d τ dThese represent the proportional gain, differential gain, and differential time constant at the actual time scale.

[0038] For a unit step setpoint, under the conditions of closed-loop stability and the object containing an integral element, a PD controller can make the setpoint tracking steady-state error approach zero. The final value of the nominal closed-loop output is: (2-3) Furthermore, the derivative action of the PD controller can provide phase lead to mitigate phase lag caused by the integral stage and pure time delay. (Based on a normalized model) After parameter scaling, the open-loop frequency response of the external PD controller, independent external loop, is: (2-4) Where v is the normalized angular frequency. Let the intersection of the open-loop frequency response and the unit circle satisfy: (2-5) Among them, v c The normalized gain crossover frequency, The phase margin is expressed in radians, and equation (2-5) also represents... and Substituting equation (2-5) into equation (2-4), we obtain a system of linear equations concerning the scaling PD controller parameters: (2-6) It can be observed that the above equations can be viewed as a system of linear equations concerning the PD controller gain parameters, where the parameters include frequency domain robustness indicators and model information. Solving this system using the corresponding linear transform domain yields the formula for the PD controller gain: (2-7) in This represents the generalized controller gain based on the scaling parameter. The differential time constant in the corresponding scaling form can then be solved as: (2-8) Unlike PD controllers derived from traditional internal model control principles or direct synthesis methods, the above expression (2-7) does not perform any low-frequency approximation of the time delay term of the controlled model. Therefore, the tuning rule we propose is very helpful for the accurate design of the time delay margin.

[0039] The ratio of phase margin to gain crossover frequency can be defined as time delay margin, which represents the maximum time delay range that closed-loop stability can tolerate. Since the time delay term has been normalized according to different models, the following relative time delay margin is used as the required time delay robustness metric: , , (2-9) Where, ω c L is the actual gain crossover frequency; m The maximum additional pure time delay that an independent external loop can tolerate before reaching the stability boundary from the nominal steady state; r dm This is the ratio of the maximum additional pure time delay to the nominal time delay. In summary, the design of a PD controller with time delay robustness constraints can be expressed by combining equations (2-7) and (2-9). We will further analyze the closed-loop stability of the system and the optimal tracking problem with time delay robustness constraints based on the proposed tuning rules.

[0040] S2.3: Stable Feasibility Domain of External PD Controller The characteristic equation of the anti-interference control closed loop combining PD and DOB in this invention is as follows: (2-10) Under nominal conditions, i.e. Under the given conditions, the nominal form of the above closed-loop characteristic equation is... It can be further simplified to: (2-11) It can be observed that the closed-loop stability under the independent framework based on PD control simultaneously corresponds to the nominal stability of the studied two-degree-of-freedom anti-interference control system. In other words, the nominal stability of the system is determined by the PD controller. For time-delay processes, the parameter stability region of the PID controller can typically be determined by traversing the frequency domain. The range of mapping parameters is used to determine this. This invention provides a decisive indicator from another perspective. The stability boundary related to the PD controller gain.

[0041] For the integral time-delay process under study, it is first necessary to clarify that a necessary condition for the PD controller to ensure the closed-loop stability of the system is that the generalized proportional gain must be satisfied. Expanding the closed-loop characteristic equation under the above nominal conditions, we can obtain: (2-12) According to this closed-loop characteristic equation, if the generalized proportional gain If the value is less than 0, the closed-loop characteristic equation of the system will have roots on the imaginary axis or in the right half-plane, leading to system instability. Therefore, to ensure the stability of the closed-loop system, it is essential to first ensure that the generalized proportional gain is non-negative. For real-world applications with inverse control characteristics, the direction of action of the PD controller should be configured to ensure... The condition is met.

[0042] The closed stable feasible region for normalized gain crossover frequency and phase margin satisfies: (2-13) The actual controller parameters are selected within this closed region, i.e., satisfying:

[0043] Furthermore, let α1 be... The solution in the interval (π / 2, π) guarantees the generalized differential gain of the PD controller for a stable integral time-delay process. The scope is as follows: (2-14) in It is an equation In the interval The solution within the given constraint range (2-14). The generalized differential gain within the given constraint range. The generalized proportional gain of the PD controller that ensures closed-loop stability The scope is as follows: (2-15) in It is an equation In the interval solution within.

[0044] α1 is the normalized angular frequency corresponding to the stability boundary of the generalized differential gain, and α2 is the normalized angular frequency corresponding to the stability boundary of the generalized proportional gain given the generalized differential gain.

[0045] To more intuitively illustrate the stability region of the PD controller described above for the integral time-delay process, the IFPTD model is used. To specifically describe the stable region of the combined variables involved, that is... and The area. In Figure 6 and Figure 7 The diagram illustrates the stability region of the PD controller designed for this specific controlled object, and plots the stability region at a relative time delay margin of [value missing]. The robust region profile and the robustness boundary represented by phase margin are shown to further demonstrate the rationality of the derived stability range. It can be observed that the distribution trends of the stability boundary and robustness index differ under different variable frameworks. Furthermore, the relative time delay margin... It can represent the overall robustness of the system to a certain extent, and is more flexible than using phase margin to represent time-delay robustness, which is commonly used in previous studies. In the subsequent optimal tracking study and analysis, we will further reveal that the relative time-delay margin shows a consistent trend with the overall robustness when representing system robustness. It is important to note that... Figure 6The controller gain has been converted from a scaling form to a concrete gain form to provide intuitive guidance for nominal stability analysis and parameter tuning.

