First-order time-delay active disturbance rejection control method for wet electrostatic precipitator in thermal power plant
By constructing and scaling the first-order self-immunity controller model of the wet electrocalender and performing robust analysis, the problems of delay uncertainty and interference in the wet electrocalender are solved, and a more efficient self-immunity control effect is achieved.
Patent Information
- Application Number
- CN202211007342.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-08-22
- Publication Date
- 2025-08-19
- Estimated Expiration
- 2042-08-22
AI Technical Summary
In the prior art, wet electrostatic precipitators have time delay uncertainty and interference in thermal power plants, resulting in high complexity of self-immunity control and it is difficult to effectively apply self-immunity controllers.
By obtaining the first-order nominal transfer function model of the wet electrocutter, constructing the first-order self-immune controller model, and performing parameter scaling and robustness analysis, designing robust adjustment criteria to improve system robustness and control effects.
It realizes effective self-immune control of wet electrocutors, reduces the complexity of control parameters, improves the robustness of the system and adapts to uncertain time delays, and improves the control effect of outlet smoke concentration.
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Figure CN115327912B_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of automatic control technology, and in particular to a first-order time-delay auto-disturbance rejection control method for a wet electrostatic precipitator in a thermal power plant. Background Art
[0002] Active disturbance rejection control (ADRC) has received significant attention in industrial control due to its robust ability to handle uncertainty and disturbances. ADRC generally handles model uncertainty, nonlinearity, and external disturbances effectively. Currently, the main methods for tuning ADRC controller parameters include experimental methods, bandwidth parameterization, frequency domain shaping, constrained optimization, and programming-based software tuning. These methods require extensive training and specialized knowledge for field engineers before they can be applied in real-time. These methods are complex and difficult to implement. To promote ADRC applications in thermal power plants and other industrial sectors and reduce the complexity of ADRC gain control, bandwidth parameterization is a promising approach. Bandwidth parameterization allows for further parameter scaling, reducing tuning complexity. However, the wet electrostatic precipitator outlet measurement point is located at the power plant chimney outlet, and the smoke concentration model inevitably has significant time delay. Therefore, it is crucial to theoretically determine the delay margin of the ADRC controller and conduct robustness analysis to determine robust control parameters for wet electrostatic precipitator control systems. Furthermore, wet ESPs are affected by the effects of preceding dry ESP and wet desulfurization systems, resulting in significant interference. The wet ESP concentration model itself also exhibits uncertainty. Addressing the uncertainty and interference inherent in time-delay ESP systems is a key issue in the design of ADRC control technology. Summary of the Invention
[0003] The present application provides a first-order time-delay auto-disturbance rejection control method for a wet electrostatic precipitator in a thermal power plant, the technical purpose of which is to resolve the uncertainty and interference of the time-delay electrostatic precipitator system and realize the auto-disturbance rejection control of the wet electrostatic precipitator.
[0004] The above technical objectives of this application are achieved through the following technical solutions:
[0005] A first-order time-delay auto-disturbance rejection control method for a wet electrostatic precipitator in a thermal power plant, comprising:
[0006] Obtain the first-order nominal transfer function model of the wet electrostatic precipitator;
[0007] Constructing a first-order active disturbance rejection controller model adapted to the first-order nominal transfer function model, and scaling parameters of the first-order active disturbance rejection controller model;
[0008] The first-order active disturbance rejection controller model is converted into a two-degree-of-freedom equivalent model, a closed-loop characteristic equation is constructed, and a stability analysis is performed on the closed-loop control system of the wet electrostatic precipitator to obtain a selection range of control parameters;
[0009] Analyzing the overall robustness of the control parameters to obtain robust adjustment criteria;
[0010] According to the robust adjustment criterion, the parameters of the first-order active disturbance rejection controller model are modified and applied to perform active disturbance rejection control on the wet electrostatic precipitator.
[0011] The beneficial effects of this application are as follows: by obtaining a first-order nominal transfer function model of the controlled system and constructing a first-order active disturbance rejection controller model adapted thereto, an active disturbance rejection controller is designed based on the first-order active disturbance rejection controller model; the parameters of the active disturbance rejection controller are scaled to establish the controlled system characteristic equation and perform stability analysis to obtain the system stability condition, i.e., the practical control parameter adjustment range; and robustness analysis and testing of the parameters are performed to provide robust adjustment criteria for the active disturbance rejection controller. Using this active disturbance rejection controller for active disturbance rejection control can improve system robustness, have a good control effect on systems with uncertain time delays, and can be applied to the closed-loop control of wet electrostatic precipitators. BRIEF DESCRIPTION OF THE DRAWINGS
[0012] Figure 1 This is a schematic diagram of the structure of the first-order active disturbance rejection controller described in this application;
[0013] Figure 2 This is a schematic diagram of the robustness measurement of the observer bandwidth under different delays in this application;
[0014] Figure 3 This is a schematic diagram of the simulation of the active disturbance rejection control of the wet electrostatic precipitator in a 1000MW coal-fired power plant. DETAILED DESCRIPTION
[0015] The technical solution of this application will be described in detail below with reference to the accompanying drawings.
