A method and control system for realizing active disturbance rejection control based on expected dynamics

Abstract

The present invention provides an implementation method and control system of an anti-disturbance control based on expected dynamics, wherein the control implementation method includes the following steps: describing the controlled industrial system using a first-order inertia plus pure delay system; designing the expected dynamic equation of the closed-loop system; based on the designed expected dynamic equation, calculating the output value of the controlled industrial system and the control quantity of the closed-loop system through an extended state observer algorithm, obtaining the tracking value of the output value of the next calculation step of the controlled industrial system and the tracking value of the next calculation step of the total disturbance of the system; based on the obtained tracking value and the expected dynamic equation, obtaining the input values ​​of the next two calculation steps of the controlled industrial system through control law calculation, and the closed-loop system adjusts the change amount of the actuator in real time through the calculation results. The present invention can significantly reduce the difficulty of parameter setting in the implementation of anti-disturbance control, quantify the parameters in the implementation of anti-disturbance control, and has a good control effect.

Description

Technical Field

[0001] The present invention relates to the field of industrial control, and in particular to a method and a control system for realizing an anti-disturbance control based on expected dynamics. Background Art

[0002] The active disturbance rejection control algorithm has been widely concerned and applied due to its simple structure, tracking and anti-interference performance, strong robustness, etc. The active disturbance rejection control algorithm, especially the first-order active disturbance rejection control algorithm, has been successfully applied in many energy systems, motor systems, microgrid systems and motion systems.

[0003] However, the ADRC algorithm faces the challenge of difficult algorithm parameter tuning when applied in actual systems. This is because the ADRC algorithm has three or more parameters that need to be tuned, among which the parameters of the first-order ADRC algorithm are β1, β2, b0 and k. p , the parameters of the high-order ADRC algorithm are more. The parameter bandwidth method can reduce the number of parameters, but the quantitative parameter setting method that takes into account the tracking and anti-interference performance under the premise of ensuring robustness is relatively lacking. "Zhao C, Li D. Control design for the SISO system with the unknown order and the unknown relative degree. ISA Transactions, 2014, 53 (4): 858-872." proposed to calculate the parameters of the ADRC algorithm based on the proportional-integral control algorithm parameters. However, this method requires continuous trial and error adjustment of β1 and β2 from small to large, which will have an adverse effect on field applications.

[0004] In order to solve the problem of quantitative parameter tuning of the first-order active disturbance rejection control algorithm, it is necessary to provide a first-order active disturbance rejection control algorithm that can achieve more outstanding control effects. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and provide an implementation method of an auto-disturbance rejection control based on expected dynamics. By designing the expected dynamic equation of a closed-loop system, the parameters of the auto-disturbance rejection control algorithm can be directly calculated, thereby completing the implementation of the auto-disturbance rejection control algorithm. The parameters of the auto-disturbance rejection control algorithm can be quantitatively calculated, and the closed-loop system control effect after adjustment is guaranteed to be ideal, providing a quantitative parameter adjustment calculation method for the wide application of the auto-disturbance rejection control algorithm.

[0006] The characteristics and beneficial effects of the present invention are:

[0007] The present invention proposes an implementation method of active disturbance rejection control based on expected dynamics, which maintains the simple structure of the original active disturbance rejection control algorithm. The parameters that need to be adjusted can be directly calculated through the constructed closed-loop system expected dynamic equation, and the adjustable parameters are retained to further optimize the effect. The closed-loop system after adjustment has a fast tracking speed and strong anti-interference ability.

[0008] In one aspect of the present invention, a method for implementing an anti-disturbance control based on expected dynamics is provided, comprising the following steps: describing a controlled industrial system using a first-order inertia plus pure delay system; designing an expected dynamic equation of a closed-loop system; based on the designed expected dynamic equation, calculating the output value of the controlled industrial system and the control quantity of the closed-loop system through an extended state observer algorithm to obtain a tracking value of the output value of the next calculation step of the controlled industrial system and a tracking value of the next calculation step of the total disturbance of the system; based on the obtained tracking value and the expected dynamic equation, obtaining input values ​​of the next two calculation steps of the controlled industrial system through control law calculation, and the closed-loop system adjusts the change of the actuator in real time through the calculation result.

