Feed-forward control compensation method based on PID type adaptive iterative learning rate

Abstract

The invention provides a feed-forward control compensation method based on a PID type adaptive iterative learning rate. The method comprises the following steps of: introducing a dynamic correction term into a PID (Proportion Integration Differentiation) inverse compensator to obtain an IPID inverse compensator; the expected displacement is input into an IPID inverse compensator; and the IPID inverse compensator outputs an approximate expected voltage signal of the piezoelectric micro-motion platform. The driver has a hysteresis effect. According to the IPID inverse compensator provided by the invention, the expected voltage under the expected displacement can be obtained under the condition that an inverse model is not reconstructed; therefore, on one hand, the process of constructing an inverse model is omitted, the difficulty of solving the inverse model by a complex hysteresis model is avoided, and the efficiency of controlling the piezoelectric micro-motion platform is improved; and on the other hand, the problems of errors and inaccurate parameter identification in the inverse model construction process are eliminated, the dynamic nonlinear hysteresis of the piezoelectric micro-motion platform is effectively inhibited, and the accuracy of the obtained expected voltage is improved.

Description

Technical Field

[0001] The invention belongs to the field of micro-nano drive technology, and in particular relates to a feedforward control compensation method based on PID type adaptive iterative learning rate. Background Art

[0002] With the rise of MEMS (micro electro mechanical system) technology, people are paying more and more attention to the microscopic world. As the exploration and research in the microscopic field continues to deepen, micro-nano systems have 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, small size, large driving force, high precision, good stability, no noise, no heat, etc. It is an ideal micro-driver and is widely used in micro-nano positioning and driving systems.

[0003] The characteristics of piezoelectric materials determine that there is a hysteresis nonlinear relationship between the input voltage and output displacement of the piezoelectric driver. This hysteresis nonlinear characteristic makes it difficult to accurately control the displacement trajectory of the piezoelectric material drive. Feedforward control is a commonly used control method in nonlinear control systems. In the drive control of piezoelectric materials, linear control between the desired displacement and the actual displacement can be achieved. In existing research, the inverse compensator used in feedforward control is based on the inverse model. Specifically, the piezoelectric system hysteresis model is first constructed, and then the inverse model for solving the piezoelectric system hysteresis model is constructed. Finally, the actual displacement and the desired displacement are input into the inverse model to obtain the desired voltage; in current research, the hysteresis model is becoming more and more complex, especially because the piezoelectric driver has dynamic hysteresis characteristics, so the frequency factor needs to be introduced into the model, and the rate correlation makes the model more complex as a whole, which makes it more difficult to solve the inverse model, and it may even be impossible to solve the accurate inverse model. Summary of the invention

[0004] In view of the difficulty in solving the inverse model caused by the increasing complexity of the current hysteresis model, the present invention designs a feedforward inverse compensator (IPID) that does not require solving the inverse model. The controller can not only realize adaptive control, but also 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 the piezoelectric material is feedforward controlled, there is no need to build an inverse model. It is only necessary to substitute the positive model into the IPID inverse proposed by the present invention to obtain the expected voltage of the piezoelectric driver. Therefore, the IPID inverse provided by the present invention fundamentally solves the problem of difficulty in solving the inverse model caused by the increasing complexity of the current model.

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

[0007] The dynamic correction term λ(k)sgn(e(k)) is introduced into the PID inverse compensator to obtain the IPID inverse compensator, where λ(k) is the current dynamic correction coefficient and e(k) is the current displacement error.

[0008] The expression of the current dynamic correction coefficient λ(k) is as follows:

[0009]

[0010] Among them, k is the current iteration number; γ is the preset parameter.

[0011] 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.

[0012] Preferably, an exponential attenuation term of the displacement error e(k) is introduced into the IPID inverse compensator.

[0013] Preferably, the IPID inverse compensator is as follows:

[0014]

[0015] Wherein, u(k) is the control signal output by the IPID inverse compensator; η p is the exponential attenuation coefficient; η d is the coefficient of differential error; η i is the coefficient of the integral error.

[0016] The expression of the exponential decay coefficient is:

[0017] η p =e -αk

[0018] Among them, α is the exponential adjustment parameter.

[0019] Preferably, the initial value u(0) of the control signal output by the IPID inverse compensator is 0.

[0020] Preferably, in the first several iterations, the displacement error e(k) is obtained by subtracting the actual output displacement of each iteration of the piezoelectric micro-motion platform from the expected displacement, 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 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 an input voltage signal.

[0021] Preferably, the driver is a piezoelectric driver.

[0022] In a second aspect, the present invention provides a piezoelectric controller for executing the aforementioned feedforward control compensation method based on a PID-type adaptive iterative learning rate.

