Feedforward compensation control method based on hysteresis positive model

Abstract

This invention employs a feedforward compensation control method based on a hysteresis positive model, addressing the challenge of avoiding the computational burden of calculating the inverse model of the hysteresis model in open-loop feedforward compensation control. It falls within the field of nonlinear hysteresis compensation. In this invention, when the input signal to the control system is u, the feedforward compensated input is u0. all =u + Δu, where θ is the hysteresis disturbance of the control system itself. d Let θ be the ideal output signal without hysteresis, and θ be the output signal of the positive hysteresis model of the control system under test when the input signal is u; K represents the gain of the control system under test; let u all The input signal to the control system is the output signal θ. c This completes the compensation control. The step of solving the inverse model, which is required in open-loop feedforward control methods, is omitted, greatly reducing the workload.

Description

Technical Field

[0001] This invention relates to a feedforward compensation control method based on a hysteresis positive model, belonging to the field of nonlinear hysteresis compensation. Background Technology

[0002] Nonlinear hysteresis is a nonlocal memory effect. Specifically, hysteresis manifests as the output signal being related not only to the current input signal but also to the peak values ​​of past input signals, resulting in a nonlinear relationship between the input and output signals. For example, in a system with an input range of 0-100V and an output range of 0-10μm, for... Figure 3 The input signal shown in (a) has the following output signal if there is no nonlinear hysteresis: Figure 3 As shown by the solid line in (b), if a hysteresis effect exists, its output signal is Figure 3 As shown by the dashed line in (b). Figure 3 Figure (c) illustrates the impact of nonlinear hysteresis on the relationship between the system's input and output signals. It reveals that the input and output of a hysteresis-free system exhibit a linear relationship, while the input and output of a hysteresis-existing system form a hysteresis loop. In engineering, this nonlinear hysteresis effect is widely present in various smart materials, such as ferroelectric materials, piezoelectric ceramic crystals, and shape memory alloys. Therefore, drive systems constructed from these materials also exhibit the same nonlinear hysteresis effect, resulting in a nonlinear relationship between the system's input and output. This reduces the system's positioning accuracy and can even lead to instability in the tracking and positioning system, posing significant challenges to the design of the system's closed-loop controller.

[0003] Currently, the main approach to solving this problem is to implement open-loop feedforward compensation control of the system. This involves modeling the system's hysteresis characteristics using existing hysteresis models, then deriving the corresponding analytical inverse model based on the forward hysteresis model, and finally connecting the analytical inverse model in series with the system, such as... Figure 1 As shown, this eliminates the system's hysteresis, making the input and output linearly related. This open-loop feedforward compensation control method requires no sensors and does not reduce the bandwidth of the drive system itself, resulting in a high response frequency. It is worth noting that completing the open-loop feedforward compensation control of the system requires two steps: First, based on the system's inherent hysteresis characteristics, a suitable hysteresis model is selected to perfectly model the system's hysteresis θ = H(u), where u and θ represent the system's input and output, respectively, and H(·) is the selected hysteresis model; second, the obtained hysteresis model is used to derive the corresponding analytical inverse model u = H. -1 (θ d ), here, θ d and u represent the input and output of the inverse model, respectively, H -1(·) represents the obtained analytical inverse model. Connecting the inverse model in series with the system, we can achieve θ≈H[H -1 (θ d )]=θ d This eliminates the effects of hysteresis and achieves system linearization. Therefore, in open-loop feedforward control methods, whether the selected hysteresis model has an analytical inverse model is crucial. (Note: The hysteresis model can be viewed as a function y = f(x), if this function has an inverse function x = f...) -1 If (y) is an inverse function, then the model has an analytic inverse. If the function does not have an inverse function, it means the model does not have an analytic inverse. However, in existing hysteresis modeling methods, only some models have analytic inverses, such as the traditional PI model and Maxwell model, while some models do not, such as the Bouc-Wen model and Hammerstein model. Regardless of whether a hysteresis model has an analytic inverse, finding its inverse model is a very difficult task. Summary of the Invention

[0004] To address the issue of reducing workload in open-loop feedforward compensation control by avoiding the need to obtain the inverse model of the hysteresis model, this invention provides a feedforward compensation control method based on a positive hysteresis model.

[0005] The present invention provides a feedforward compensation control method based on a hysteresis positive model, comprising:

[0006] When the input signal to the system under control is u, the input after feedforward compensation is u. all =u + Δu, where,

[0007] Hysteresis interference of the control system itself θ d Let θ be the ideal output signal that does not contain hysteresis behavior, and let θ be the output signal of the positive hysteresis model of the control system under test when the input signal is u.

