A model reference adaptive disturbance rejection optimal control method

Abstract

The application discloses a model reference self-adapting anti-interference optimization control method, which utilizes a model reference system to generate a first control signal through a model reference self-adapting method; a second control signal generated by a PD controller after disturbance compensation in an actual system is acquired; the first control signal and the second control signal are added as a total control signal, the total control signal is utilized to control an object to be controlled, and an actual system output is acquired; the actual system output and the total control signal are input into an extended state observer in the actual system to obtain an estimated value of total disturbance, and the estimated value of total disturbance is utilized to perform feedback compensation on total disturbance of the actual system; an error between a reference model output in the model reference system and the actual system output is utilized to construct a Lyapunov function based on the error, an adaptive law is obtained, the first control signal is updated, the effect of system self-adapting and reducing output error is achieved, and the system is more stable and has stronger anti-disturbance capability.

Description

Technical Field

[0001] This invention discloses a model reference adaptive disturbance rejection optimization control method, which belongs to the field of active disturbance rejection control technology. Background Technology

[0002] Active Disturbance Rejection Control (ADRC) is a control technique that originated from a reflection on classical control theory. It is based on the standard form of feedback systems (integrator cascade type) and aims to improve the robustness of engineering control. Its core idea is to start with PID control, which is dominant in industry, and to introduce the concept of ADRC by improving nonlinear PID. The algorithm is simple and can maintain control accuracy even under the influence of unknown strong nonlinearities and uncertain strong disturbances.

[0003] Active disturbance rejection control currently mainly includes three aspects: nonlinear tracking differentiators, extended state observers (ESOs), and the design of a series of active disturbance rejection control laws.

[0004] ESO can estimate not only the state but also the "total disturbance," giving ADRC a significant advantage in handling nonlinearity, uncertainty, and disturbances. Satisfactory control performance can be achieved by adjusting the controller and observer bandwidths. However, for ADRC, the bandwidth of real-world systems is often limited, and high bandwidth can introduce high-frequency noise. Limited bandwidth can lead to inaccurate ESO estimation, resulting in significant estimation errors and affecting system dynamics. Summary of the Invention

[0005] The purpose of this application is to provide a model reference adaptive disturbance rejection optimization control method to solve the problems of unsatisfactory system dynamics when bandwidth is limited and the introduction of high-frequency noise when bandwidth is high in existing active disturbance rejection control technology.

[0006] This invention provides a model reference adaptive disturbance rejection optimization control method, comprising:

[0007] The first control signal u is generated using a model reference system and a model reference adaptation method. ad ;

[0008] In the actual system, the second control signal u′ generated by the PD controller after disturbance compensation is obtained. adrc ;

[0009] The first control signal u ad Second control signal u′ adrc The sum is used as the total control signal u, which is then used to control the controlled object to obtain the actual system output y. p ;

[0010] The actual system output y p The total control signal u is input into the extended state observer in the actual system to obtain an estimate of the total disturbance. Reuse Feedback compensation is provided for the total disturbance of the actual system;

[0011] Using the reference model output y in the model reference system m and the actual system output y p The error between the two signals is used to construct an error-based Lyapunov function to obtain an adaptive law, which is then used to update the first control signal u. ad .

[0012] Preferably, the actual system output y p It satisfies the first formula, which is:

[0013]

[0014] In the formula, For y p The second derivative of f, where f is the total perturbation. k is an estimate of the total disturbance. p k is the proportional gain of the PD controller. d Z1 is the differential coefficient of the PD controller, r is the setpoint, z1 is the estimated value of the actual system output, and z2 is the first derivative of the actual system output. The estimated value, b0 is the gain parameter, u is the total control signal, u ad This is the first control signal.

[0015] Preferably, the first control signal u is updated. ad Specifically, it includes:

[0016] Update the first control signal u using the second formula ad The second formula is:

[0017]

[0018] In the formula, b0 is the gain parameter, k c =Γ1+Γ2+Γ3, where P, Γ1, Γ2, and Γ3 are all positive definite matrices, and B k T ∈R 2 Let e ​​be a constant row vector, e∈R 2 Output y for the reference model m and the actual system output y p The column vector consists of the error between them and the first derivative of the error.

[0019] Preferably, e is determined according to a third formula, which is:

[0020] e = x m -x p

[0021] In the formula, x m Let x be the state vector of the model reference system. p This is the state vector of the actual system.