[0023] In a third aspect, the present invention provides a piezoelectric micro-motion platform dynamic system, which includes a piezoelectric driver and the aforementioned piezoelectric controller; the piezoelectric controller outputs a control signal to the piezoelectric driver according to the displacement error of the piezoelectric driver.

[0024] Beneficial effects of the present invention:

[0025] 1. The IPID inverse compensator proposed in the present invention can obtain the expected voltage under the expected displacement without reconstructing the inverse model; therefore, on the one hand, the present invention 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 controlling the piezoelectric micro-motion platform; on the other hand, it eliminates the errors and inaccurate parameter identification problems that occur in the inverse model construction process, effectively suppresses the dynamic nonlinear hysteresis of the piezoelectric micro-motion platform, and improves the accuracy of the obtained expected voltage.

[0026] 2. The IPID inverse compensator proposed in the present invention is applicable to any hysteresis model, such as the common Prandtl-Ishlinskii model, Bouc-Wen model and Preisach model, etc. It is only necessary to substitute the identified hysteresis model into the IPID inverse process to obtain the desired voltage under the desired displacement.

[0027] 3. The IPID inverse compensator provided by the present invention can track the desired trajectory with high precision after 6 to 7 iterations, thereby achieving rapid convergence of piezoelectric control.

[0028] 4. The IPID inverse method proposed in the present invention is not only applicable to static models, but also to dynamic models. Since the piezoelectric driver will definitely have dynamic hysteresis characteristics during use, the rate-dependent characteristic will be introduced into the model. The introduction of rate-dependency 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 or difficult solutions. The IPID inverse proposed in the present invention can avoid the construction of a dynamic inverse model and greatly improve the accuracy of the feedforward control of the dynamic model. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A schematic diagram of the principle of an IPID inverse compensator for feedforward control provided in an embodiment of the present invention.

[0030] Figure 2 FIG. 4 is an output displacement map of the DRPI model used for comparison in the iteration process in the embodiment of the present invention.

[0031] Figure 3 A comparison diagram of the output voltages of the IPID inverse compensator provided in an embodiment of the present invention and the DI inverse compensator constructed using a DRPI model.

[0032] Figure 4 A voltage error diagram of the IPID inverse compensator provided in an embodiment of the present invention relative to the DI inverse compensator constructed by the DRPI model.

[0033] Figure 5 This is a maximum iteration error convergence curve diagram of the IPID inverse compensator provided in an embodiment of the present invention.

[0034] Figure 6 A displacement error curve diagram of a piezoelectric driver controlled by an IPID inverse compensator provided in an embodiment of the present invention.

[0035] Figure 7 A relationship diagram between the output displacement and the expected displacement of the piezoelectric driver controlled by the IPID inverse compensator provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings.

[0037] A feedforward control compensation method based on PID type adaptive iterative learning rate, with a piezoelectric micro-motion platform as the controlled object; by optimizing the control signal of the piezoelectric driver in the piezoelectric micro-motion platform, the control accuracy of the piezoelectric micro-motion platform is improved; in some other embodiments, any other driver with hysteresis characteristics can be used as the controlled object. The principle of the IPID inverse compensator used in the feedforward control compensation method in this embodiment is as follows Figure 1 shown.

[0038] During 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 all in the form of vectors.

[0039] First, u(0)=0, e(0)=e(1) and the expected displacement and the identified hysteresis model are set. Here, u(0)=0 means that the initial voltage before the first iteration is zero.

[0040] The first iteration process is as follows: Substitute the initial voltage into the hysteresis model of Y = H[u(k)] to obtain the displacement signal under the initial voltage. d Subtract and get the first error signal e(1). Calculate the voltage after the first iteration:

[0041] Then, the iteration process is repeated k times, where the iteration formula is shown in formula (3). Where k = 2, 3, 4...

[0042]

[0043] Wherein, u(0)=0 means that the value of the output voltage is set to zero before the first iteration; e(0)=e(1) means that the differential error of the first iteration is zero; Y(k) represents the model displacement obtained by substituting the output voltage generated by the kth iteration into the hysteresis model of the piezoelectric micro-motion platform; Y=H[u(k)] is a mathematical model that describes the hysteresis nonlinearity between the input voltage and output displacement of the piezoelectric actuator; y d It can be set to the desired displacement; e(k) is the difference between the model displacement Y(k) and the desired displacement y after the kth iteration. d u(k) represents the output voltage after the kth iteration; η p is the error coefficient in the iterative process, which is an exponential decay coefficient; η d is the coefficient of differential error in the iterative process; η i is the coefficient of the integral error in the iteration process. The other unknown coefficients are all constants.

[0044] Exponential decay coefficient η p The expression is:

[0045] η p =e -αk

[0046] Among them, α is a preset exponential adjustment parameter.