[0009] In some embodiments, the controlled industrial system is described by a first-order inertia plus pure delay system, and the mathematical expression is:

[0010]

[0011] Among them, the output value Y(s) and input value U(s) of the first-order inertia plus pure delay system are represented by y(Υ) and u(Υ) respectively in each calculation step, Υ represents the calculation step, s represents the differential operator, K represents the gain, T represents the time constant, L represents the pure lag time, and e represents the input delay;

[0012] Based on the controlled industrial system, the expected dynamic equation of the closed-loop system is designed, and the mathematical expression is:

[0013]

[0014] Among them, G d (s) represents the transfer function of the expected dynamic equation of the closed-loop system, λ represents the adjustable factor, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves. The value range of λ is [0.05,1].

[0015] In some embodiments, based on the expected dynamic equation, the current calculation step value y(Y) output by the first-order inertia plus pure delay system and the current calculation step value u(Y) input are calculated together using the extended state observer algorithm to obtain the tracking value of the next calculation step value y(Y+1) output by the first-order inertia plus pure delay system. The tracking value of the total disturbance of the first-order inertia plus pure delay system in the next calculation step

[0016] and The extended state observer algorithm is as follows:

[0017]

[0018] Wherein, h is the sampling period, β1, β2 and b0 are the parameters to be tuned for the ADRC implementation method;

[0019] β1, β2 and b0 are calculated by the following formula:

[0020] Among them, γ represents the magnification of b0, and the value range of γ is [0.1,105); k w represents the adjustment factor of the extended state observer algorithm, k w The larger the value, the faster the closed-loop system moves. w The smaller the k, the slower the closed-loop system moves. w The value range is [0.05,105].

[0021] In some embodiments, the total disturbance of the first-order inertia plus pure delay system is obtained as the tracking value of the next calculation step And the tracking value of the next calculation step value y(Υ+1) output by the first-order inertia plus pure delay system Combined with the next calculation step value r(Υ+1) of the set value output of the first-order inertia plus pure delay system, the next two calculation step values ​​u(Υ+2) of the first-order inertia plus pure delay system input are obtained through the control law algorithm;

[0022] The calculation method of the next two calculation step sequence values ​​u(Υ+2) of the first-order inertia plus pure delay system input is as follows:

[0023]

[0024] or

[0025]

[0026] Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula:

[0027]

[0028] The next calculation step sequence value u(Υ+1) of the first-order inertia plus pure delay system input is updated to the next two calculation step sequence value u(Υ+2) of the first-order inertia plus pure delay system input. The controlled industrial system adjusts the change of the actuator in real time based on u(Υ+2) to realize the control quantity adjustment of the closed-loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a block diagram of the active disturbance rejection control system of the present invention.

[0030] Figure 2 It is a step diagram of the method for implementing the active disturbance rejection control based on expected dynamics of the present invention.

[0031] Figure 3 It is the set value, the output value of the method of the present invention and the output value of the comparative method. DETAILED DESCRIPTION

[0032] Various exemplary embodiments of the present invention will be described in detail below in conjunction with specific embodiments. The description of the exemplary embodiments is merely illustrative and is not intended to be any limitation on the present invention and its application or use. The present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to make the present invention thorough and complete and to fully express the scope of the present invention to those skilled in the art. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps described in these embodiments should be interpreted as being merely exemplary and not as a limitation.

[0033] All terms (including technical terms or scientific terms) used in the present invention have the same meanings as those understood by ordinary technicians in the field to which the present invention belongs, unless otherwise specifically defined. It should also be understood that terms defined in general dictionaries should be interpreted as having meanings consistent with their meanings in the context of the relevant technology, and should not be interpreted in an idealized or extremely formal sense, unless explicitly defined herein.

[0034] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0035] refer to Figure 1 This embodiment provides an active disturbance rejection control system based on expected dynamics, including a control law calculator for performing control law calculation, an extended state observer for performing extended state observer algorithm calculation, and a controlled industrial system controller; the control law calculator, the extended state observer, and the controlled industrial system controller are communicatively connected to implement an active disturbance rejection control implementation method based on expected dynamics.