[0046] SS3. Optimization of external PD controller parameters under relative time delay margin constraints: For the target relative time delay margin of the external loop, the relationship between phase margin, normalized gain crossover frequency, and PD controller scaling parameters is established to determine the stable feasible region. The optimal normalized gain crossover frequency is obtained by maximizing the generalized proportional gain, thus obtaining the PD controller parameters. The parameter tuning of the PD controller is transformed into an optimization problem within the stable region, thereby achieving optimal tracking under time delay robust constraints.

[0047] S3.1: Maximum Generalized Scale Gain Problem Larger generalized proportional gain It can achieve faster tracking response, but it may also introduce weaker robustness and even compromise the closed-loop stability of the system. Smaller... This would have the opposite effect. This invention considers the idea of ​​maximum proportional gain optimization for integral time-delay processes based on relative time-delay margin constraints, that is, given a relative time-delay margin r... dm Under the constraints, the tuning of the external PD controller parameters is transformed into a maximum generalized proportional gain problem within the stable feasible region, which is specifically expressed as: (3-1) This means that the proposed optimization aims to achieve a certain level of robustness against time delays. Find the maximum generalized proportional gain .according to The phase margin in equation (3-1) Replace with Generalized proportional gain can be obtained. Regarding gain crossover frequency expression In other words, if a relative time delay margin is specified in advance, then the optimization task becomes the optimization of that relative time delay margin. The following scope of regulations Found inside The maximum value of v. c ′ Corresponding to The positive real solutions. Based on this boundary condition, we can obtain the following at the endpoints of the interval: Furthermore, the aforementioned S2.3 has already indicated... The nonnegativity of , therefore in the interval Memory in a maximum This maximum value can be analyzed. Regarding vc first derivative The distribution of the roots is used to determine this. The corresponding stationary point equation for the maximum value of the generalized proportional gain is: (3-2) S3.2: Uniqueness of the Optimal Normalized Gain Crossover Frequency To analyze whether the root of the above expression lies in the interval The distribution within is first transformed into the following form: (3-3) The intermediate variable in the formula is Define the left and right sides of equation (3-3) as functions of the intermediate variable. Then we can find The distribution of the roots corresponds to the distribution of these two functions in the interval The number of intersections. It is the critical v c The critical variable corresponding to ′ has a range of Due to the function In its form, it is in The interval is monotonically decreasing, and the asymptote is... Based on this property, in Figure 8 The text shows two functions in the interval... The curve in the image.

[0048] It is worth noting that, according to the aforementioned analysis, in the interval Memory in a maximum ,therefore In the interval There exists at least one solution, indicating that the two curves intersect at least once. (The following is a definition / rule:) Let's consider the intersection point: First: :at this time In the interval There is only one intersection point and that intersection point satisfies And the corresponding function value satisfies .

[0049] second: :at this time In the interval There is only one intersection point and that intersection point satisfies And the corresponding function value satisfies .

[0050] third: :at this time In the interval There is only one intersection point and that intersection point satisfies And the corresponding function value satisfies .

[0051] fourth: :at this time In the interval There is only one intersection point and that intersection point satisfies And the corresponding function value satisfies .

[0052] In summary, the two functions intersect at only one point within the specified interval. That is, the first derivative of the generalized proportional gain... In terms of the interval There is always only one solution. Therefore, the optimal tracking problem (3-1) based on time-delay robustness constraints can be transformed into tracking within a specified relative time-delay margin. Below, in the interval The unique solution to equation (3-2) is found using numerical methods. The problem can be solved directly using Newton's iteration method, the bisection method, or other numerical methods.

[0053] S3.3: Optimal PD controller parameter recovery According to equations (2-7) and (3-2), if the model of the controlled integral time-delay process is obtained, then the unique robustness at a certain specified level can be determined. The optimal PD controller under constraints. The unique solution of the stationary point equation within the feasible interval is determined as the optimal normalized gain crossover frequency. and in accordance with , , , Obtain the optimal scaling PD controller parameters. and They are respectively and The corresponding optimal generalized proportional gain and optimal generalized differential gain. According to , , , Restore the optimal controller parameters at the actual time scale.

[0054] By adjusting the value of the relative time lag margin From 1 to 3, Figure 9 and Figure 10 The optimal The resulting maximum sensitivity function, which is the comprehensive robustness index under the single-loop framework. In the model's time constant Relative to 1 to 4 The distribution of . Figure 9 and Figure 10 Both trends indicate that the trade-off between the robustness of the control system to model uncertainty and control performance can also be measured by time-delay robustness, i.e., relative time-delay margin. To reflect. Larger. This indicates a more robust system, while providing a smaller optimal value. This results in a slower tracking response.

