Nonlinear system command filter control method, system and controller based on dominance function

Abstract

This invention discloses a command filtering control method, system, and controller for nonlinear systems based on a dominant function, belonging to the field of intelligent control technology. The command filtering control method includes the following steps: S1: establishing an uncertain strict feedback nonlinear dynamic system model; S2: designing a general command filter based on a dominant function; S3: determining the desired output trajectory of the nonlinear system and calculating the tracking error; S4: designing a control input signal u to make the tracking error approach zero. This invention, by designing a novel general command filter based on a dominant function, allows the command filter parameters to be arbitrarily positive numbers and enables the control system to maintain global stability. Furthermore, this control method can significantly reduce the complexity of control design, making the design of intelligent controllers simpler and easier.

Description

Technical Field

[0001] This invention relates to the field of intelligent control technology, and in particular to a nonlinear system command filtering control method, system, and controller based on a dominant function. Background Technology

[0002] Command filtering is a control strategy used to improve system controllability. Based on filter and feedback control principles, it reduces the impact of high-frequency noise by filtering system commands, thereby achieving a smoother system response and better control accuracy. The key to command filtering control lies in selecting an appropriate controller architecture to ensure system stability and rapid response.

[0003] The design of high-order control systems using command filtering controllers typically requires the derivatives of intermediate commands. However, calculating these derivatives often leads to an explosive increase in control design complexity, known as "differential explosion." Currently, the following method is commonly used when filtering commands: Figure 1 The method shown, where α is the instruction before filtering, α f This is the filtered instruction, and y is the error generated by the instruction filtering: y = α - α f The filtered instruction α is used. f Control design can avoid the "differential explosion," while the existing filter's command α... f The derivative is usually Where c0 is a constant, this method greatly reduces the complexity of control design, but existing instruction sets still have the following shortcomings:

[0004] (1) The selection of parameters for the command filter is very difficult; because the parameters of the command filter need to be calculated based on the maximum value of the derivative of α, the selection of parameters is very difficult.

[0005] (2) The introduction of command filters leads to the inability of the control system to be globally stable; the parameters of the existing command filters depend on the initial values ​​of the system state variables. When the initial values ​​change, the filter parameters also need to change accordingly, so the control system cannot be globally stable.

[0006] (3) If there are unknown parameters in the controlled system, the filter parameters cannot be selected; since the command filter parameters need to be calculated based on the maximum value of the derivative of α, the maximum value of the derivative of α cannot be calculated when there are unknown parameters in the controlled system. Summary of the Invention

[0007] To address the aforementioned problems, this invention aims to provide a nonlinear system command filtering control method, system, and controller based on a dominant function, which overcomes the difficulty in selecting filter parameters and significantly reduces the complexity of control design.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0009] A command filtering control method for nonlinear systems based on a dominant function is characterized by comprising the following steps:

[0010] S1: Establish an uncertain strict feedback nonlinear dynamic system model;

[0011] S2: Design a general instruction filter based on the dominance function;

[0012] S3: Determine the desired output trajectory of the nonlinear system and calculate the tracking error;

[0013] S4: Design the control input signal u to make the tracking error approach 0.

[0014] Furthermore, the uncertain strict feedback nonlinear dynamic system model in step S1 is as follows:

[0015]

[0016] In the formula, Let x1, ..., x2 be the state vector of the nonlinear dynamic system. n Let be the physical quantity in the system; u∈R is the control input signal, and y∈R is the output signal of the system; It is a known nonlinear characteristic function of the system. Let be an unknown nonlinear characteristic function of the system, and satisfy . in, It is a known continuously differentiable function, i = 1, ..., n.

[0017] Furthermore, the general instruction filter based on the dominant function in step S2 is... In the formula, φ(·) is about The dominant function, It concerns x1, ..., x n A function; if there exists a positive number y * Make |y|≥y * ,but It is established, where d0, d1, d2, ..., d n It is an arbitrary constant.