[0036] refer to Figure 2 A technical solution for implementing the active disturbance rejection control method based on expected dynamics under the active disturbance rejection control system specifically includes the following steps:

[0037] S1: The controlled industrial system is described by a first-order inertia plus pure delay system. The mathematical expression is:

[0038]

[0039] Among them, the output value Y(s) and input value U(s) of the first-order inertia plus pure delay system are represented by y(Υ) and u(Υ) respectively in each calculation step, Υ represents the calculation step, s represents the differential operator, K represents the gain, T represents the time constant, L represents the pure lag time, and e represents the input delay;

[0040] In this embodiment, the gain of the first-order inertia plus pure delay system is -10 8 ≤K≤10 8 And K is not zero, the time constant of the first-order inertia plus pure delay system is 0<T≤10 8 , the pure lag time of the first-order inertia plus pure delay system is 0<L≤10 8 In the actual controlled industrial system (transfer function is ), the gain of the first-order inertia plus pure delay system is K=1, the time constant of the first-order inertia plus pure delay system is T=6.6181, and the pure lag time of the first-order inertia plus pure delay system is L=3.48.

[0041] S2: Based on the controlled industrial system, the expected dynamic equation of the closed-loop system is designed. The mathematical expression is:

[0042]

[0043] Among them, G d (s) represents the transfer function of the expected dynamic equation of the closed-loop system, λ represents the adjustable factor, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves. The value range of λ is [0.05,1]. In the actual controlled industrial system, the value range of λ is 0.4.

[0044] S3: Based on the expected dynamic equation, the current calculation step value y(Υ) output by the first-order inertia plus pure delay system and the current calculation step value u(Υ) input are calculated together using the extended state observer algorithm to obtain the tracking value of the next calculation step value y(Υ+1) output by the first-order inertia plus pure delay system The tracking value of the total disturbance of the first-order inertia plus pure delay system in the next calculation step

[0045] and The extended state observer algorithm is as follows:

[0046]

[0047] Wherein, h is the sampling period, β1, β2 and b0 are the parameters to be tuned for the ADRC implementation method;

[0048] β1, β2 and b0 are calculated by the following formula:

[0049] Among them, γ represents the magnification of b0, k w represents the adjustment factor of the extended state observer algorithm, k w The larger the value, the faster the closed-loop system moves. w The smaller the value, the slower the closed-loop system moves. In this embodiment, the value range of h is [0.00001, 102]; the value range of γ is [0.1, 105), and k w The value range of is [0.05,105]. In the actual controlled industrial system, the value of h is 0.0005; the value of γ is 2, k w The value of is 40; the calculated b0 value is 2, β1 value is 7.9222 and β2 value is 15.6903.

[0050] S4: The tracking value of the total disturbance of the first-order inertia plus pure delay system in the next calculation step And the tracking value of the next calculation step value y(Υ+1) output by the first-order inertia plus pure delay system Combined with the next calculation step value r(Υ+1) of the set value output of the first-order inertia plus pure delay system, the next two calculation step values ​​u(Υ+2) of the first-order inertia plus pure delay system input are obtained through the control law algorithm;

[0051] The calculation method of the next two calculation step sequence values ​​u(Υ+2) of the first-order inertia plus pure delay system input is as follows:

[0052]

[0053] or

[0054]

[0055] Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula:

[0056]

[0057] In the actual controlled industrial system, the control law adopted is The value of h is 0.0005; the value of γ is 2, and the value of k w The value of is 40; the calculated k p The value is 0.1533.

[0058] S5: Update the next calculation step sequence value u(Υ+1) of the first-order inertia plus pure delay system input to the next two calculation step sequence value u(Υ+2) of the first-order inertia plus pure delay system input obtained in step S4. The controlled industrial system adjusts the change of the actuator in real time based on u(Υ+2) to realize the control adjustment of the closed-loop system.

[0059] refer to Figure 3 , showing the set value, output value and output value obtained by the active disturbance rejection control implementation method of this embodiment (Zhao C, Li D. Control design for the SISO system with the unknown order and the unknown relative degree. ISA Transactions, 2014, 53 (4): 858-872.) of the comparison method; wherein the parameters of the active disturbance rejection control algorithm of the comparison method are b0 value of 10, β1 value of 100, β2 value of 50 and k p The value is 1.2, the thin solid line is the set value obtained by using the method of this embodiment, the thick solid line is the output value of the method of this embodiment, and the dotted line is the output value of the comparative method.