[0055] For integral time-delay processes with minimal phase lag and high noise attenuation requirements, the derivative action introduces frequent control movements. In such cases, a system with the same level of time-delay robustness can be used. A pure proportional P controller can be used to replace the PD controller. Furthermore, the optimal gain crossover frequency can be utilized. As a solution At a certain time-delay robustness level Down The initial value is used to calculate the corresponding gain crossover frequency.

[0056] S3.4: Second-order filter of PD controller In practical applications, to avoid excessive control action at the initial moment of the step response and to attenuate noise generated during output signal measurement, a filter is usually added to the ideal derivative action in PID control. In this invention, to maintain the integrity of design formula (2-7), the filter of the PD controller is separated from the individual derivative action, thus obtaining the following complete main controller form: (3-4) From this formula, it can be seen that the measured noise passes through a circuit with a damping coefficient of... The attenuation is achieved after a second-order filter. Mechanistically, the main function of this filter is to ensure the roll-off characteristic of the PD controller's amplitude-frequency curve, that is, to ensure that the PD controller gain approaches zero at high frequencies, and to attenuate high-frequency measurement noise without excessively altering the mid-to-low frequency tracking and robustness characteristics. For convenience, this invention selects a filter time constant... This ensures that noise attenuation is achieved without excessively impacting the system's robustness and performance.

[0057] SS4: Design of a DOB low-pass filter based on quantitative time-delay robustness Based on the transfer function model G p The relative order of (s) determines the structure of the DOB low-pass filter. Based on the PD controller parameters, the closed-loop characteristic equation of DOB with uncertain time delay is established. The minimum critical time delay is obtained, and the allowable range of the time constant of the DOB low-pass filter is determined according to the condition that the minimum critical time delay is greater than the nominal time delay.

[0058] S4.1: DOB low-pass filter structure While the aforementioned PD controller based on time-delay robust constraints achieves good setpoint tracking performance for integral time-delay processes, it cannot completely attenuate unknown disturbances in the system. This invention employs DOB (Distance-on-Board) to attenuate and suppress unknown external disturbances. Figure 5 As shown, The low-pass filter is the most crucial component of the interference observer structure. A higher bandwidth allows it to reproduce a wider spectral range of the nominal model, resulting in faster and more accurate reflection of deviations (lumped disturbances) between the actual process and the nominal model, thus providing better anti-interference performance. However, an excessively large filter bandwidth also introduces more high-frequency noise signals into the control system, increasing the control's sensitivity to noise and leading to frequent actuator movements.

[0059] according to Figure 5 The control block diagram shown illustrates the output and setpoint signals of a DOB-based control system. and disturbance signals The transfer function between them can be established as follows: (4-1) In the low frequency range The low-pass filter used generally meets the following conditions. Therefore, under nominal conditions According to equation (4-1), it is not difficult to conclude that: (4-2) It's easy to see that a major advantage of DOB is its ability to be seamlessly integrated into well-designed PD feedback control systems. DOB inner loops can be added without affecting the tracking response, enhancing the system's anti-interference performance. Without using DOB, i.e. Therefore, a PD controller needs to be designed. A very large gain is needed in the low-frequency range to ensure the attenuation of interference, and the required PD controller gain is often difficult to achieve in practice.

[0060] Since the relative order of the integral time delay process (2-1) under study is 2, in order to ensure the physical realizability of the DOB part, we adopt the following second-order low-pass filter based on the regularized parameter expression, whose numerator order is 0 and whose regularized normalized filter time constant is... , τ q This represents the DOB filter time constant at the actual time scale. Reduce This is equivalent to increasing the bandwidth of the DOB filter, which can enhance the estimation speed of low-frequency lumped disturbances, but it will also increase the sensitivity to high-frequency noise and high-frequency model errors.

[0061] (4-3) Compared to other filters with the same or higher relative order, this filter achieves a better trade-off in terms of anti-interference performance, robustness in tolerating uncertain time delays, and noise attenuation.

[0062] Since the open-loop transfer function under the two-degree-of-freedom equivalent transformation becomes the following equation, the stability analysis of the system under uncertain time delay becomes more complex with the addition of DOB.

[0063] (4-4) The complex transformation from equation (2-4) to equation (4-4) would disrupt the aforementioned analytical design approach based on independent outer loops. Therefore, this invention proposes a method that quantifies the impact of DOB insertion on the original external loop, thus avoiding analytical design after the transformation. The difficulty lies in defining the filter time constant design that satisfies the preferences of the controlled process in a coal-fired power plant before quantitative design. This means ensuring that the tolerable uncertain time delay interval is greater than the nominal time delay and is continuous.

[0064] S4.2: Minimum Critical Delay Ratio and Filter Parameter Range The uncertain time delay ratio θ is defined as θ = L / L0, where L is the actual time delay and L0 is the nominal time delay. Based on equation (2-10), the closed-loop characteristic equation of the system when the time delay deviates from the nominal value can be obtained. : (4-5) in This represents the ratio between the uncertain time delay and the nominal time delay. First, it is ensured that the generalized control gain of the PD controller is within the aforementioned bounded region; therefore, the tolerable range of the uncertain time delay is entirely determined by… Filter scaling time constant To determine.