[0016] This implementation case discloses an auto-disturbance rejection control method for a closed-loop control system with a first-order time delay. The control method is mainly for a first-order model with uncertain time delay, and can also be applied to any model from the first order to the higher order. The implementation process is as follows: Figure 1 shown.
[0017] The first-order time-delay auto-disturbance rejection control method for a wet electrostatic precipitator in a thermal power plant comprises:
[0018] S1: Obtain a first-order nominal transfer function model of a wet electrostatic precipitator (or convert a high-order wet electrostatic precipitator process model into a first-order nominal transfer function model).
[0019] Specifically, the controlled system can be a first-order or higher order wet electric model. When the controlled system is a first-order or higher order wet electric model, it is converted into an approximate first-order wet electric model by the Sigurd method, and finally the wet electric first-order nominal transfer function model G is obtained. p , expressed as:
[0020]
[0021] Where s represents the Laplace operator; K represents the gain; T represents the time constant; and L represents the delay constant.
[0022] The first-order nominal transfer function model is equivalently expressed as a state-space model, and the state-space model is expressed as:
[0023]
[0024] Among them, x1 represents the system state vector and is equivalent to y; u(t) represents the change in secondary current (control input); y(t) represents the outlet smoke concentration (wet electrostatic precipitator output); u(tL) represents the control input of the lag time L; d(tL) represents the disturbance, which includes external disturbance and internal disturbance; b0 = K / T.
[0025] Most first-order and higher-order wet electrical models are converted into approximate first-order wet electrical models through the Sigurd method, so that the method described in this application can control the approximate first-order model. Therefore, this application also has good applicability to first-order and higher-order wet electrical models.
[0026] S2: constructing a first-order active disturbance rejection controller model adapted to the first-order nominal transfer function model, and scaling parameters of the first-order active disturbance rejection controller model.
[0027] The first-order active disturbance rejection controller model is expressed as:
[0028]
[0029]
[0030] in, Express the estimated value of the process output y in equation (2); represents the lumped interference term The estimated value of; L0 represents the defined nominal delay; β1 and β2 represent the observer gain; r represents the reference signal; k p represents the controller gain;
[0031] After constructing the first-order ADRC model, parameter scaling is performed on the first-order ADRC model, including observer parameter scaling and feedback controller parameter scaling. The observer parameter scaling includes:
[0032]
[0033] Feedback controller parameter scaling includes:
[0034]
[0035] Among them, ω o represents the bandwidth parameter of the observer; ω c represents the bandwidth parameter of the controller; λ represents an adjustable positive parameter; represents the normalized Laplace operator; τ is the process characteristic parameter representing the normalized delay, represents the normalized observer bandwidth.
[0036] S3: Convert the first-order active disturbance rejection controller model into a two-degree-of-freedom equivalent model, construct a closed-loop characteristic equation, and perform stability analysis on the closed-loop control system of the wet electrostatic precipitator to obtain a selection range of control parameters.
[0037] The parameter-scaled first-order ADRC model is converted into a two-degree-of-freedom (2-DOF) equivalent model. This 2-DOF equivalent model divides the closed-loop control system into a feedforward link and a feedback link. There is no coupling between the two links, and the entire closed-loop control system is divided into a two-DOF model. After calculation, the open-loop transfer function of Equations (2) to (4) is expressed as:
[0038]
[0039] Then the closed-loop characteristic equation of the closed-loop control system is The closed-loop characteristic equation is scaled and converted to:
[0040]
[0041] When the closed-loop characteristic equation (8) satisfies all its roots It falls in the left half plane of the complex plane, that is:
[0042]
[0043] According to formula (9), the actual control parameter selection range of the closed-loop control system is finally obtained, which is expressed as:
[0044]
[0045] S4: Analyze the overall robustness of the control parameters to obtain a recommended value range for the control parameters of the first-order active disturbance rejection controller model.
[0046] Specifically, the overall robustness of the control parameters is analyzed, and its inspection indicators include gain margin GM, stability margin SM and relative delay margin r dm , the specific analysis is as follows:
[0047] (1) Gain margin GM represents the system frequency response G op The amplitude at the frequency where the phase of (jω) is equal to -180° is |G op The gain margin GM indicates the amount of gain that can be increased before a closed-loop control system becomes unstable.
[0048] (2) Stability margin SM represents |1+G op The minimum value of (jω)|, the larger the SM, the higher the G op The greater the distance between (jω) and the point (-1,0), the better the system robustness.