[0008] K represents the gain of the system to be controlled;

[0009] will u all The input signal to the control system is the output signal θ. c Complete compensation control.

[0010] As a preferred method, K is obtained as follows:

[0011] An experimental platform was built, and a full-scale low-frequency sinusoidal input signal was input into the control system exhibiting hysteresis. The output signal of the control system was acquired, and the difference Δu between the maximum and minimum values ​​of the low-frequency sinusoidal input signal was calculated. Simultaneously, the difference Δθ between the maximum and minimum values ​​of the corresponding output signal was calculated to obtain...

[0012] As preferred, θ d = Ku.

[0013] As preferred, the obtaining method of the hysteresis positive model is:

[0014] The hysteresis positive model H(·) of the system to be controlled is established, and the input signal sequence U=[u(1), u(2), …, u(n)] T The input sequence U is input into the system to be controlled, and the corresponding output signal sequence Θ=[θ(1), θ(2), …, θ(n)] of the system to be controlled is collected T Wherein u(1), u(2), …, u(n), θ(1), θ(2), …, θ(n) are the corresponding input signals and output signals at sampling time 1, 2, …, n respectively, the hysteresis positive model H(·) is parameter identified by using the input signal and the output signal, and the hysteresis positive model θ=H(u) is obtained.

[0015] The present application has the beneficial effects that, in the prior art, the open-loop feedforward compensation for the hysteresis effect needs to solve the analytical inverse model of the hysteresis model, in order to avoid the large workload caused by solving the analytical inverse of the hysteresis model, the present application directly uses the hysteresis positive model to estimate the hysteresis disturbance of the system, and then completes the compensation of the hysteresis disturbance. Since the present application does not need to solve the analytical inverse model of the hysteresis model, the present application has many advantages. First, the present application omits the step of solving the inverse model in the open-loop feedforward control method, greatly reducing the corresponding workload; second, the present application is suitable for all hysteresis models, without considering whether the selected model has an analytical inverse; finally, the present application can not only feedforward compensate the hysteresis disturbance, but also feedforward compensate other predictable disturbances, providing a new idea for the field of disturbance feedforward compensation. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The traditional open-loop feedforward compensation control method;

[0017] Figure 2 The principle diagram of the open-loop feedforward disturbance compensation method based on the hysteresis positive model proposed by the present application;

[0018] Figure 3 The system nonlinear hysteresis effect, wherein (a) is the system input signal, (b) is the influence of the hysteresis effect on the system output, and (c) is the relationship between the input and the output.

[0019] Figure 4For the effect of the method of the present application on the compensation of hysteresis interference, wherein (a) is a composite frequency signal of 20Hz, 40Hz and 60Hz input; (b) is the relationship between the input and the output before compensation; (c) is the relationship between the input and the output after compensation. DETAILED DESCRIPTION

[0020] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0021] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0022] The present application will be further described below with reference to the drawings and specific embodiments, but is not limited by the present application.

[0023] In view of the problem that the existing technology needs to solve the analytical inverse model of the hysteresis model for open-loop feedforward compensation of the hysteresis effect, in order to avoid solving the analytical inverse of the hysteresis model, the present embodiment directly uses the hysteresis positive model to complete the open-loop feedforward compensation, that is, the hysteresis positive model is used to estimate the hysteresis interference, the input signal of the system is designed according to the estimated interference, and then the compensation of the hysteresis interference is completed, so that the input and output of the to-be-controlled system are in a linear relationship, which lays a foundation for the design of the subsequent system controller.

[0024] The present embodiment regards the hysteresis behavior of the system itself as a kind of interference, estimates this interference by using the hysteresis positive model, adjusts the input signal of the system on the basis of the obtained interference, and then compensates for the influence of the hysteresis interference of the system itself, so that the input and output of the system are in a linear relationship, and the interference feedforward compensation method is as shown in Figure 2 Here, K represents the gain of the system, H(·) represents the selected hysteresis model, is the interference estimated by using the hysteresis model, u all represents the system input signal after hysteresis compensation. By using this interference feedforward compensation method, the specific implementation strategy of the present embodiment is as follows:

[0025] Step 1: Build an experimental platform, input a full-scale low-frequency sinusoidal signal into a system with hysteresis effect, collect the output signal of the system, calculate the difference Δu between the maximum and minimum values of the input signal, and calculate the difference Δθ between the maximum and minimum values of the output signal, and obtain the gain K of the system by using the ratio of the above two differences, that is,

[0026]

[0027] Step 2: Select a model H(·) to model the hysteresis of the system, design a sequence of sinusoidal input signals U = [u(1), u(2), …, u(n)] with different amplitudes and different frequencies T Input into the system, collect the corresponding output signal sequence Θ = [θ(1), θ(2), …, θ(n)] T , where u(1), u(2), …, u(n), θ(1), θ(2), …, θ(n) are the input values and output values corresponding to sampling times 1, 2, …, n respectively, the input and output data are used to complete the parameter identification of the hysteresis model H(·), and finally complete the hysteresis modeling of the system θ = H(u).