[0018] Furthermore, in step S3, let the desired output trajectory of the nonlinear system be y. d Then the tracking error e1 = x1 - y d .

[0019] Furthermore, the specific operation of step S4 includes the following steps:

[0020] S401: Define intermediate variable α1 according to the first-order subsystem.

[0021]

[0022] In the formula, ε1 and k1 are arbitrarily positive design parameters;

[0023] S402: Design the instruction filter based on the dominance function for the first-order subsystem.

[0024]

[0025] In the formula, τ1 and c1 are arbitrarily positive design parameters. It is about The dominant function, α 1，f It is the signal obtained after filtering the virtual control quantity α1, and λ(t) is a time-varying function;

[0026] S403: Calculate the tracking error e i =x i -α i-1 i = 2;

[0027] S404: Calculate the intermediate variable α based on the i-th order subsystem. i ,

[0028]

[0029] S405: Design the instruction filter based on the dominant function for the i-th order subsystem as follows:

[0030]

[0031] S406: Let i = i + 1 and perform the update iteration. If i = n + 1, stop the calculation; otherwise, go to step S403:

[0032] S407: Let the system control input signal be u = α n The resulting u is the system control input signal of the command filter based on the dominant function.

[0033] Furthermore, the specific expression for λ(t) in step S402 is as follows: In the formula, T s It is any positive design parameter.

[0034] Furthermore, the present invention also includes a nonlinear system command filter controller based on a dominant function, the controller being used to execute the control method as described above.

[0035] Furthermore, the present invention also includes a nonlinear system command filtering control system based on a dominant function, the control system including the controller as described above.

[0036] The beneficial effects of this invention are:

[0037] 1. This invention designs a command filter based on a dominant function. Compared to existing command filters, the parameters of the command filter based on the dominant function can be any positive number, overcoming the difficulty in selecting filter parameters. Traditional command filters do not design filter functions based on the characteristic function of the controlled object system. Therefore, specific filter parameters must be selected to ensure system stability, and parameter selection depends on the initial state value of the system. The dominant function is selected based on the characteristics of the controlled object. When the error amplitude increases, the dominant function grows faster than the system characteristic function, thus ensuring that the response of the command filter is fast enough so that the output signal of the filter can always track the input signal. The filter error converges under any filter parameters and initial state value conditions. Therefore, the command filter based on the dominant function can maintain the global stability of the control system, even when there are unknown parameters in the controlled system.

[0038] 2. The command filtering control method based on the dominant function in this invention greatly reduces the complexity of the overall control design, making the design of intelligent controllers very simple and easy. Differentiating the command signal generates many complex nonlinear signals, and the number of these complex signals increases exponentially with the system order. Filtering the command signal generates a new signal, which is then used to construct the controller. Since the derivative of the new signal can be obtained by subtracting the input and output signals of the filter, the generation of many complex nonlinear signals through differentiation is avoided, greatly reducing the complexity of the controller. Attached Figure Description

[0039] Figure 1 This refers to the instruction filtering method in the existing technology.

[0040] Figure 2 The system output y and the desired output trajectory y in the simulation experiment of this invention are shown. d Line graph.

[0041] Figure 3 The figures show the response curves of system state variables x2 and x3 in the simulation experiment of this invention.

[0042] Figure 4 This is a graph of the system control input signal u in the simulation experiment of this invention. Detailed Implementation

[0043] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0044] Example 1:

[0045] A command filtering control method for nonlinear systems based on the dominant function includes the following steps.

[0046] S1: Establish an uncertain strict feedback nonlinear dynamic system model;

[0047] Specifically, the uncertain strict feedback nonlinear dynamic system model is as follows:

[0048]

[0049] In the formula, Let x1, ..., x2 be the state vector of the nonlinear dynamic system. n Let be the physical quantity in the system; u∈R is the control input signal, and y∈R is the output signal of the system; It is a known nonlinear characteristic function of the system. Let be an unknown nonlinear characteristic function of the system, and satisfy . in, It is a known continuously differentiable function, i = 1, ..., n.

