A feedforward control compensation method based on PID type adaptive iterative learning rate

Abstract

The application provides a feedforward control compensation method based on a PID type adaptive iteration learning rate; the method is: a dynamic correction term is introduced into a PID inverse compensator to obtain an IPID inverse compensator; a desired displacement is input into the IPID inverse compensator; and the IPID inverse compensator outputs an approximate desired voltage signal of a piezoelectric micro-motion platform. The driver has a hysteresis effect. The IPID inverse compensator provided by the application can obtain a desired voltage under a desired displacement without reconstructing an inverse model. Therefore, the application avoids the process of constructing an inverse model, avoids the difficulty of solving an inverse model of a complex hysteresis model, improves the efficiency of controlling the piezoelectric micro-motion platform, eliminates the error in the process of constructing an inverse model and the problem of inaccurate parameter identification, effectively suppresses the dynamic nonlinear hysteresis of the piezoelectric micro-motion platform, and improves the accuracy of the obtained desired voltage.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of micro-nano driving, and particularly relates to a feedforward control compensation method based on a PID type adaptive iterative learning rate. BACKGROUND

[0002] With the rise of MEMS (micro electro mechanical system) technology, people pay more and more attention to the micro world, and the exploration and research in the micro field are deepening, and the micro-nano system has become one of the research hotspots. Traditional drivers have large inertia, slow response and poor reliability, while piezoelectric ceramics have the advantages of fast response speed, small size, large driving force, high precision, good stability, no noise and no heating, and is an ideal micro driver, which is widely used in micro-nano positioning and driving systems.

[0003] The characteristics of piezoelectric materials determine that there is a hysteresis nonlinearity relationship between the input voltage and the output displacement of the piezoelectric driver. This hysteresis nonlinearity makes it difficult to accurately control the displacement trajectory of the piezoelectric material. As a commonly used control method in nonlinear control systems, feedforward control can realize linearization control between the expected displacement and the actual displacement in the driving control of piezoelectric materials. In the existing research, the inverse compensator used in feedforward control is constructed based on the inverse model. Specifically, a piezoelectric system hysteresis model is first constructed, then a solution inverse model of the piezoelectric system hysteresis model is constructed, and finally the actual displacement and the expected displacement are input into the inverse model to obtain the expected voltage. In the current research, the hysteresis model is becoming more and more complex, especially since the piezoelectric driver has dynamic hysteresis characteristics, so the frequency factor needs to be introduced into the model, and the rate dependence makes the overall model more complex, which increases the difficulty of solving the inverse model, and even may not be able to solve the accurate inverse model. SUMMARY

[0004] The application designs a feedforward inverse compensator (IPID) without solving the inverse model for the difficulty of solving the inverse model caused by the increasingly complex hysteresis model. The controller not only can realize adaptive control, but also can achieve the purpose of reducing the system convergence error and improving the system convergence speed. At the same time, the IPID inverse compensator can be used in feedforward control. In this way, before feedforward control of the piezoelectric material, it is not necessary to construct an inverse model. Only the positive model needs to be substituted into the IPID inverse proposed in the application, and the expected voltage of the piezoelectric driver can be obtained. Therefore, the IPID inverse provided by the application solves the problem of difficulty in solving the inverse model caused by the increasingly complex model from the root.

[0005] In a first aspect, the present application provides a feedforward control compensation method based on PID type adaptive iteration learning rate, which comprises the following steps:

[0006] A dynamic correction term λ(k)sgn(e(k)) is introduced into the PID inverse compensator to obtain an IPID inverse compensator; wherein λ(k) is a current dynamic correction coefficient; e(k) is a current displacement error.

[0007] The expression of the current dynamic correction coefficient λ(k) is as follows:

[0008]

[0009] Wherein k is the current iteration number; γ is a preset parameter.

[0010] The desired displacement is input into the IPID inverse compensator; the IPID inverse compensator outputs a control signal of the driver. The driver has a hysteresis effect.

[0011] As a preferred, an exponential decay term of displacement error e(k) is introduced into the IPID inverse compensator.