[0065] Stability depends on whether the roots of the closed-loop characteristic equation (4-5) lie in the right half-plane, that is, It is stable if and only if hour Under this premise, it is necessary to find all uncertain time delays under a stable controller. This makes the closed-loop characteristic equation At a certain filter time constant The following satisfies The uncertain time delay term Separating equation (4-5) from its components, we can obtain: (4-6) Where the left and right sides are defined as follows: and . In the complex plane, it is a clockwise unit circle. And for... It exhibits nonlinear characteristics in the complex plane, and its amplitude is expressed as follows: , (4-7) The intermediate variable is: According to the above formula, we can find that... This indicates and It contains at least one intersection point on the complex plane. In other words, with The roots of the closed-loop characteristic equation expressed in terms of solutions In the interval There is at least one within the range. But for In this context, it is difficult to obtain its solution analytically. Instead, we can use a numerical solution method based on interpolation to obtain the set of solutions. Represented as The solutions can be described by their set as follows: (4-8) in yes In the interval The corresponding angle. It should be noted that the solutions to the above transcendental equations provide an infinite number of critical time delays. For the dust removal process of coal-fired flue gas, the main focus is on the minimum critical time delay calculated from (4-8). According to the shaving principle, if this value... If the value is greater than 1, then the interval All uncertain time delays within this range can guarantee the stability of the system. Therefore, it is necessary to define the critical minimum time delay corresponding to this. The filter time constant is adjusted to provide a fixed PD controller for... The boundary range of the filter during quantization adjustment. To better illustrate, in Figure 11 The time constants for different models are given. The external loop has a relative time delay margin. The minimum critical time delay test of the optimal tracking PD controller was conducted. It can be found that when... When reduced to a certain point, A sudden drop will occur. Further reduction will lead to A value less than 1 indicates that there is unstable delay within the nominal delay range.

[0066] To satisfy the good stability constraint for uncertain time delays This invention uses different time-delay robustness levels in the outer ring. After extensive evaluation, Filter time constant range The critical time constant is strictly limited to be greater than 0.4. Compared to the value of 0.25 recommended for general models in previous studies on DOB-based control, the critical time constant defined in this invention exhibits stronger time-delay robustness. Based on this defined critical filtering time constant, the quantization disturbance rejection design under time-delay robustness constraints is presented below.

[0067] S4.3: Quantitative Analysis of Disturbance Immunity Performance From equation (4-1), we can see that, under nominal conditions, the closed-loop transfer function from the control system disturbance to the system output is: (4-9) Generally, most disturbances in the controlled processes of coal-fired power plants are distributed in the low-frequency range, meaning that the changes in the regulated variable after being disturbed are slow time-varying processes. Based on this property, if it can be guaranteed... The smaller the amplitude in the low-frequency range, the less the system output is affected by disturbances, meaning the control system has a stronger ability to attenuate unknown disturbances. Again, using the model from step S23... To illustrate, we will use three different filter time constants. Below, control system The amplitude characteristic curve is as follows Figure 12 As shown, note that the PD controller gain has now been tuned according to the aforementioned optimization design method. It can be observed that... The smaller, The lower the amplitude in the low-frequency range, the better the anti-interference capability.

[0068] On the other hand, if the PD controller generates a certain relative time delay margin for the control system through the preceding analysis and design process... Therefore, the design of the DOB will only affect latency robustness within that range. This can be seen from... Figure 11 To illustrate more intuitively, due to the design of the external circuit... ,when When increased to a sufficiently large value, the final It can only approach 3. Based on this finding, we can... Filter design is carried out quantitatively, that is, in terms of interference suppression and its external... A trade-off is made between the effects of time delay and robustness. This allows the anti-interference performance to be quantitatively characterized very clearly through this time-delay robustness metric, without having to deconstruct the open-loop transfer function of the two-degree-of-freedom control system. In this way, the filter time constant specified above is used. Within the calibration range, you can start by adjusting a conservative value and gradually adjust it. The value, until the relative delay margin of the entire loop is determined from the design. Reduce to the specified value .

[0069] SS5. Coordination and parameter setting of external PD controller and internal DOB filter: Keeping the PD controller parameters unchanged, the time constant of the DOB low-pass filter is adjusted within the allowable range. The target DOB low-pass filter time constant is determined based on the relationship between the relative time delay margin of the closed-loop system after adding DOB compensation and the target relative time delay margin.

[0070] Based on time-delay robustness, the internal filter and external PD controller of the DOB control system are comprehensively designed. The analytical design of the PD in steps SS2 and SS3, and the quantitative adjustment of the DOB in step SS4, provide considerable flexibility in developing control systems with specific time-delay robustness. For example, when strong anti-interference performance is required, the outer-loop PD design can be appropriately relaxed, reserving sufficient relative time-delay margin. The filter's time constant can be further reduced within the calibration range. Conversely, when rapid tracking of the setpoint is required, the design of the external PD loop can be enhanced based on a relatively conservative inner-loop filter time constant.

