A system disturbance response-based auto disturbance rejection controller tuning method

Abstract

The application discloses a kind of based on system disturbance response's self anti-interference controller setting method, comprising the following steps: determining the model order of controller and controlled object;According to model order, data vector and model parameter vector are set;Select the initial value of calculation of feedback gain matrix and data covariance matrix;Recursive calculation feedback gain matrix, data covariance matrix and the estimated value of the model parameter vector, until the estimated value of model parameter vector tends to be stable;According to stable value, calculate the coefficient estimate of controlled object model;Based on each coefficient estimate, design self anti-interference controller parameter.The method of the application can guarantee system closed loop and system set value unchanged, only according to the disturbance response of system setting self anti-interference controller parameter, overcome the problems existing in prior art, the method of the application has good tracking and anti-interference performance, help to further promote the field application of self anti-interference controller in thermal process control.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic control, and in particular relates to a tuning method for an active disturbance rejection controller based on system disturbance response. Background Art

[0002] Currently, the primary control strategy for large-scale industrial processes, such as thermal and chemical processes, is proportional–integral–derivative (PID) control. This is due to the PID controller's simplicity, ease of implementation, and high reliability. However, with the increasing demands for control in industrial production, traditional PID controllers have struggled to achieve satisfactory control results. This is primarily due to their inability to handle industrial challenges such as strong nonlinearity, multivariable coupling, and multiple disturbances. Active Disturbance Rejection Control (ADRC) is a robust and adaptable control method that does not rely entirely on system models. Its core goal is to achieve invariance to internal and external disturbances through an extended state observer and error feedback. Therefore, ADRC has gradually gained widespread application as a potential alternative to PID in industrial control.

[0003] In engineering applications, ADRC parameter tuning generally requires prior model knowledge obtained from open-loop step tests of the controlled object. However, in actual thermal processes, it is often not allowed to cut off the system's feedback loop for open-loop testing, nor is it allowed to arbitrarily change the system set value. Therefore, in thermal processes, ADRC is difficult to tune while ensuring that the system closed loop and set value remain unchanged. Summary of the Invention

[0004] The technical purpose of the present invention is to address the problem of difficulty in tuning ADRC parameters while ensuring system closed-loop and unchanged set values ​​in thermal processes and other similar application scenarios. This invention proposes a tuning method for an active disturbance rejection controller based on the system disturbance response. The aim is to enable more effective tuning of ADRC parameters in actual thermal process applications and other similar applications, providing good support for further promoting the application of active disturbance rejection controllers in control field.

[0005] A method for tuning an active disturbance rejection controller based on system disturbance response, characterized by comprising the following steps:

[0006] 1) Determine the model order of the controller and the controlled object;

[0007] 2) According to the model orders of the controller and the controlled object, as well as the output data of the controlled object, set the data vector h(k) and the model parameter vector θ, where k represents a discrete time sequence number, the system disturbance is a signal formed by zero-mean white noise v(k) passing through the noise model, and the data vector h(k) consists of the output data of the controlled object and an estimated value of the white noise data, wherein the estimated value of the white noise data is correlated with the output data of the controlled object and the estimated value of the model parameter vector;

[0008] 3) Selecting the initial values ​​for the feedback gain matrix K(k) and the data covariance matrix P(k);

[0009] 4) Calculating the feedback gain matrix K(k) and the data covariance matrix P(k) based on the data vector h(k);

[0010] 5) Calculate the estimated value of the model parameter vector according to the following formula

[0011]

[0012] Among them, z(k) represents the output data of the controlled object at time k;

[0013] 6) Recursively calculate steps 4) and 5) until the estimated value of the model parameter vector is Stable value

[0014] 7) According to the stable value Calculate the estimated values ​​of each coefficient of the delay factor polynomial of the controlled object model

[0015] 8) Based on the estimated values ​​of the coefficients Design the parameters of the active disturbance rejection controller.

[0016] On the basis of the above scheme, further improved or preferred schemes also include:

[0017] Furthermore, in step 1):

[0018] In step 1):

[0019] The model structure of the controlled object is:

[0020]

[0021] Among them, z -1 represents the unit delay operator, G represents the pulse transfer function of the controlled object, and Represents the coefficients of the denominator and numerator delay factor polynomials of the controlled object model, n a 、n bRespectively represent the orders of the denominator and numerator delay factor polynomials of the controlled object model;

[0022] The model structure of the controller is:

[0023]

[0024] Where R represents the impulse transfer function of the controller, and Represent the coefficients of the denominator and numerator delay factor polynomials of the controller model, n p 、n q are the orders of the denominator and numerator delay factor polynomials of the controller model, respectively.

[0025] Furthermore, in step 2), the data vector h(k) and the model parameter vector θ are respectively:

[0026]

[0027] in, represents the estimated value of white noise data;

[0028]

[0029] in, is the estimated value of the model parameter vector.