[0012] As a preferred, the IPID inverse compensator is as follows:

[0013]

[0014] Wherein u(k) is the control signal output by the IPID inverse compensator; η p is an exponential decay coefficient; η d is a coefficient of differential error; η i is a coefficient of integral error.

[0015] The expression of the exponential decay coefficient is as follows:

[0016] η p =e -αk

[0017] Wherein α is an exponential adjustment parameter.

[0018] As a preferred, the initial value u(0) of the control signal output by the IPID inverse compensator is 0.

[0019] As a preferred, in the first several iterations, the displacement error e(k) is obtained by subtracting the actual output displacement of the piezoelectric micro-motion platform from the desired displacement in each iteration, and the IPID inverse compensator outputs a control signal to the piezoelectric driver until the displacement error e(k) is less than the error threshold, and then the IPID inverse compensator starts to output a control signal to the driver. The piezoelectric micro-motion platform hysteresis model is used to generate a corresponding displacement signal according to the input voltage signal.

[0020] As a preference, the driver is a piezoelectric driver.

[0021] In a second aspect, the present application provides a piezoelectric controller for performing the aforementioned PID-type adaptive iterative learning rate based feedforward control compensation method.

[0022] In a third aspect, the present application provides a piezoelectric micro-motion platform dynamics system, which comprises a piezoelectric driver and the aforementioned piezoelectric controller; the piezoelectric controller outputs a control signal to the piezoelectric driver according to a displacement error of the piezoelectric driver.

[0023] The present application has the following advantages:

[0024] 1. The IPID inverse compensator proposed by the present application can obtain the expected voltage under the expected displacement without reconstructing the inverse model; therefore, the present application, in one aspect, saves the process of constructing the inverse model, avoids the difficulty of solving the inverse model of the complex hysteresis model, and improves the efficiency of the control of the piezoelectric micro-motion platform; in another aspect, the present application eliminates the error in the process of constructing the inverse model and the inaccuracy of parameter identification, effectively suppresses the dynamic nonlinear hysteresis of the piezoelectric micro-motion platform, and improves the accuracy of the expected voltage.

[0025] 2. The IPID inverse compensator proposed by the present application is applicable to any hysteresis model, such as the common Prandtl-Ishlinskii model, Bouc-Wen model and Preisach model. Only the identified hysteresis model needs to be substituted into the process of IPID inverse, and the expected voltage under the expected displacement can be obtained.

[0026] 3. The IPID inverse compensator provided by the present application can track the expected trajectory with high precision after 6-7 iterations, and realizes the rapid convergence of the piezoelectric control.

[0027] 4. The IPID inverse method proposed by the present application is not only applicable to static models, but also to dynamic models. Since the piezoelectric driver will have dynamic hysteresis characteristics in use, the rate correlation will be introduced into the model. The introduction of the rate correlation makes the model more complex as a whole, which increases the difficulty of solving the inverse model of the dynamic model. And in the process of solving the dynamic inverse model, there are often problems of inaccurate solution or difficulty in solving. The IPID inverse proposed by the present application can avoid constructing the dynamic inverse model, and greatly improve the precision of the feedforward control of the dynamic model. BRIEF DESCRIPTION OF DRAWINGS

[0028] Figure 1 The principle diagram of the IPID inverse compensator for feedforward control provided by the embodiment of the present application.

[0029] Figure 2The output displacement graph of the DRPI model in the iteration process for the embodiment of the present application as a contrast.

[0030] Figure 3 The output voltage contrast graph of the IPID inverse compensator provided by the embodiment of the present application and the D-I inverse compensator constructed by the DRPI model.

[0031] Figure 4 The voltage error graph of the IPID inverse compensator provided by the embodiment of the present application relative to the D-I inverse compensator constructed by the DRPI model.

[0032] Figure 5 The maximum iteration error convergence curve graph of the IPID inverse compensator provided by the embodiment of the present application.

[0033] Figure 6 The displacement error curve graph of the IPID inverse compensator provided by the embodiment of the present application for controlling the piezoelectric driver.

[0034] Figure 7 The output displacement and expected displacement relationship graph of the IPID inverse compensator provided by the embodiment of the present application for controlling the piezoelectric driver. DETAILED DESCRIPTION

[0035] The present application will be further described below in conjunction with the drawings.