[0047] Correction coefficient λ k The expression of (t) is:

[0048]

[0049] Among them, γ is the preset optimization parameter.

[0050] The piezoelectric system hysteresis model can adopt the PI model or other existing hysteresis models.

[0051] Finally, after reaching the maximum number of iteration steps, the expected voltage corresponding to the expected displacement is output.

[0052] When performing feedforward control, it is only necessary to connect the IPID inverse compensator in series before the control system of the piezoelectric micro-motion platform. This allows the linearization control of the piezoelectric actuator between the desired displacement and the actual displacement to be achieved without building an inverse model.

[0053] In order to verify the effectiveness of the IPID inverse compensator, the following simulation verification is carried out. The expected displacement to be tracked is set to y d =-3cos(2πt)+6, such as Figure 2 The blue solid line in the figure is shown, and the red dotted line is the actual output displacement. In the patent publication number CN118153308A, the effectiveness of the feedforward inverse compensator (called: DI inverse compensator) constructed based on the DRPI model has been verified. Therefore, the expected displacement is used as the input of the DI inverse compensator, and the expected voltage is predicted as follows Figure 3 Next, the desired displacement is used as the input of the IPID inverse compensator provided in this embodiment, the initial voltage u0(t) = 0, and the number of iteration steps is set to k; after k iterations, the output voltage of the IPID inverse compensator is obtained as follows: Figure 3 shown.

[0054] Depend on Figure 2 It can be seen that as the number of iterations increases, the output of the DRPI model gradually approaches the expected displacement. At the same time, the input of the DRPI model also gradually approaches the expected voltage. Figure 3 In addition, with the increase of the number of iterations, the maximum relative error between the model output and the expected displacement gradually decreases and tends to 0.

[0055] Then by Figure 4 It can be seen that the output voltages of the DI inverse compensator and the IPID inverse compensator are almost completely matched. At this time, the error between the model input and the expected voltage is less than 0.01V. This shows 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 expected trajectory of the platform. Figure 5 and Figure 6 It can be seen that the present invention can achieve the error between the displacement output by the model and the expected displacement in the simulation verification within 10 iterations through adaptive parameter adjustment. -3 When the error is at this level, even if the error is not zero, the iterative error in the final output voltage will not have much impact on the result of the feedforward control. Figure 6 It can be seen that the error obtained by solving the IPID inverse compensator does not change much in 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 final iteration process to be small enough or equal to zero, so that it can be considered that there is no error value caused by the solution method. The remaining errors are basically caused by the inaccurate description of the hysteresis phenomenon by the model itself.

[0056] Finally, according to Figure 7As shown, the output displacement of the IPID inverse compensator shows an approximately linear relationship with the desired displacement, which further demonstrates that the IPID inverse compensator can accurately predict the voltage required for the desired trajectory of the platform.

[0057] From the results, it can be seen that the IPID inverse compensator provided in this embodiment has higher accuracy and is highly consistent with the experimental data. At the same time, compared with the feedforward inverse compensator based on the inverse model construction, the IPID inverse compensator does not need to rebuild the inverse model, the calculation process is simpler and the response speed is faster.

[0058] Table 1 below gives the parameter values ​​of the PID inverse compensator used in the test of this embodiment in the fitting effect diagram.

[0059] Table 1

[0060]

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 expression of the current dynamic correction coefficient λ(k) is as follows: Among them, k is the current iteration number; γ is the preset parameter; The desired displacement is input into the IPID inverse compensator; the IPID inverse compensator outputs a control signal to the piezoelectric actuator.

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

3. A feedforward control compensation method based on PID type adaptive iterative learning rate according to claim 2, characterized in that: The IPID inverse compensator is as follows: Wherein, u(k) is the control signal output by the PID inverse compensator; η p is the exponential attenuation coefficient; η d is the coefficient of differential error; η i is the coefficient of the integral error; The expression of the exponential decay coefficient is: or p =e -αk ; Among them, α is the exponential adjustment parameter.

4. A feedforward control compensation method based on PID type adaptive iterative learning rate according to claim 3, characterized in that: The initial value u(0) of the control signal output by the IPID inverse compensator is 0.

5. A feedforward control compensation method based on PID type adaptive iterative learning rate according to claim 3, characterized in that: 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 expected displacement in each iteration. The IPID inverse compensator outputs a control signal to the piezoelectric driver until the displacement error e(k) is less than the error threshold.

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

7. A piezoelectric controller, characterized in that: Used to execute a feedforward control compensation method based on a PID type adaptive iterative learning rate as described in any one of claims 1-5.

8. A piezoelectric micro-motion platform dynamics system, characterized in that: It comprises a piezoelectric driver and a piezoelectric controller as claimed in claim 7; the piezoelectric controller outputs a control signal to the piezoelectric driver according to a displacement error of the piezoelectric driver.

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