[0050] S2: Design a general instruction filter based on the dominance function;

[0051] Specifically, the general instruction filter based on the dominance function is: In the formula, φ(·) is about The dominant function, defined as follows:

[0052] like It concerns x1, ..., x n The function, i.e. If there exists a positive number y * Make |y|≥y * ,but It is established, where d0, d1, d2, ..., d n If is an arbitrary constant, then φ(·) is about The dominant function.

[0053] S3: Determine the desired output trajectory of the nonlinear system and calculate the tracking error;

[0054] Specifically, given the desired output trajectory y d , where y d Its derivative is bounded, and the expected output trajectory y d The system output signal y needs to track the signal; therefore, the tracking error e1 = x1 - y d .

[0055] S4: Design the control input signal u to make the tracking error approach 0.

[0056] Specifically, the goal of the control method of this invention is to design a control input signal u such that the tracking error e1 tends to or approaches 0. The specific design process includes the following steps:

[0057] S401: Define intermediate variable α1 according to the first-order subsystem.

[0058]

[0059] In the formula, ε1 and k1 are arbitrarily positive design parameters; design parameters are system parameters that the designer can specify and adjust.

[0060] S402: Design the instruction filter based on the dominance function for the first-order subsystem.

[0061]

[0062] In the formula, τ1 and c1 are arbitrarily positive design parameters. It is about The dominant function, α 1，f It is the signal obtained after filtering the virtual control quantity α1, where λ(t) is a time-varying function.

[0063] In the formula, T s It is an arbitrary positive design parameter

[0064] S403: Calculate the tracking error e i =x i -α i-1 i = 2;

[0065] S404: Calculate the intermediate variable α based on the i-th order subsystem. i ,

[0066]

[0067] In the formula, ε i and k i It is an arbitrary positive design parameter;

[0068] S405: Design the instruction filter based on the dominant function for the i-th order subsystem as follows:

[0069]

[0070] In the formula, τ i and c i It is any positive design parameter. It is about The dominant function. α i，f It is the virtual control quantity α i The signal obtained after filtering.

[0071] S406: Let i = i + 1 and perform the update iteration. If i = n + 1, stop the calculation; otherwise, go to step S403:

[0072] S407: Let the system control input signal be u = α n The resulting u is the system control input signal of the command filter based on the dominant function.

[0073] Simulation experiment:

[0074] In this invention, a command filtering control model of a strictly feedback nonlinear system is constructed using the Simulink module in Matlab. The control method in this invention is simulated, and the specific model and controller are described below.

[0075] This simulation experiment uses an uncertain nonlinear system as an example.

[0076]

[0077] In the formula, ρ1=ρ2=0,ρ2=|x2|.

[0078] Given the desired output trajectory y d =0.5(sit+sin(0.5t)), calculate the tracking error e1=x1-y d ;

[0079] Calculate the intermediate variable α1 defined in the first-order subsystem.

[0080]

[0081] In the formula, ε1=1, k1=2;

[0082] Design the instruction filter based on the dominance function corresponding to the first-order subsystem as follows:

[0083]

[0084] In the formula, τ1=0.02, c1=0.1, T s =20, y2=α 1，f -α1;

[0085] Calculate the tracking error e i =x i -α i-1 i = 2;

[0086] Calculate the intermediate variable α of the i-th order subsystem i ,

[0087]

[0088] In the formula, ε2=ε3=1, k2=k3=2;

[0089] Design the instruction filter based on the dominance function for the i-th order subsystem as follows:

[0090]

[0091] In the formula, τ2=0.02 and c3=0.1 are arbitrarily positive design parameters. y3=α 2，f -α2.

[0092] Let i = i + 1 for the update iteration. If i = 4, stop the calculation; otherwise, calculate the tracking error e. i =x i -α i-1 ,:

[0093] S407: Set the system control input signal to... The resulting u is the system control input signal of the command filter based on the dominant function.