[0036] A feedforward control compensation method based on a PID type adaptive iteration learning rate, taking a piezoelectric micro-motion platform as a controlled object; by optimizing the control signal of the piezoelectric driver in the piezoelectric micro-motion platform, the control precision of the piezoelectric micro-motion platform is improved; in some other embodiments, any other driver with hysteresis characteristics can be taken as a controlled object. The principle of the IPID inverse compensator used in the feedforward control compensation method in the embodiment is as shown in the figure. Figure 1

[0037] In the iteration process of the IPID inverse compensator, the expected displacement used is the displacement vector in the entire time period. Therefore, the corresponding output voltage, model displacement and error are in the form of vectors.

[0038] First, set u(0) = 0, e(0) = e(1) and the expected displacement and the identified hysteresis model. Here u(0) = 0 represents that the initial voltage before the first iteration is zero.

[0039] The first iteration process is as follows: the initial voltage is substituted into the hysteresis model Y = H[u(k)], and the displacement signal under the initial voltage can be obtained. Subtract the model displacement signal Y from the expected displacement signal y d , and the first error signal e(1) is obtained. Calculate the voltage after the first iteration: ​

[0040] Then, the iteration process is repeated k times, where the iteration formula is shown in equation (3). Where k = 2, 3, 4…

[0041]

[0042] Where u(0) = 0 represents the value of the output voltage before the first iteration is set to zero; e(0) = e(1) represents the differential error of the first iteration is zero; Y(k) represents the output voltage generated by the kth iteration is substituted into the hysteresis model of the piezoelectric micro-motion platform to obtain the model displacement; Y = H[u(k)] is a mathematical model describing the hysteresis nonlinearity between the input voltage of the piezoelectric driver and the output displacement; y d The desired displacement can be set as required; e(k) is the displacement error between the model displacement Y(k) and the desired displacement y d after the kth iteration; u(k) represents the output voltage obtained after the kth iteration; η p is the coefficient of the error in the iteration process, and η d is the coefficient of the differential error in the iteration process; η i is the coefficient of the integral error in the iteration process. The remaining unknown coefficients are constants.

[0043] The expression of the exponential decay coefficient η p is:

[0044] η p = e -αk

[0045] Where α is a preset exponential adjustment parameter.

[0046] The expression of the correction coefficient λ k (t) is:

[0047]

[0048] Where γ is a preset optimization parameter.

[0049] The hysteresis model of the piezoelectric system can use the PI model or other existing hysteresis models.

[0050] Finally, after reaching the maximum number of iterations, the expected voltage corresponding to the expected displacement is output.

[0051] When performing feedforward control, only the IPID inverse compensator needs to be connected in series in the control system of the piezoelectric micro-motion platform. Linear control between the desired displacement and the actual displacement of the piezoelectric driver can be realized without the need to construct an inverse model.

[0052] To verify the effectiveness of the IPID inverse compensator, the following simulation was performed. The tracked desired displacement was set to y. d = -3cos(2πt) + 6, as shown Figure 2 The solid blue line in the diagram represents the actual output displacement, while the dashed red line represents the actual output displacement. The effectiveness of the feedforward inverse compensator (referred to as the DI inverse compensator) constructed based on the DRPI model has been verified in patent publication CN118153308A. Therefore, using the desired displacement as the input to the DI inverse compensator, the predicted desired voltage is as follows... Figure 3 The blue dashed line in the diagram illustrates this. Next, the desired displacement is used as the input to the IPID inverse compensator provided in this embodiment, with an initial voltage u0(t) = 0 and the iteration step number set to k. After k iterations, the output voltage of the IPID inverse compensator is as follows: Figure 3 As shown.

[0053] Depend on Figure 2 It can be seen that as the number of iterations increases, the output of the DRPI model gradually approaches the desired displacement. Simultaneously, the input of the DRPI model also gradually approaches the desired voltage. For example... Figure 3 As shown. Furthermore, as the number of iterations increases, the maximum relative error between the model output and the desired displacement gradually decreases and tends towards 0.