[0030] Furthermore, in step 3), the initial values ​​of the given feedback gain matrix K(k) and data covariance matrix P(k) are calculated as: P(0)=10 12 I, I represents the identity matrix.

[0031] Furthermore, in step 4), the calculation formulas for calculating the gain matrix K(k) and the data covariance matrix P(k) are:

[0032]

[0033] Furthermore, in step 6), the stable value

[0034] The present invention has the following beneficial effects:

[0035] The present invention discloses an active disturbance rejection controller tuning method based on system disturbance response. The method can tune the parameters of the active disturbance rejection controller based solely on the system disturbance response while ensuring that the system closed loop and system set values ​​remain unchanged. This solves the problem of difficulty in tuning ADRC parameters in existing control application scenarios such as thermal processes, where it is not allowed to disconnect the system feedback loop for open-loop testing, or when the system set value parameters are changed. The method also has good tracking and anti-disturbance performance, which can help further promote the application of active disturbance rejection controllers in control fields such as thermal processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of a closed-loop system in discrete form.

[0037] Figure 2 This is a flow chart of the active disturbance rejection controller tuning method based on system disturbance response of the present invention.

[0038] Figure 3 This is the changing process of the estimated values ​​of the closed-loop system model parameters in the example given.

[0039] Figure 4 The following is a comparison chart of the system output simulation effects in the example given.

[0040] Figure 5 The following is a comparison chart of the simulation effects of the control quantities in the given example. DETAILED DESCRIPTION

[0041] The following further describes in detail the active disturbance rejection controller tuning method based on system disturbance response proposed by the present invention with reference to the accompanying drawings and specific examples.

[0042] Figure 1 The schematic diagram of a typical closed-loop system in discrete form is shown in Figure 1, where u(k) and z(k) are the input and output variables of the system, v(k) is the noise data caused by the system disturbance, which is assumed to be zero-mean white noise in this paper, r(k) is the control given signal (without loss of generality, it is usually set to zero), G(z -1 )、R(z -1 ), H v (z -1 ) are the controlled object model, feedback channel controller model and noise model respectively, z -1 Represents the unit delay operator.

[0043] The G(z -1 )、R(z -1 ), H v (z -1 ) can be expressed as:

[0044]

[0045] The definitions of the delay factor polynomials in the above structural formulas are:

[0046]

[0047] Where n a 、n b 、n p 、n q are the model orders of the corresponding delay factor polynomials.

[0048] Figure 2 This is a flow chart of a method for tuning a thermal process automatic disturbance rejection controller based on system disturbance response proposed by the present invention. The specific steps are as follows:

[0049] 1) Determine the model order of the controller and the controlled object, including:

[0050] Determine the model order of the controlled object based on prior knowledge of the controlled object or identification goals;

[0051] The model structure of the controlled object is:

[0052]

[0053] Where G represents the pulse transfer function of the controlled object, and Represent the coefficients of the denominator and numerator delay factor polynomials of the controlled object model, n a 、n b represent the orders of the denominator and numerator delay factor polynomials of the controlled plant model respectively;

[0054] The existing controller model is known. Assume that the existing controller has the following model structure:

[0055]

[0056] Where R represents the impulse transfer function of the controller, and Represent the coefficients of the denominator and numerator delay factor polynomials of the controller model, n p 、n q represent the orders of the denominator and numerator delay factor polynomials of the existing controller model, respectively.

[0057] 2) According to the model orders of the controller and the controlled object, as well as the output data of the controlled object, a data vector h(k) and a model parameter vector θ are set, where k represents a discrete time sequence number. The present invention assumes that the system disturbance is a signal formed by zero-mean white noise v(k) passing through a noise model. The white noise data is unmeasurable and is replaced by an estimated value of the white noise data during calculation. Therefore, the data vector h(k) is set to consist of the output data of the controlled object and an estimated value of the white noise data. The estimated value of the white noise data is correlated with the output data and the estimated value of the model parameter vector.

[0058] The data vector h(k) and the model parameter vector θ are:

[0059]

[0060] in, represents the estimated value of white noise data;

[0061]

[0062] in, is the estimated value of the model parameter vector.

[0063] In the above formula, k represents the discrete time sequence number, k, i, n a 、n b 、n p 、n q They are all integers. z(k) represents the output data of the controlled object at time k, z(k-1) represents the output data of the controlled object at time k-1, and so on. The meanings of other symbols related to k can be deduced.

[0064] 3) Select the initial values ​​for calculating the feedback gain matrix K(k) and the data covariance matrix P(k), including:

[0065] P(0)=10 12 I, I represents the identity matrix.

[0066] 4) Calculate the feedback gain matrix K(k) and the data covariance matrix P(k) according to the data vector h(k). The calculation formulas of the feedback gain matrix K(k) and the data covariance matrix P(k) are:

[0067]

[0068] 5) Calculate the estimated value of the model parameter vector The calculation formula is as follows:

[0069]

[0070] 6) Recursively calculate steps 4) and 5) until the estimated value of the model parameter vector is tends to a stable value

[0071]

[0072] 7) according to the stable value calculating the coefficient estimates of the controlled object model

[0073]

[0074] 8) based on the coefficient estimates designing the active disturbance rejection controller parameters.