[0071] This invention primarily focuses on establishing robustness against external time delays; therefore, when considering... When selecting, the relative delay margin of a well-designed external loop is important. It should first be larger than the approximate range of the actual estimated uncertain time delay, and need to be unaffected by the excessive influence of the added DOB. Therefore, the recommended value of the design time constant is expressed as... This reduces the maximum tolerable time delay of the control system after adding DOB to 80% of the original. The design process of a two-degree-of-freedom control based on time-delay robustness constraints for integral time-delay processes can be summarized as follows: First, identify the nominal model of the integration process and select an initial relative time delay margin value that is larger than the approximate range of the estimated uncertain time delay. .

[0072] Second: In Under constraints, based on the maximum generalized proportional gain rule described in step SS3, calculate the gain crossover frequency with optimal tracking under time-delay robustness constraints. This allows us to obtain the optimal PD controller parameters.

[0073] Third: Keep the PD controller parameters unchanged, and use the calculated parameters according to equation (2-7). and initial value Determine the optimal PD controller gain under time-delay robustness constraints.

[0074] Fourth: Using relative time lag margin as an indicator, Filter Adjust from larger value to This ensures that the final relative delay margin satisfies .

[0075] For most controlled integral time-delay processes, different control requirements mainly fall into three modes: performance-driven, trade-off-driven, and robustness-driven. It's easy to see that these three models correspond to small, medium, and large time-delay robustness levels, respectively. According to... Figure 9 and Figure 10 Based on the correlations between the different indicators shown, a set of applicable time-delay robustness levels is recommended here. (or This allows for the optimization of control parameters. This rule applies to most integral processes under the above requirements, and the obtained maximum sensitivity function can fall within the normal range.

[0076] (5-1) Meanwhile, at these recommended levels of delay robustness, the required variables , The fitted double-exponential function can be approximated using the parameters given in Table 1. Thus, for a given integral process, the constraints can be easily calculated. Approximate optimal PD controller and quantization design filter.

[0077] (5-2) Equation (5-2) adopts the form in which the exponential coefficients directly include positive and negative signs, which is consistent with the way the parameters p2, p4, q2 and q4 are recorded as negative values ​​in Table 1.

[0078] Table 1 shows the estimated coefficients of the optimal tracking and quantization disturbance rejection parameters of the fitted DOB system in Equation (5-2). The fitted parameters in Table 1 can be used as quick estimates of the controller's initial parameters. To avoid fitting errors affecting stability, the actual parameters used are... and The stable feasible region determined in step SS3 and the DOB stability condition determined in step SS4 should still be satisfied respectively.

[0079] SS6: Lumped Disturbance Estimation and Control Variable Synthesis (Optimal) After completing the controller parameter design in steps SS1-SS5, proceed to step SS6, applying the determined PD controller parameters and target DOB filter time constant to the online closed-loop control of the final-stage electric field. Let the outlet dust concentration setpoint be R(s) and the measured outlet dust concentration be Y(s), then the concentration deviation signal is E(s) = R(s) - Y(s). Input the concentration deviation into the external PD controller to generate the basic control quantity for the final-stage electric field. Lumped disturbance estimate after DOB low-pass filter processing according to and in accordance with Will As a disturbance compensation, it is superimposed on the basic control quantity U in the opposite direction to the lumped disturbance. c (s) forms a secondary current control quantity applied to the controlled object in the final stage electric field. When the gain K of the controlled object is negative, a reverse action direction should be configured at the input or output of the controller so that when the dust concentration at the outlet is higher than the set value, the resulting control action can improve the dust removal output of the final stage electric field.

[0080] SS7: Final Stage Electric Field Execution and Feedback Update (Preferred) The control increment ΔI(t) of the secondary current of the final-stage electric field is allocated according to the fourth electric field allocation coefficient λ4 and the fifth electric field allocation coefficient λ5, where λ4≥0, λ5≥0 and λ4+λ5=1; according to , Generate secondary current commands I for the fourth and fifth electric fields respectively. 4,cmd I 5,cmd I 4,0 and I 5,0 These are the reference secondary currents I and I corresponding to the electric field. 4,min I 4,max I 5,min and I 5,max These represent the lower and upper limits of the secondary current allowed by the corresponding high-frequency power supply, respectively, with sat indicating the amplitude limiting operation; the corresponding high-frequency power supply is controlled to adjust the actual secondary current, and the concentration deviation calculation, lumped disturbance estimation, disturbance compensation, and secondary current adjustment are repeatedly performed based on the updated measured value of the outlet dust concentration.

[0081] To reduce the impact of sudden changes in secondary current commands on the operating state of the high-frequency power supply and electric field, the command changes in adjacent control cycles can also satisfy: , Where, ΔI4,max and ΔI 5,max These represent the maximum permissible secondary current variations in adjacent control cycles for the fourth and fifth electric fields, respectively. The high-frequency power supply adjusts the actual secondary current according to these secondary current commands, and the control system repeatedly performs concentration deviation calculation, lumped disturbance estimation, disturbance compensation, and secondary current adjustment based on the updated measured outlet dust concentration. In the event of continuous spark discharge, intensified back corona discharge, failure of the dust concentration detection signal, or a high-frequency power supply failure, closed-loop incremental regulation can be paused, and the corresponding electric field can be switched to a safe setpoint or the original operating control mode.