[0094] The simulation results are attached. Figure 2-4 As shown, in the appendix Figure 2 In the diagram, the solid blue line represents the system output y, and the dashed red line represents the desired output trajectory y. d From the appendix Figure 2 As can be seen from the diagram, the instruction filter controller u based on the dominant function designed by S401-S407 can enable the system output y to track the desired output trajectory y. d .

[0095] In the appendix Figure 3 In the diagram, the blue solid line represents system state variable x2, and the red solid line represents system state variable x3. (From the attached diagram...) Figure 3 As can be seen from the diagram, the instruction filter controller u based on the dominant function designed by S401-S407 can keep the system state variables x2 and x3 bounded and stable.

[0096] Appendix Figure 4 For the system controller response curve u, from the attached Figure 4 As can be seen from the data, the response curve of the instruction filter controller u based on the dominant function designed by S401-S407 is bounded and stable.

[0097] Example 2:

[0098] Based on the instruction filtering control method provided in Embodiment 1 above, the present invention also provides a nonlinear system instruction filtering controller based on a dominant function, wherein the controller is used to execute the control method described in Embodiment 1.

[0099] Example 3:

[0100] Based on the instruction filtering controller provided in Embodiment 2 above, the present invention also provides a nonlinear system instruction filtering control system based on the dominant function, wherein the control system includes the controller described in Embodiment 2.

[0101] Example 4:

[0102] Based on the instruction filtering control method provided in Embodiment 1 above, the present invention also provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the temperature compensation method as described in Embodiment 1.

[0103] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A nonlinear system command filter control method based on a dominance function, characterized by, Includes the following steps, S1: Establish an uncertain strict feedback nonlinear dynamic system model; S2: Design a general instruction filter based on the dominance function; S3: Determine the desired output trajectory of the nonlinear system and calculate the tracking error; S4: design control input signal u to make tracking error tend to 0; The uncertain strict feedback nonlinear dynamic system model in step S1 is as follows: ； wherein is the state vector of the nonlinear dynamic system, is a physical quantity in the system; is the control input signal, is the output signal of the system; is a known system nonlinear characteristic function, is an unknown nonlinear characteristic function of the system, and satisfies wherein is a known continuous differentiable function, ; The general instruction filter based on the dominance function in step S2 is: In the formula, It is about The dominant function, It is about A function; if there exists a positive number make ,but Established, among which It is an arbitrary constant.

2. The nonlinear system command filtering control method based on the dominant function according to claim 1, characterized in that, In step S3, let the desired output trajectory of the nonlinear system be... Then the tracking error .

3. The nonlinear system command filtering control method based on the dominant function according to claim 2, characterized in that, Step S4 includes the following steps: S401: Define intermediate variables based on the first-order subsystem. , ； In the formula, and It is an arbitrary positive design parameter; S402: The instruction filter based on the dominance function corresponding to the first-order subsystem is designed as follows: ； In the formula, and It is any positive design parameter. It is about The dominant function, It is a virtual control quantity The signal obtained after filtering. It is a time-varying function; S403: Calculate tracking error , ; S404: According to the... i Calculating intermediate variables in a subsystem , ； S405: Design No. i The command filter based on the dominant function corresponding to the order subsystem is: ； S406: Order If updates and iterations are carried out, If the calculation stops, proceed to step S403; otherwise, proceed to step S403. S407: Set the system control input signal to... The result u This refers to the system control input signal based on the dominant function-based instruction filter.

4. The command filtering control method for nonlinear systems based on the dominant function according to claim 3, characterized in that, In step S402 The specific expression is In the formula, It is any positive design parameter.

5. A nonlinear system command filter controller based on a dominant function, characterized in that: The controller is used to execute the control method according to any one of claims 1-4.

6. A nonlinear system command filtering control system based on a dominant function, characterized in that: The control system includes the controller as described in claim 5.

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