[0022] Preferably, the first control signal u is generated using a model reference system and a model reference adaptive method. ad Specifically, it includes:

[0023] The first control signal u is given according to the fourth formula. ad The fourth formula is:

[0024]

[0025] In the formula, k1, k2, and k3 are adjustable parameters, and b0 is the gain parameter.

[0026] The model-referenced adaptive disturbance rejection optimization control method of the present invention has the following advantages compared with the prior art:

[0027] This invention employs a control strategy that combines Model Reference Adaptive Control (MRAC) and Active Disturbance Rejection Control (ADRC), achieving satisfactory results that ADRC alone cannot achieve. Specifically:

[0028] (1) When the ADRC bandwidth parameter is low, the system will produce overshoot. Only by increasing the bandwidth can the overshoot be reduced or eliminated, but high bandwidth will introduce noise. However, the Model Reference Active Disturbance Rejection Control (MRADRC) of this invention can adjust the independent gain parameter k c This eliminates the estimation error of ESO, increases the stability of the system, and does not introduce noise;

[0029] (2) In terms of disturbance rejection capability, MRADRC also has superior performance compared to ADRC, and k c The larger the value, the stronger the anti-interference ability of MRADRC;

[0030] (3) MRADRC introduces an independent gain parameter k c This can increase the flexibility of control system design. Attached Figure Description

[0031] Figure 1 This is the control structure diagram corresponding to the method of the present invention;

[0032] Figure 2 In the example, (a) and (b) represent ω. o =10,ω c =5 and ω o =50,ω c Comparison of ADRC and MRADRC simulation results at =5;

[0033] Figure 3 In (a), ω0 = 10, ω c When ω = 5, the control signal generated by MRADRC is (b) ω0 = 10, ω c The control signal generated by ADRC when =5;

[0034] Figure 4 (a) in the equation is k c =The effect of 20 on the MRADRC control effect, (b) is k c =400 influence diagram on MRADRC control effect, (c) is k c =800 Effect diagram on MRADRC control effect, (d) is k c The effect of 2000 on the MRADRC control effect;

[0035] Figure 5 (a) in the equation is k c =20 MRAC control quantity u ad Comparison chart, (b) represents k c =400 MRAC control quantity u ad Comparing the graphs, (c) represents k. c =800 MRAC control quantity u ad Comparison chart, (d) represents k c =2000 MRAC control quantity u ad Comparison chart;

[0036] Figure 6 In the diagram, (a) represents the value of k after the step perturbation is added. c Comparison of disturbance rejection performance between MRADRC and ADRC at 30°C, (b) shows the performance after adding a step disturbance, k c Comparison of disturbance rejection performance between MRADRC and ADRC at 500, (c) shows the performance after adding a step disturbance, k c Comparison of disturbance rejection performance of MRADRC and ADRC at 3000, (d) after adding step disturbance, is k c Comparison of interference immunity performance between MRADRC and ADRC at 300,000;

[0037] Figure 7 In the diagram, (a) represents the value of k after adding a sinusoidal perturbation. c Comparison of disturbance rejection performance between MRADRC and ADRC at 50°, (b) shows the performance after adding sinusoidal disturbance, k c Comparison of disturbance rejection performance between MRADRC and ADRC at 500, (c) shows the performance after adding sinusoidal disturbance, k c Comparison of disturbance rejection performance between MRADRC and ADRC at 2000, (d) shows the performance after adding sinusoidal disturbance, k c Comparison of the anti-interference performance of MRADRC and ADRC at 30000. Detailed Implementation

[0038] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0039] To ensure the system maintains the desired dynamic response even with limited bandwidth, this invention introduces a model reference adaptive control (MRADRC) approach. This approach combines the advantages of active disturbance rejection control (ADRC) estimation, disturbance compensation, and error correction to make the system output approximate the reference model, achieving the desired control effect while also providing greater flexibility in controller design. The control algorithm used in this invention is Model Reference Active Disturbance Rejection Control (MRADRC).