[0082] Through the above steps, this embodiment first obtains the first-order integral model of the final-stage electric field with pure time delay using static calibration and step tests; then, a normalized model is established using the nominal time delay as the scale, and the stable feasible region and optimal parameters of the external PD controller are determined through relative time delay margin constraints; further, the stable parameter range of the DOB low-pass filter is determined based on the closed-loop characteristic function containing uncertain time delay ratios, and the target filtering time constant is determined in a coordinated manner. This allows for the estimation and compensation of model mismatch and external disturbances using the internal DOB while maintaining the tracking performance and time delay robustness of the external loop. The controller parameters determined in this embodiment can be configured in the high-frequency power controllers of the fourth and fifth electric fields to form a closed-loop regulation of the secondary current of the final-stage electric field. The static power supply combination of the first three electric fields, the nominal model of the final-stage electric field, the external PD controller parameters, and the internal DOB filter parameters together constitute a dry electrostatic precipitator control parameter system suitable for wide-load operation of coal-fired units.

[0083] Example 2: Dry Electrostatic Precipitator Control System for Thermal Power Units like Figure 2 As shown in Example 1, this example provides a dry electrostatic precipitator control system for thermal power units based on integral time delay (DOB), including a data acquisition and model identification module 10, a control structure and model scaling module 20, an external loop controller design module 30, an internal loop stability boundary design module 40, a coordination parameter determination module 50, and a final-stage electric field controller 60.

[0084] The data acquisition and model identification module 10 communicates with the unit load signal interface 100, the electric field secondary current acquisition interface 110, and the outlet dust concentration detection device 90 to acquire the unit load, the secondary current of the first to fifth electric fields, and the outlet dust concentration. Based on the static test data, it determines the set values ​​of the secondary current of the first three electric fields, and identifies the integral first-order plus pure time delay transfer function model based on the step response data of the secondary current of the fourth and fifth electric fields and the outlet dust concentration, and outputs the object gain, time constant, and nominal time delay.

[0085] The control structure and model scaling module 20 is used to establish a two-degree-of-freedom control structure composed of an external PD controller and an internal DOB based on the transfer function model, generate a normalized model using nominal time delay as the scale, and extract independent external loops that do not include DOB compensation.

[0086] The external loop controller design module 30 is used to receive the normalized model and the target relative time delay margin, determine the relationship between the phase margin, the normalized gain cross frequency and the PD controller scaling parameters, find the optimal normalized gain cross frequency that maximizes the generalized proportional gain within the stable feasible region, and output the proportional gain, differential gain and differential time constant at the actual time scale.

[0087] The inner loop stability boundary design module 40 is used to determine the structure of the second-order DOB low-pass filter based on the relative order of the normalized model, establish the DOB closed-loop characteristic equation with uncertain time delay ratio, obtain the minimum critical time delay ratio, and determine the allowable range of the normalized DOB filter time constant accordingly.

[0088] The coordination parameter setting module 50 is used to keep the external loop controller parameters unchanged, adjust the normalized DOB filter time constant within the allowable range, determine the target DOB filter time constant based on the relationship between the relative time delay margin of the closed loop system after adding DOB compensation and the target relative time delay margin, and write the PD controller parameters and the target DOB filter time constant into the final stage electric field controller 60.

[0089] The final-stage electric field controller 60 communicates with the fourth electric field high-frequency power supply 70, the fifth electric field high-frequency power supply 80, and the outlet dust concentration detection device 90, respectively, to perform closed-loop regulation of the final-stage electric field according to the configured parameters. In a preferred embodiment, the final-stage electric field controller 60 includes a lumped disturbance estimation and control quantity synthesis unit 61 and a final-stage electric field command allocation and feedback update unit 62; unit 61 obtains the disturbance-compensated control quantity based on the outlet dust concentration deviation, the nominal transfer function model, and the equivalent secondary current of the final-stage electric field; unit 62 generates the secondary current commands of the fourth and fifth electric fields based on the preset allocation coefficient, the upper and lower limits of the secondary current, and the change constraints of adjacent control cycles, and repeatedly adjusts according to the updated outlet dust concentration.

[0090] The above modules can be implemented by processors, memory, and input / output interfaces in a distributed control system, industrial control computer, or programmable controller. Each module can be an independent program unit or integrated into the same control device. The memory stores model parameters, controller parameters, operating condition correspondences, and control programs. The processor calls the data and programs to complete the control method described in Example 1.

[0091] The objectives of this invention have been fully and effectively achieved through the above embodiments. Those skilled in the art will understand that this invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments described above. Although the invention has been described with reference to what is currently considered the most practical and preferred embodiments, it should be understood that the invention is not limited to the disclosed embodiments, and any modifications that do not depart from the functional and structural principles of the invention will be included within the scope of the claims.