[0075] After obtaining the model parameter estimates of the controlled object, the active disturbance rejection controller parameters are tuned, and there are various mature methods in the prior art. This step can use the prior art, and thus will not be described here.

[0076] Figure 3 、 Figure 4 and Figure 5 Example simulation effect diagram for verifying the effectiveness and superiority of the present application, the specific circumstances are as follows:

[0077] For the thermal process, consider the following closed-loop system, which is based on the discrete-time sequence controlled object model:

[0078] z(k) = 1.45z(k-1) - 0.65z(k-2) + 1.10u(k-1) - 0.70u(k-2) + v(k) + 0.9v(k-1) + 0.18v(k-2)

[0079] In the formula, u(k), z(k) are the input data and output data of the model, and the noise v(k) is white noise with zero mean and standard deviation of 0.5.

[0080] The above model can be expressed by the delay operator z -1 , which can be converted to the following form:

[0081] (1-1.45z -1 +0.65z -2 )z(k) = (1.10z -1 -0.70z -2 )u(k) + (1+0.9z -1 +0.18z -2 )v(k)

[0082] Thus, we can get:

[0083]

[0084] The controller model based on discrete time series is:

[0085] u(k)=1.35u(k-1)-0.35u(k-2)-0.65z(k)+0.45z(k-1)-0.10z(k-2)

[0086] Only the output data z(k) of the controlled object is used, according to Figure 2 Flowchart, step 4) and step 5) are recursively calculated. During the 3000-step recursion, the estimated values ​​of the closed-loop system model parameters change as follows: Figure 3 As shown, it can be seen that the estimated value of the parameter vector tends to a stable value during the recursive process Next, we solve the estimated values ​​of the model parameters according to the stable values ​​of the estimated values ​​of the model parameter vector, and solve the equations as follows:

[0087]

[0088] Finally, the estimated values ​​of the model parameters are obtained Wherein, d1 and d2 are the noise model parameters written into the model parameter vector.

[0089] Next, the PI controller parameters are adjusted according to the true values ​​of the model parameters to {k p =3.50,k i =2.95}, according to the model parameter estimation values ​​obtained by the present invention The ADRC controller parameters are designed as {b0=1.0,ω c =2.4,ω0=5ω c},ω c and ω0 are the specific parameters of the ADRC. The simulation is set to a closed-loop system setpoint step at 1s and a control variable step disturbance at 10s. The simulation results are shown in Figure 4 and Figure 5 The experimental results show that the ADRC tuned by the present invention has better setpoint tracking and control variable disturbance suppression performance than the PI tuned by the real model, and the control variable changes of both are within the allowable range. This demonstrates the effectiveness and superiority of the proposed method for tuning the active disturbance rejection controller based on system disturbance response.

[0090] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for tuning an active disturbance rejection controller based on system disturbance response, characterized in that: The following steps are involved: 1) Determine the model order of the controller and the controlled object; The model structure of the controlled object is: in, represents the unit delay operator, represents the pulse transfer function of the controlled object, and Respectively represent the coefficients of the denominator and numerator delay factor polynomials of the controlled object model, Respectively represent the orders of the denominator and numerator delay factor polynomials of the controlled object model; The model structure of the controller is: in, R represents the impulse transfer function of the controller, and Represent the coefficients of the denominator and numerator delay factor polynomials of the controller model, denote the orders of the denominator and numerator delay factor polynomials of the controller model respectively; 2) According to the model order of the controller and the controlled object, as well as the output data of the controlled object, set the data vector and the model parameter vector , k Represents a discrete time sequence number, and the system disturbance is zero-mean white noise v ( k ) is a signal formed by the noise model, the data vector It is composed of the output data of the controlled object and the estimated value of the white noise data, wherein the estimated value of the white noise data is related to the output data of the controlled object and the estimated value of the model parameter vector; The data vector and the model parameter vector They are: in, represents the estimated value of white noise data; in, is the estimated value of the model parameter vector; k represents a discrete time sequence number, express k The output data of the controlled object at all times, express k -1 Output data of the controlled object at time; 3) Select the feedback gain matrix and the data covariance matrix The initial value of calculation; 4) According to the data vector Calculate the feedback gain matrix and the data covariance matrix ; Calculate the feedback gain matrix and the data covariance matrix The calculation formulas are: 5) Calculate the estimated value of the model parameter vector according to the following formula : in, express k Output data of the controlled object at all times; 6) Recursively calculate steps 4) and 5) until the estimated value of the model parameter vector is Stable value ; 7) According to the stable value Calculate the estimated values ​​of each coefficient of the delay factor polynomial of the controlled object model ; 8) Based on the estimated values ​​of the coefficients Design the parameters of the active disturbance rejection controller.

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