[0040] Figure 1 The control structure used in this invention includes a model reference system and an actual system;

[0041] The model reference system includes a reference model and an adaptive mechanism connected in sequence; the actual system is a second-order active disturbance rejection control (ADRC) closed-loop system. In this embodiment of the invention, the model reference system is a system formed through a model reference adaptive method, and the reference model is the transfer function of an ideal second-order ADRC closed-loop system. The actual system is a standard second-order ADRC closed-loop system. Figure 1 In this context, u0 represents the control signal generated by the PD controller in the actual system; u′ adrc This is the second control signal generated by the PD controller in the actual system after disturbance compensation; u adThe first control signal is generated for MRAC using a model reference adaptive method. This invention combines ADRC and MRAC, specifically: MRAC generates an independent first control signal, which is added to the second control signal generated by the PD controller in the actual system after disturbance compensation. This sum is then fed into the ESO as the total control signal. The total disturbance is estimated using the total control signal and the actual system output. Compensation can eliminate the impact of the disturbance on the actual system. The ideal output of the model reference system (i.e.,...) is then used. Figure 1 The reference model output y m ) and the actual system output (i.e. Figure 1 y in p The error between the two systems is calculated using Lyapunov functions to derive an adaptive law, which continuously reduces the error, gradually bringing the actual system closer to the model reference system. The detailed method corresponding to this idea is as follows:

[0042] Step 1: Using a model reference system, generate the first control signal u through a model reference adaptive method. ad .

[0043] In this embodiment of the invention, the model reference system is a system formed through a model reference adaptive method, and the reference model is the transfer function of an ideal second-order ADRC closed-loop system. The model reference adaptation method is a method already in the art and will not be described in detail here.

[0044] Step 2: Obtain the second control signal u′ generated by the PD controller after disturbance compensation in the actual system. adrc .

[0045] In this embodiment of the invention, the actual system is a second-order active disturbance rejection control closed-loop system, in which u0 is the control signal generated by the PD controller in the actual system; u′ adrc This is the second control signal generated by the PD controller in the actual system after disturbance compensation.

[0046] Step 3: Set the first control signal u ad Second control signal u′ adrc The sum is used as the total control signal u, which is then used to control the controlled object to obtain the actual system output y. p .

[0047] Step 4: Output y from the actual system p The total control signal u is input into the extended state observer in the actual system to obtain an estimate of the total disturbance. Reuse Feedback compensation is provided for the total disturbance of the actual system.

[0048] Step 5: Utilize the ideal output of the model reference system (i.e., the output y of the reference model in the model reference system). m ) and the actual system output y p The error between the two signals is used to construct a Lyapunov function, which yields an adaptive law to update the first control signal u. ad .

[0049] The actual system output y in the above method p It satisfies the first formula, which is:

[0050]

[0051] In the formula, For y p The second derivative of f, where f is the total perturbation. k is an estimate of the total disturbance. p k is the proportional gain of the PD controller. d Z1 represents the differential coefficient of the PD controller, r is the setpoint, and z1 is the actual system output y. p The estimated value, z2 is the first derivative of the actual system output. The estimated value, b0 is the gain parameter, u is the total control signal, u ad This is the first control signal.

[0052] Furthermore, update the first control signal u ad Specifically, it includes:

[0053] Update the first control signal u using the second formula ad The second formula is:

[0054]

[0055] In the formula, b0 is the gain parameter, k c =Γ1+Γ2+Γ3, where P, Γ1, Γ2, and Γ3 are all positive definite matrices, and B k T ∈R 2 Let e ​​be a constant row vector, e∈R 2 Output y for the reference model m and the actual system output y p The column vector formed by the errors between them and their first derivatives is determined according to the third formula, which is: e = x m -x p .

[0056] In the formula, x m Let x be the state vector of the model reference system. p This is the state vector of the actual system.

[0057] The first control signal u is generated using a model reference system and a model reference adaptation method. ad Specifically, it includes:

[0058] The first control signal u is given according to the fourth formula. ad The fourth formula is:

[0059]

[0060] In the formula, k1, k2, and k3 are adjustable parameters (real numbers), and b0 is the gain parameter.

[0061] In this invention, the adaptive law u ad The derivation process is as follows:

[0062] like Figure 1 As shown, let the state vector of the model reference system be... Therefore, its state equation can be obtained as follows:

[0063]

[0064] In equation (1), Let x be the state vector of the model reference system. m First derivative, k p k is the proportional gain of the PD controller. d denoted by , where r is the differential coefficient of the PD controller, and r is the setpoint.

[0065] Combination Figure 1 According to ADRC knowledge, the actual system output y p satisfy:

[0066]

[0067] In equation (2), y p For the actual system output, For y p The second derivative of f, where f is the total perturbation. k is an estimate of the total disturbance. p k is the proportional gain of the PD controller. d Z1 represents the derivative coefficient of the PD controller, r is the setpoint, and z1 is the derivative coefficient of y. p The estimated value, z2 is the first derivative of the actual system output. The estimated value, b0 is the gain parameter, u is the total control signal, u ad This is the first control signal.