[0054] Then by Figure 4 It can be seen that the output voltages of the DI inverse compensator and the IPID inverse compensator are almost perfectly matched. At this point, the error between the model input and the desired voltage is less than 0.01V. This indicates that the prediction results of the two inverse compensators are similar. Since the DI inverse compensator itself also has errors, it should be considered that the IPID inverse compensator provided in this embodiment can effectively predict the voltage required for the platform's desired trajectory. Figure 5 and Figure 6 It can be seen that, through adaptive parameter tuning, this invention can ensure that the error between the displacement output by the model and the expected displacement in the simulation verification is less than 10 within 10 iterations. -3 The error is on the order of nm. When the error is on the order of nm, even if the error is not zero, the iterative error in the final output voltage will not have a significant impact on the result of the feedforward control. Furthermore, from... Figure 6 It can be seen that the error obtained by the IPID inverse compensator does not change much in its overall shape, but the overall error value is reduced. The operation process of the IPID inverse compensator only needs to control the error in the last iteration to be small enough or equal to zero. It can be assumed that there is no error value caused by the solution method. The remaining error is basically caused by the model itself's inaccurate description of the hysteresis phenomenon.

[0055] Finally, according to Figure 7As shown, the output displacement of the IPID inverse compensator presents approximate linear relationship with the expected displacement, which further indicates that the IPID inverse compensator can accurately predict the voltage required by the platform to achieve the expected trajectory.

[0056] From the effect, it can be seen that the method of the IPID inverse compensator provided in the embodiment has higher accuracy, and is highly consistent with the experimental data. Meanwhile, compared with the feedforward inverse compensator based on the inverse model, the IPID inverse compensator does not need to reconstruct the inverse model, and the calculation process is simpler and the response speed is faster.

[0057] The following Table 1 gives the parameter values of the PID inverse compensator used in the test of the embodiment in the fitting effect diagram.

[0058] Table 1

[0059]

Claims

1. A feedforward control compensation method based on PID type adaptive iterative learning rate, characterized in that: Introducing dynamic correction term in PID inverse compensator The IPID inverse compensator is obtained; wherein, λ(k) is the current dynamic correction coefficient; e(k) is the current displacement error; The current dynamic correction coefficient λ(k) is expressed as follows: wherein k is the current iteration number; and γ is a preset parameter; The expected displacement is input into the IPID inverse compensator; and the IPID inverse compensator outputs a control signal to the piezoelectric driver.

2. The PID-type adaptive iterative learning rate based feedforward control compensation method according to claim 1, characterized in that: An exponential decay term of displacement error e(k) is introduced into the IPID inverse compensator.

3. The PID-type adaptive iterative learning rate based feedforward control compensation method of claim 2, wherein: The IPID inverse compensator is as follows: where u(k) is the control signal output by the PID inverse compensator; η p is an exponential decay coefficient; η d is a coefficient of the derivative error; η i is a coefficient of the integral error; The expression of the exponential decay coefficient is as follows: η p = e -αk ; wherein α is an exponential adjustment parameter.

4. The PID-type adaptive iterative learning rate based feedforward control compensation method of claim 3, wherein: The initial value u(0) of the control signal output by the IPID inverse compensator is 0.

5. The PID-type adaptive iterative learning rate based feedforward control compensation method of claim 3, wherein: In the first several iterations, the displacement error e(k) is obtained by subtracting the actual output displacement of the piezoelectric micro-drive platform in each iteration from the expected displacement; the IPID inverse compensator outputs a control signal to the piezoelectric driver until the displacement error e(k) is less than an error threshold.

6. The feedforward control compensation method based on PID type adaptive iteration learning rate according to any one of claims 1-5, characterized in that: The driver is a piezoelectric driver.

7. A piezoelectric controller characterized by: A method for performing a PID-type adaptive iterative learning rate based feedforward control compensation method as claimed in any one of claims 1-5.

8. A piezoelectric micromachined platform dynamics system, characterized by: A piezoelectric controller according to claim 7 is included; and the piezoelectric controller outputs a control signal to the piezoelectric driver according to the displacement error of the piezoelectric driver.

Images