[0060] The specific simulation process is as follows: at the beginning of the simulation, the system is in a steady state, at 10s the set value is changed from 0 to 1, at 100s the closed loop is disturbed by the control quantity, from 0 to 1, until a steady state is reached at 200s. As can be seen from the figure, the method for implementing the auto-disturbance rejection control of this embodiment can have a fast tracking speed and a strong anti-disturbance capability, can significantly reduce the difficulty of parameter setting in the implementation of the auto-disturbance rejection control, and shows a strong application potential, thus illustrating the effectiveness of the method of this embodiment, and can simply and conveniently implement the auto-disturbance rejection control algorithm.

[0061] Although the inventors have elaborated and listed the basic principles, main features and technical solutions of the present invention in relatively detail, it should be understood that it is obvious for those skilled in the art to modify the above embodiments or adopt equivalent alternatives. Any modification or improvement made without departing from the spirit of the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method for implementing active disturbance rejection control based on expected dynamics, characterized in that: The following steps are involved: Step 1: describe the controlled industrial system using a first-order inertia plus pure delay system; design the expected dynamic equation of the closed-loop system; In step 1, the controlled industrial system is described by a first-order inertia plus pure delay system, and the mathematical expression is: Among them, the output value Y(s) and input value U(s) of the first-order inertia plus pure delay system are represented by y(Υ) and u(Υ) respectively in each calculation step, Υ represents the calculation step, s represents the differential operator, K represents the gain, T represents the time constant, L represents the pure lag time, and e represents the input delay; Based on the controlled industrial system, the expected dynamic equation of the closed-loop system is designed, and the mathematical expression is: Among them, G d (s) represents the transfer function of the expected dynamic equation of the closed-loop system, λ represents the adjustable factor, the larger the λ is, the slower the closed-loop system moves, and the smaller the λ is, the faster the closed-loop system moves. The value range of λ is [0.05,1]; Step 2: Based on the designed expected dynamic equation, the output value of the controlled industrial system and the control quantity of the closed-loop system are calculated by the extended state observer algorithm to obtain the tracking value of the output value of the next calculation step of the controlled industrial system and the tracking value of the next calculation step of the total disturbance of the system; Based on the expected dynamic equation, the current calculation step value y(Υ) output by the first-order inertia plus pure delay system and the current calculation step value u(Υ) input are calculated together using the extended state observer algorithm to obtain the tracking value of the next calculation step value y(Υ+1) output by the first-order inertia plus pure delay system The tracking value of the total disturbance of the first-order inertia plus pure delay system in the next calculation step and The extended state observer algorithm is as follows: Wherein, h is the sampling period, β1, β2 and b0 are the parameters to be tuned for the ADRC implementation method; β1, β2 and b0 are calculated by the following formula: Among them, γ represents the magnification of b0, and the value range of γ is [0.1,105); k w represents the adjustment factor of the extended state observer algorithm, k w The larger the value, the faster the closed-loop system moves. w The smaller the k, the slower the closed-loop system moves. w The value range of is [0.05,105]; Step 3: Based on the obtained tracking value and the expected dynamic equation, the input values ​​of the next two calculation steps of the controlled industrial system are calculated by the control law, and the closed-loop system adjusts the change of the actuator in real time according to the calculation results; In step 3, the total disturbance of the first-order inertia plus pure delay system is obtained as the tracking value of the next calculation step And the tracking value of the next calculation step value y(Υ+1) output by the first-order inertia plus pure delay system Combined with the next calculation step value r(Υ+1) of the set value output of the first-order inertia plus pure delay system, the next two calculation step values ​​u(Υ+2) of the first-order inertia plus pure delay system input are obtained through the control law algorithm; The calculation method of the next two calculation step sequence values ​​u(Υ+2) of the first-order inertia plus pure delay system input is as follows: or Among them, k p is the parameter to be adjusted in the implementation of the active disturbance rejection control, which is calculated by the following formula: The next calculation step sequence value u(Υ+1) of the first-order inertia plus pure delay system input is updated to the next two calculation step sequence value u(Υ+2) of the first-order inertia plus pure delay system input. The controlled industrial system adjusts the change of the actuator in real time based on u(Υ+2) to realize the control quantity adjustment of the closed-loop system.

2. An active disturbance rejection control system based on expected dynamics, characterized in that: include: A control law calculator for performing control law calculation, an extended state observer for performing extended state observer algorithm calculation, and a controlled industrial system controller; The control law calculator, the extended state observer and the controlled industrial system controller are communicatively connected to implement the method for realizing the active disturbance rejection control based on expected dynamics as described in claim 1.

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