[0028] Step 3: When the input signal of the system to be controlled is u, the ideal output without hysteresis behavior is calculated using the system gain K d = Ku, and the modeling output containing hysteresis behavior is calculated using the established model H(·) θ = H(u).

[0029] Step 4: When the input signal of the system to be controlled is u, the hysteresis disturbance of the system itself can be estimated as

[0030] Step 5: When the input signal of the system to be controlled is u, to compensate for the estimated disturbance The input signal at this time needs to be adjusted, and the adjustment amount can be calculated as

[0031] Step 6: When the input signal of the system to be controlled is u, the final input u of the system after design all = u + Δu.

[0032] At this point, the disturbance feedforward compensation control of the system has been completed. Through the above steps, it can be found that this method is simple to implement, directly uses the hysteresis positive model to estimate the hysteresis disturbance, and does not need to solve the corresponding inverse model. Therefore, the method greatly simplifies the workload of hysteresis compensation, and does not need to consider whether the selected model has an analytical inverse. In order to verify the effectiveness of the method of the present application for compensating the hysteresis behavior of the system, a composite sinusoidal signal with frequencies of 20 Hz, 40 Hz and 60 Hz is input into the system, as shown in Figure 4 (a). Figure 4 (b) of the prior art shows the result before compensation of the hysteresis disturbance, and Figure 4 (c) of the present application shows the result after compensation of the hysteresis disturbance by the method of the present application. It can be found that the compensated input and output are approximately a straight line, which fully verifies the effectiveness of the method of the present application.

[0033] The embodiment also provides a feedforward compensation control device based on a hysteresis positive model, comprising a first gain module, a hysteresis positive model module, a subtractor, a second gain module and an adder; the hysteresis positive model module is used to simulate the hysteresis characteristic of a controlled system by using a hysteresis positive model, and the output of the controlled system is obtained according to the input signal of the controlled system;

[0034] The input signal u is simultaneously input to the first gain module, the hysteresis positive model module and the adder, the gain coefficient of the first gain module is K, and K represents the gain of the controlled system; the first gain module outputs an ideal output signal θ d = Ku, θ d The output signal θ of the hysteresis positive model module is simultaneously input to the subtractor, and the subtractor outputs The input is input to the second gain module, the gain coefficient of the second gain module is 1 / K, and the output of the second gain module is The input signal u is simultaneously input to the adder, and the adder outputs the input u after feedforward compensation all = u + Δu, and u all is input to the controlled system, the controlled system outputs a signal θ c , and the compensation control is completed.

[0035] In the open-loop feedforward compensation control, in order to avoid obtaining the inverse model of the hysteresis model, the hysteresis effect is regarded as a disturbance of the system, the disturbance is estimated by using the hysteresis positive model, the input signal of the system is designed according to the estimated disturbance, the designed signal has compensated the disturbance in advance before the input signal of the controlled system, and then the hysteresis disturbance influence of the system is eliminated, and finally the system is a linear system. The open-loop feedforward compensation control is realized by the hysteresis positive model in the application, instead of the corresponding inverse model, so that the analytical inverse of the hysteresis model is not required in the application, the workload in the feedforward control method is greatly reduced, and whether the selected hysteresis model has an analytical inverse does not need to be considered. Compared with the previous compensation method, the application is suitable for all hysteresis models, and has stronger universality and applicability.

[0036] Although the application is described herein with reference to particular embodiments, it should be understood that these examples are merely illustrative of the principles and applications of the present application. It should therefore be understood that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It should be understood that the features described in connection with one embodiment can be used in conjunction with other embodiments described herein. It should be understood that the features described in connection with one embodiment can be used in conjunction with other embodiments described herein.