Claims

1. A method for controlling dry electrostatic precipitators in thermal power units based on integral time-delay (DOB), characterized in that, It should include at least the following steps: SS1. The setpoints of the secondary currents for the first three electric fields were determined through static experiments. A step experiment was conducted on the secondary currents of the fourth and fifth electric fields of the final stage to obtain the step response data of the outlet dust concentration. The integral first-order plus pure time-delay transfer function model G from the secondary current to the outlet dust concentration was then identified. p (s); SS2. Based on the transfer function model G p (s) Construct a two-degree-of-freedom control structure containing an external PD controller and an internal DOB low-pass filter. Scale the transfer function model with nominal time delay to obtain a normalized model and extract the independent outer loop that does not include DOB compensation. SS3. Set the target relative time delay margin for the external loop, establish the relationship between phase margin, normalized gain crossover frequency and PD controller scaling parameters, determine the stable feasible region, and obtain the optimal normalized gain crossover frequency by maximizing the generalized proportional gain to obtain the PD controller parameters. SS4. Based on the transfer function model G p The relative order of (s) determines the structure of the DOB low-pass filter. Based on the PD controller parameters, the closed-loop characteristic equation of DOB with uncertain time delay is established. The minimum critical time delay is obtained, and the allowable range of the time constant of the DOB low-pass filter is determined according to the fact that the minimum critical time delay is greater than the nominal time delay. SS5. Keeping the PD controller parameters unchanged, adjust the DOB low-pass filter time constant within the allowable range, and determine the target DOB low-pass filter time constant based on the relationship between the relative time delay margin of the closed-loop system after adding DOB compensation and the target relative time delay margin.

2. The method according to claim 1, characterized in that, In step SS1, the set values ​​of the secondary currents for the first three electric fields are determined through static testing, including at least: (1) Initial power supply configuration: Adjust the secondary currents of the fourth and fifth electric fields to the lower limit of the corresponding high-frequency power supply's allowable adjustment range, and adjust the secondary currents of the first, second, and third electric fields to the corresponding initial set values ​​that bear the main dust removal load; (2) Step adjustment of the front current: reduce the secondary current value of the high-frequency power supply of the first three electric fields in a step-by-step manner according to the preset gradient, and obtain the dust concentration at the outlet of the dry electrostatic precipitator after each adjustment. (3) Determination of critical current combination: When the outlet dust concentration reaches the allowable deviation range of the preset dust concentration control value, stop reducing the secondary current of the first electric field, the second electric field and the third electric field, and record the current combination of the secondary current of the first three electric fields; (4) Variable load repeated calibration: Change the load of the thermal power unit and repeat the above process to obtain the correspondence between the secondary current setting values ​​of the first three electric fields and the unit load within the wide load range of the unit.

3. The method according to claim 1 or 2, characterized in that, In step SS1, applying a step excitation to the secondary current of the fourth and fifth electric fields in the final stage includes at least the following: selecting a typical unit load as the dynamic test condition, keeping the unit load and the initial set values ​​of the secondary current of the first three electric fields unchanged during the step excitation; increasing the secondary current of the fourth and fifth electric fields from their respective initial values ​​by a preset step amplitude at the same step moment; collecting the secondary current of the fourth and fifth electric fields and the outlet dust concentration according to a unified sampling sequence to form an input-output response sequence containing steady-state data before step excitation, step change data, and response data after step excitation.

4. The method according to any one of claims 1 to 3, characterized in that, In step SS1, the identification of the integral first-order plus pure time-delay transfer function model includes at least the following: using the average value u=(I4+I5) / 2 of the secondary current I4 of the fourth electric field and the secondary current I5 of the fifth electric field as the model input, and the outlet dust concentration y as the model output, the integral first-order time-delay transfer function model is identified based on the input data before and after the step excitation and the outlet dust concentration response data. K is the object gain of the controlled object under the nominal operating condition, T is the time constant, L0 is the nominal time delay, and s is the Laplace complex frequency domain variable.

5. The method according to claim 4, characterized in that, In step SS2, the two-degree-of-freedom control structure includes an outlet dust concentration setpoint tracking channel and a lumped disturbance compensation channel. The external PD controller is located in the outlet dust concentration setpoint tracking channel, and the internal DOB is located in the lumped disturbance compensation channel. When designing the PD controller, the lumped disturbance compensation channel does not participate in the frequency domain analysis of the independent external loop. , , Model G p (s) parameter scaled to , Let L0 be the normalized complex frequency domain variable with time scale. τ represents the normalized object gain, and τ is the time scale ratio.

6. The method according to claim 5, characterized in that, In step SS3, the PD controller parameters are scaled to... , For scaling gain, To scale the differential gain, The normalized differential time constant satisfies , , , k p k d τ d For the actual time scale, these are the proportional gain, differential gain, and differential time constant; Furthermore, according to the normalization model PD controller after parameter scaling Construct an independent outer loop open-loop transfer function , determine The normalized gain cross frequency v with an amplitude equal to 1 c and make ,according to , , Determine the actual time delay margin L m and relative time delay margin r dm v is the normalized angular frequency, v c ω is the normalized gain crossover frequency. c This is the actual gain crossover frequency. Phase margin, actual time delay margin L m The relative time delay margin r is the maximum additional pure time delay that an independent external loop can tolerate before reaching the stability boundary from the nominal steady state. dm The ratio of the maximum additional pure time delay to the nominal time delay, where j is the imaginary unit.