[0049] (3) When the system delay is uncertain, the relative delay margin r dm Expressed as:
[0050]
[0051] Among them, r d =(L-L0) / L0, which represents the time-delay disturbance of the uncertain time-delay L around the nominal value L0; L represents the upper limit of the uncertain lag L, represents the lower limit of the uncertain time delay L. When there is an uncertain time delay, that is, L≠L0, the open-loop transfer function of equation (7) is converted to:
[0052]
[0053] When the relative delay margin r dm Equal to r d When, for any integer N≥0 and frequency -∞<ω<+∞, r d Need to meet:
[0054]
[0055] By scaling the parameter space The gain margin GM, stability margin SM and relative delay margin r dm Conduct assessments, such as Figure 2 As shown, there are For SM, GM, r dm Through the analysis of the curve, it is required to ensure both a more appropriate SM margin and r dm Cannot be too small, and finally get the robust adjustment criterion:
[0056] (1) With The change of relative delay margin r dm and the stability margin SM cannot reach the desired maximum value at the same time; The parameters can be adjusted according to the size of τ;
[0057] (2) Adjusting the parameter λ will reduce the robustness of the closed-loop control system, but the closed-loop control response speed of the system will increase, and vice versa;
[0058] (3) For actual parameter adjustment, the recommended range of control parameters is λ∈(0,2], λ=1, Suitable for most situations.
[0059] S5: Modify and apply the parameters of the first-order active disturbance rejection controller model according to the robust adjustment criterion, and perform active disturbance rejection control on the wet electrostatic precipitator.
[0060] Specifically, the robust adjustment criterion summarized in step S4 is used to modify and apply the parameters of the first-order active disturbance rejection controller model according to the characteristics of the wet electrostatic precipitator itself.
[0061] In order to better demonstrate the practical effect of this application, the simulation of the method described in this application in the wet electrostatic precipitator outlet concentration control system will be demonstrated below. The relevant operating data of this simulation are all taken from the actual wet electrostatic precipitator of the on-site 1000MW coal-fired power plant.
[0062] First, let's understand the working process of a wet electrostatic precipitator (abbreviated as "wet electrostatic precipitator"): the flue gas enters the wet electrostatic precipitator, and water is sprayed onto the discharge electrode and corona area through the nozzle. After the water droplets with relatively low resistivity combine with the dust in the corona area, the resistivity of the dust decreases. Then, the high-frequency power supply provides DC high voltage to the discharge electrode, causing the negatively charged dust particles to move toward the collecting electrode under the force of the electric field. The fine water mist sprayed on the surface of the collecting electrode forms a continuous water film, and the dust captured by the flowing water is washed into the hopper and then enters the water reservoir. The control input of the wet electrostatic precipitator outlet concentration model is the secondary current of the high-voltage and high-frequency power supply unit, and its output is the dust concentration at the wet electrostatic precipitator outlet measured by the turbidity instrument. This measuring point corresponds to the chimney outlet end, so the system has a large time delay.
[0063] The simulated wet electricity nominal model is obtained by analyzing the step response test data and is expressed as:
[0064]
[0065] During the simulation, the system also includes the effects of parameter perturbations, time delay uncertainty, and vibration interference reflected by the on-site time series data.
[0066] The ADRC controller (3) is designed for the simulated electrostatic precipitator system. Since the τ of the wet electrostatic system is 20 / 22.6=0.885, according to the robust adjustment criterion, λ=0.8 and The results of the 20-minute simulation experiment are as follows: Figure 3 As shown in the figure, the time-delayed anti-disturbance control method of this application has a better control effect than the PID control method, and the outlet dust concentration is reduced from 4mg / Nm 3 Adjusted to 3mg / Nm 3 nearby.
[0067] When wet electrostatic precipitator control is actually implemented on site, the wet electrostatic precipitator optimization control system uses an embedded industrial computer as the hardware platform and obtains necessary operating data from the power plant DCS system through the Modbus TCP protocol, such as the wet electrostatic outlet smoke concentration and the unit operating power. The control strategy of this application is written into the wet electrostatic precipitator optimization control system in the form of a program, and the real-time optimal wet electrostatic precipitator high-frequency power supply secondary current and voltage setting values are obtained through calculation. The optimal wet electrostatic secondary current and voltage setting values are designed based on the robust adjustment criterion to adjust the outlet dust concentration to the predetermined setting value r = 5mg / Nm 3 .