Claims

1. A feedforward compensation control method based on a hysteresis positive model, characterized by, The method comprises: The input signal of the system to be controlled is u, the input after feedforward compensation is u all = u + Δu, where The hysteresis disturbance of the system to be controlled itself θ d The ideal output signal not containing hysteresis behavior, θ is the output signal of the positive model of the system to be controlled when the input signal is u; K represents a system gain to be controlled; u all The input to be controlled system, to be controlled system output signal θ c , complete compensation control.

2. The hysteresis-positive-model-based feedforward compensation control method according to claim 1, characterized by, The method for obtaining K comprises: The experimental platform is built, a full-scale low-frequency sinusoidal input signal is input to a to-be-controlled system with hysteresis effect, an output signal of the to-be-controlled system with hysteresis effect is collected, a difference Δu between a maximum value and a minimum value of the low-frequency sinusoidal input signal is calculated, a difference Δθ between a maximum value and a minimum value of the corresponding output signal is calculated, and a difference Δu-Δθ is obtained 3. The hysteresis-positive-model-based feedforward compensation control method according to claim 1, characterized by, θ d = Ku.

4. The hysteresis-positive-model-based feedforward compensation control method according to claim 1, characterized by, The method for obtaining the hysteresis positive model comprises: establishing a hysteresis positive model H(·) of the system to be controlled, determining an input signal sequence U = [u(1), u(2), …, u(n)] T inputting the input sequence U into the system to be controlled, collecting a corresponding output signal sequence Θ = [θ(1), θ(2), …, θ(n)] of the system to be controlled T wherein u(1), u(2), …, u(n), θ(1), θ(2), …, θ(n) are input signals and output signals corresponding to sampling time 1, 2, …, n respectively, the hysteresis positive model H(·) is parameter identified by using the input signals and the output signals, and a hysteresis positive model θ = H(u) is obtained.

5. A feedforward compensation control device based on a hysteresis plus model, characterized by The device comprises a first gain module, a hysteresis positive model module, a subtracter, a second gain module and an adder; the hysteresis positive model module is used to simulate the hysteresis characteristic of the system to be controlled by using a hysteresis positive model, and the output of the system to be controlled is obtained according to the input signal of the system to be controlled; The input signal u is input to the No. 1 gain module, the hysteresis positive model module and the adder at the same time, the gain coefficient of the No. 1 gain module is K, K represents the gain of the system to be controlled; the No. 1 gain module outputs the ideal output signal θ not containing the hysteresis behavior d = Ku, θ d The output signal θ of the hysteresis positive model module is input to the subtractor at the same time, the subtractor outputs The input signal u is input to the No. 2 gain module, the gain coefficient of the No. 2 gain module is 1 / K, the output of the No. 2 gain module The input signal u is input to the adder at the same time, the adder outputs the input u after feedforward compensation all = u + Δu, u all The input signal u is input to the system to be controlled, the output signal θ of the system to be controlled c , and the compensation control is completed.

6. The hysteresis-positive-model-based feedforward compensation control device according to claim 5, characterized by, The method for obtaining K comprises: The experimental platform is built, a full-scale low-frequency sinusoidal input signal is input to a to-be-controlled system with hysteresis effect, an output signal of the to-be-controlled system with hysteresis effect is collected, a difference Δu between a maximum value and a minimum value of the low-frequency sinusoidal input signal is calculated, a difference Δθ between a maximum value and a minimum value of the corresponding output signal is calculated, and a difference Δu-Δθ is obtained 7. The hysteresis-positive-model-based feedforward compensation control device according to claim 5, characterized by, The method for obtaining the hysteresis positive model in the hysteresis positive model module comprises: establishing a hysteresis positive model H(·) of the system to be controlled, determining an input signal sequence U = [u(1), u(2), …, u(n)] T inputting the input sequence U into the system to be controlled, collecting a corresponding output signal sequence Θ = [θ(1), θ(2), …, θ(n)] of the system to be controlled T wherein u(1), u(2), …, u(n), θ(1), θ(2), …, θ(n) are input signals and output signals corresponding to sampling time 1, 2, …, n respectively, the hysteresis positive model H(·) is parameter identified by using the input signals and the output signals, and a hysteresis positive model θ = H(u) is obtained.

8. A storage device readable by a computer, the storage device storing a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the feedforward compensation control method based on the hysteresis positive model according to any one of claims 1 to 4.

9. A hysteresis positive model based feed forward compensation control device comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to realize the steps of the feedforward compensation control method based on the hysteresis positive model according to any one of claims 1 to 4.

10. A computer program product comprising a computer program, characterized in that, The computer program is executed by the processor to realize the steps of the feedforward compensation control method based on the hysteresis positive model according to any one of claims 1 to 4.

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