[0068] Let the state variables of the actual system be...

[0069] The ESO estimation error is The state equation of the actual system is then:

[0070]

[0071] Let the system's generalized error vector be:

[0072]

[0073] From equations (1), (3), and (4), the generalized error state equation can be obtained as follows:

[0074]

[0075]

[0076]

[0077] In equation (6), k1, k2, and k3 are adjustable parameters of the model reference system, and b0 is the gain parameter.

[0078] Assume when k1 = k1 * k2=k2 * k3=k3 * At that time, the actual system and the model reference system achieve a perfect match, that is, μ = 0 in equation (3), which satisfies:

[0079]

[0080] In equation (7), k1, k2, and k3 are adjustable parameters of the model reference system. These are the values ​​of k1, k2, and k3 when the actual system and the model reference system achieve a match.

[0081] Substituting equations (6) and (7) into equation (5), we get:

[0082]

[0083] Construct a positive definite quadratic form as a Lyapunov function:

[0084]

[0085] In equation (9), P, Both are positive definite matrices, e T For the transpose of e, for transpose, for transpose, for The transpose of .

[0086] Differentiating both sides of the above equation with respect to time yields:

[0087]

[0088] because and If it is a constant, then

[0089]

[0090] Because A m To be a stable matrix, we can choose a positive definite matrix Q such that A m T P+PA m =-Q holds true. Combining equation (11), equation (10) can be transformed into

[0091]

[0092] because

[0093]

[0094] For the system to be stable, the following must be satisfied: Can make

[0095]

[0096] (15)

[0097]

[0098] Combining equation (8), we can obtain

[0099]

[0100] Therefore, the model reference adaptive law can be derived as follows:

[0101] Where k c =Γ1+Γ2+Γ3.

[0102] The embodiments of this invention are mainly aimed at MRADRC (structure as shown in the figure). Figure 1 ) and a single ADRC (structure and Figure 1 Two control strategies (with the same actual system) are compared in terms of parameter adjustment, system stability, and anti-disturbance performance, thus demonstrating the superiority of the MRADRC control strategy.

[0103] (1) Comparison of MRADRCA and ADRC control effects under the same bandwidth

[0104] Figure 1 The reference signal uses a unit step, i.e., r(t) = 1(t), with a step time of 1 second; the controlled object model uses... The reference model uses the standard second-order ADRC ideal closed-loop system transfer function, i.e. For example, to obtain a comparison of the control effects of ADRC and MRADRC. Figure 2 As shown.

[0105] Where b0 = 1, and the adaptive law gain k c =2000. For example... Figure 2 As shown in (a), ADRC will overshoot when the observer bandwidth is low, but MRADRC can be adjusted by changing the independent parameter k. c Achieve good results; such as Figure 2 As shown in (b), for ADRC to achieve the same good results as MRADRC, the observer bandwidth ω must be increased. o The value is around 50. Therefore, under the same low bandwidth conditions, MRADRC has better control performance than ADRC.

[0106] like Figure 3 The diagram shows the same bandwidth (ω0=10, ω c Comparison of MRADRC and ADRC control quantities under parameters b0 (b0=1) and b0 (b0=5) (k) c =2000), where Figure 3 u shown in (a) ad This refers to the control signal generated by the model reference system in the MRADRC control strategy (i.e., the first control signal mentioned above). Figure 3 (b) shows u adrc This refers to the control signal in a single ADRC control strategy (i.e., the control signal that directly enters the controlled object). It can be seen that ADRC overshoots around 2 seconds, at which point MRAC will generate a negative control signal u through an adaptive law. ad Therefore, in the MRADRC control strategy, the negative value of u ad This will offset the overshoot caused by insufficient bandwidth in ADRC, thereby stabilizing the system.

[0107] (2)k c Impact of value on MRADRC control effect

[0108] like Figure 4 This is a comparison graph showing the effect of MRADRC control under different values, with the observer bandwidth ω in four cases. o Both are 10, controller bandwidth ω c All are 5, and the b0 value is 1 for all. (From...) Figure 4 It can be seen that, with bandwidth and b0 value remaining unchanged, increasing k... c The overshoot of the output response gradually decreases, indicating that k c The larger the value, the better the control effect.