[0068] Finally, the specific embodiments described herein are merely illustrative of the spirit of the present invention. A first-order, time-delayed, active disturbance rejection control method for wet electrostatic precipitators in power plants is proposed. This framework, primarily targeting a class of first-order systems with time delays, consists of an extended state observer (ESO) and a feedback proportional control link. The present method can also be applied to higher-order systems, exceeding the first order. Furthermore, its scope of application is not limited to electrostatic precipitator control systems. Systems with the same or similar structures as the models targeted by this invention can also employ the robust tuning method proposed in this invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the invention or exceeding the scope defined by the appended claims. The term "connection" in this invention refers to direct or indirect connection. Although this document frequently uses terms such as active disturbance rejection controller, time delay, gain margin (GM), stability margin (SM), relative delay margin (RDM), controller bandwidth, observer bandwidth, and wet electrostatic precipitator outlet concentration model, the use of other terms is not excluded. These terms are used only to more conveniently describe and explain the essence of the present invention; any additional limitation construed in them would be contrary to the spirit of the present invention.
Claims
1. A first-order time-delay auto-disturbance rejection control method for a wet electrostatic precipitator in a thermal power plant, characterized in that: include: Obtain the first-order nominal transfer function model of the wet electrostatic precipitator; Constructing a first-order active disturbance rejection controller model adapted to the first-order nominal transfer function model, and scaling parameters of the first-order active disturbance rejection controller model; The first-order active disturbance rejection controller model is converted into a two-degree-of-freedom equivalent model, a closed-loop characteristic equation is constructed, and a stability analysis is performed on the closed-loop control system of the wet electrostatic precipitator to obtain a selection range of control parameters; Analyzing the overall robustness of the control parameters to obtain robust adjustment criteria; According to the robust adjustment criterion, the parameters of the first-order active disturbance rejection controller model are modified and applied to perform active disturbance rejection control on the wet electrostatic precipitator. The first-order nominal transfer function model is expressed as: Where s represents the Laplace operator; K represents the gain; T represents the time constant; L represents the delay constant; The first-order nominal transfer function model is equivalently expressed as a state-space model, and the state-space model is expressed as: Where x1 represents the system state vector and is equivalent to y; u(t) represents the change in secondary current, i.e., the control input; y(t) represents the outlet dust concentration, i.e., the output of the wet electrostatic precipitator; u(tL) represents the control input with a lag time of L; d(tL) represents the disturbance, which includes external and internal disturbances; b0 = K / T; t represents time; The first-order active disturbance rejection controller model is expressed as: in, Express the estimated value of the process output y in equation (2); represents the lumped interference term The estimated value of; L0 represents the defined nominal delay; β1 and β2 represent the observer gain; r represents the reference signal; k p represents the controller gain; Parameter scaling is performed on the first-order active disturbance rejection controller model, including observer parameter scaling and feedback controller parameter scaling. The observer parameter scaling includes: Feedback controller parameter scaling includes: Among them, ω o represents the bandwidth parameter of the observer; ω c represents the bandwidth parameter of the controller; λ represents an adjustable positive parameter; represents the normalized Laplace operator; τ is the process characteristic parameter representing the normalized delay, represents the normalized observer bandwidth.
2. The method according to claim 1, wherein The open-loop transfer function of equations (2) to (4) is expressed as: Then the closed-loop characteristic equation of the closed-loop control system is The closed-loop characteristic equation is scaled and converted to: When the closed-loop characteristic equation (8) satisfies all its roots It falls in the left half plane of the complex plane, that is: According to formula (9), the actual control parameter selection range of the closed-loop control system is finally obtained, which is expressed as:
3. The method according to claim 2, wherein The comprehensive robustness of the control parameters is analyzed, and its inspection indicators include gain margin GM, stability margin SM and relative delay margin r dm , analyze the inspection indicators, including: The gain margin GM represents the system frequency response G op The amplitude at the frequency where the phase of (jω) is equal to -180° is |G op The reciprocal of (jω)|; Stability margin SM represents |1+G op The minimum value of (jω)|; When the system delay is uncertain, the relative delay margin r dm Expressed as: Among them, r d =(L-L0) / L0, which represents the time-delay disturbance of the uncertain time-delay L around the nominal value L0; L represents the upper limit of the uncertain time-delay L, represents the lower limit of the uncertain lag L; When there is an uncertain time delay, that is, L≠L0, the open-loop transfer function of equation (7) is converted to: When the relative delay margin r dm Equal to r d When, for any integer N≥0 and frequency -∞<ω<+∞, r d Need to meet: By scaling the parameter space The gain margin GM, stability margin SM and relative delay margin r dm Evaluations are performed to obtain robust adjustment criteria, including: along with The change of relative delay margin r dm and the stability margin SM cannot reach the desired maximum value at the same time; Make compromise adjustments based on the size of τ; Adjusting the parameter λ will reduce the robustness of the closed-loop control system, but the closed-loop control response speed of the system will increase, and vice versa; For actual parameter adjustment, the recommended range of control parameters is λ∈(0,2], 4. The method according to claim 3, wherein The recommended range of the control parameter is λ=1,