7. The method according to claim 6, characterized in that, In step SS3, based on the normalized object gain Define generalized proportional gain and generalized differential gain ; and in accordance with , Determine the normalized differential time constant ; and make phase margin and normalized gain cross frequency v c The closed stable feasible region satisfies ≥0, v c ≥0、 The parameters of the external PD controller actually used are selected within the above-mentioned stable and feasible domain.

8. The method according to claim 7, characterized in that, In step SS3, according to Generalized proportional gain Represented as the normalized gain crossover frequency v c objective function Within the feasible range Inner calculation to obtain generalized proportional gain The normalized gain crossover frequency that yields the maximum value, v c 'for Find the positive real solutions; solve the stationary point equations within the feasible interval: The unique solution of the stationary point equation within the feasible interval is determined as the optimal normalized gain crossover frequency. ,according to , , , Obtain the optimal scaling PD controller parameters. and They are respectively and The corresponding optimal generalized proportional gain and optimal generalized differential gain.

9. The method according to claim 8, characterized in that, In step SS3, according to , , The optimal controller parameters under the actual time scale are restored, and a second-order filter element separate from the derivative action is configured for the PD controller. , τ f The filtering time constant and C f Damping coefficient of (s) This is to attenuate the high-frequency measurement noise in the outlet dust concentration detection signal and make the high-frequency gain of the PD controller approach zero.

10. The method according to claim 8, characterized in that, In step SS4, the normalized model The rational part has a relative order of 2. The DOB low-pass filter is configured as a second-order low-pass filter with binomial coefficients, a numerator order of zero, and a DC gain of 1. , The normalized filter time constant and satisfying , τ q The time constant of the DOB filter is given by the actual time scale. The uncertain time delay ratio θ is defined as θ = L / L0, where L is the actual time delay and L0 is the nominal time delay; according to the normalized model... External PD controller and DOB low-pass filter Establish the DOB closed-loop characteristic equation containing the uncertain time delay ratio θ, and find the set of critical time delay ratios {θ} that make the closed-loop characteristic roots reach the imaginary axis. i The smallest positive value among them is determined as the minimum critical time delay ratio θ1; based on θ1>1, a set of stable filter parameters that can cover the nominal time delay is determined, and the normalized filter time constant is set. Limited to .

11. The method according to claim 9, characterized in that, In step SS5, the relative time delay margin r of the outer loop is first... dm Set the value to be greater than the expected range of uncertain time delay ratio variation, keep the external PD controller parameters determined in step SS3 unchanged, and start from the initial normalized filter time constant that satisfies the stability condition in step SS4. Begin by gradually decreasing the normalized filter time constant until the target normalized filter time constant is determined. This ensures that the relative time delay margin of the closed-loop system after adding DOB compensation meets the requirements. This means that the maximum tolerable total time delay ratio of the closed-loop system after adding DOB compensation is 80% of the maximum tolerable total time delay ratio before adding DOB compensation. The relative time delay margin of the closed-loop system after adding DOB compensation; Based on control performance requirements, the following modes are adopted: tracking performance priority mode, time delay robustness priority mode, or time delay robustness priority mode. Among these, in the tracking performance priority mode... In comprehensive performance mode, In the time-delay robustness-first mode, .

12. A dry electrostatic precipitator control system for thermal power units based on integral time-delay (DOB), characterized in that, At least including: The data acquisition and model identification module is used to collect the unit load, secondary current of each electric field and outlet dust concentration, determine the set value of the secondary current of the first three electric fields, and identify the integral first-order plus pure time delay transfer function model with the average value of the secondary current of the fourth and fifth electric fields as input and the outlet dust concentration as output. The control structure and model scaling module is used to construct a two-degree-of-freedom control structure containing an external PD controller and an internal DOB low-pass filter based on the transfer function model, obtain a normalized model using the nominal time delay as the scale, and extract the independent outer loop that does not take DOB compensation into account. The external loop controller design module is used to set the target relative time delay margin for independent external loops, establish the relationship between phase margin, normalized gain cross frequency and PD controller scaling parameters, determine the stable feasible region, and obtain the optimal normalized gain cross frequency and PD controller parameters by maximizing the generalized proportional gain. The inner loop stability boundary design module is used to determine the DOB low-pass filter structure based on the relative order of the transfer function model, establish the DOB closed-loop characteristic equation with uncertain time delay, obtain the minimum critical time delay ratio, and determine the allowable range of the DOB low-pass filter time constant. The coordination parameter setting module is used to keep the PD controller parameters unchanged, adjust the DOB low-pass filter time constant within the allowable range, determine the target DOB low-pass filter time constant based on the relationship between the relative time delay margin of the closed-loop system after adding DOB compensation and the target relative time delay margin, and configure the PD controller parameters and the target DOB low-pass filter time constant in the final stage electric field controller.

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