[0109] Figure 5 The following shows the four types of k mentioned above. c Value, the control quantity u generated by MRAC ad The comparison chart, from Figure 5 As can be seen from this, at the moment when overshoot occurs, as k... c As the value increases, the MRAC generates a negative control quantity u through the adaptive law. ad The larger the absolute value, the greater its "counteracting force" against overshoot; therefore, the smaller the overshoot, the better the control effect.

[0110] (3) Comparison of interference immunity capabilities between MRADRC and ADRC

[0111] exist Figure 1 A step disturbance with an amplitude of 5 and a step time of 3s is added to the total control signal u shown. Let ω... o =10, ω c =5, b0=1. For example... Figure 6 The figure shows a comparison of the disturbance rejection performance of MRADRC and ADRC after adding a step disturbance. Figure 6 It can be seen that adding a perturbation will have a significant impact on the system, at k c When the value is small, both MRADRC and ADRC exhibit poor disturbance rejection performance, but as k increases... c As the value increases, the disturbance rejection capability of MRADRC improves, and the impact of disturbances on the system weakens.

[0112] exist Figure 1 A sinusoidal disturbance with frequency 1, phase 0, and amplitude 3 is added to the total control signal u shown. Let ω... o =10, ω c =5, b0=1. For example... Figure 7 The figure shows the effect of adding a sinusoidal perturbation at different k values. c Comparison of interference immunity performance between MRADRC and ADRC at certain values. Figure 7 It can be seen that, under low bandwidth conditions, as k... c As the value increases, the overshoot and fluctuations caused by disturbances to the MRADRC system are significantly reduced, and the system stability is significantly improved. However, ADRC has poor disturbance rejection performance due to the limitation of bandwidth parameters.

[0113] This invention employs a control strategy that combines Model Reference Adaptive Control (MRAC) and Active Disturbance Rejection Control (ADRC), achieving satisfactory results that ADRC alone cannot achieve. Specifically:

[0114] (1) When the ADRC bandwidth parameter is low, the system will produce overshoot. Only by increasing the bandwidth can the overshoot be reduced or eliminated, but high bandwidth will introduce noise. However, the Model Reference Adaptive Disturbance Rejection Optimal Control (MRADRC) proposed in this application can adjust the independent gain parameter k.c This eliminates the estimation error of ESO, increases the stability of the system, and does not introduce noise;

[0115] (2) In terms of disturbance rejection capability, MRADRC also has superior performance compared to ADRC under the same bandwidth conditions, and k c The larger the value, the stronger the anti-interference ability of MRADRC;

[0116] (3) MRADRC introduces an independent gain parameter k c This can increase the flexibility of control system design.

[0117] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A model reference adaptive disturbance rejection optimization control method, characterized in that, include: The first control signal is generated using a model reference system and a model reference adaptation method. ; In the actual system, the second control signal generated by the PD controller after disturbance compensation is obtained. ; The first control signal Second control signal Sum as the overall control signal Using the master control signal Control the controlled object and obtain the actual system output. ; Output of the actual system and total control signal The input is fed into the extended state observer of the actual system to obtain an estimate of the total disturbance. reuse Feedback compensation is provided for the total disturbance of the actual system; Using the reference model output in the model reference system and actual system output The error between the two signals is used to construct an error-based Lyapunov function, which yields an adaptive law to update the first control signal. Specifically, it includes: Update the first control signal using the second formula The second formula is: ， In the formula, For gain parameters, , All are positive definite matrices. A constant row vector, Output for reference model and actual system output The column vector consists of the error between them and the first derivative of the error.

2. The model reference adaptive disturbance rejection optimization control method according to claim 1, characterized in that, Actual system output It satisfies the first formula, which is: ， In the formula, for The second derivative, For the total disturbance, This is an estimate of the total disturbance. The proportional gain of the PD controller. The differential coefficients of the PD controller are... For setting value, This is an estimated value output by the actual system. Output the first derivative of the actual system The estimated value, For gain parameters, This is the main control signal. This is the first control signal.

3. The model reference adaptive disturbance rejection optimization control method according to claim 1, characterized in that, According to the third formula, the formula is as follows: ， In the formula, For the state vector of the model reference system, This is the state vector of the actual system.

4. The model reference adaptive disturbance rejection optimization control method according to claim 1, characterized in that, The first control signal is generated using a model reference system and a model reference adaptation method. Specifically, it includes: The first control signal is given according to the fourth formula. The fourth formula is: ， In the formula, It is an adjustable parameter. This is the gain parameter.

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