阅读说明：本技术 一种针对高相对度压电电机的开闭环迭代学习控制方法 (Open-close loop iterative learning control method for high-relative-degree piezoelectric motor ) 是由 韦蕴珊 翁志斌 赵志甲 许清媛 万凯 于 2020-04-27 设计创作，主要内容包括：本发明公开一种针对高相对度压电电机的开闭环迭代学习控制方法,所述方法包括：对压电电机的期望输出轨迹进行采样,得到期望输出轨迹序列；将控制输入电压作用到所述压电电机中并采样输出结果,得到所述压电电机的实际输出位置序列；根据所述压电电机的实际输出位置序列和所述期望输出轨迹序列形成误差序列；根据所述误差序列、开环迭代学习控制增益和闭环迭代学习控制增益形成迭代学习控制律；根据所述迭代学习控制律更新下一次迭代的控制输入电压,并将更新好的电压重新作用到所述压电电机中,直至误差指标小于容许范围时停止迭代。本发明能够使得电机系统不受高相对度的限制,且能够在达到精确跟踪控制的基础上减少迭代次数,节省能源消耗。(The invention discloses an open-close loop iterative learning control method for a high-relativity piezoelectric motor, which comprises the following steps: sampling an expected output track of the piezoelectric motor to obtain an expected output track sequence; applying control input voltage to the piezoelectric motor and sampling an output result to obtain an actual output position sequence of the piezoelectric motor; forming an error sequence according to the actual output position sequence of the piezoelectric motor and the expected output track sequence; forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain; and updating the control input voltage of the next iteration according to the iterative learning control law, and reapplying the updated voltage to the piezoelectric motor until the error index is smaller than the allowable range, and stopping the iteration. The invention can ensure that the motor system is not limited by high relativity, reduce iteration times on the basis of achieving accurate tracking control and save energy consumption.)

1. An open-close loop iterative learning control method for a high-relative-degree piezoelectric motor is characterized by comprising the following steps:

step 1, obtaining an expected output track of a piezoelectric motor, and sampling the expected output track of the piezoelectric motor according to a sampling period of the piezoelectric motor to obtain an expected output track sequence of the piezoelectric motor;

step 2, applying a control input voltage to the piezoelectric motor to obtain an actual output position of the piezoelectric motor;

step 3, sampling the actual output position of the piezoelectric motor according to the sampling period to obtain an actual output position sequence of the piezoelectric motor;

step 4, forming an error sequence according to the actual output position sequence of the piezoelectric motor and the expected output track sequence of the piezoelectric motor;

step 5, forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain;

step 6, updating the control input voltage of the next iteration according to the iterative learning control law;

and 7, repeatedly executing the steps 2-6 until the error index is smaller than the allowable range, and stopping iteration.

2. The iterative learning control method for the open-close loop of the high-relative-degree piezoelectric motor according to claim 1, wherein the model of the piezoelectric motor is as follows:

wherein x is_1,k(t) and x_2,k(t) is the motor position and motor speed, y_k(t) is the position of the motor,representing moving masses, K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_dThe time for which the motor is running;

the model of the piezoelectric motor can be modeled as a discrete system as follows:

wherein the content of the first and second substances,C＝[1 0]。

3. the iterative learning control method for the open-close loop of the high-relative-degree piezoelectric motor according to claim 1, wherein the initial control input voltage is:

wherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

4. The iterative learning control method for the open-close loop of the high-relativity piezoelectric motor according to claim 1, wherein the actual output position sequence of the piezoelectric motor is as follows:

wherein, T_SIs the sampling period of the piezoelectric motor, T_dFor the time of operation of the piezoelectric motor, G is the system relative degree。

5. The open-close loop iterative learning control method for the high-relative-degree piezoelectric motor according to claim 1, wherein the error sequence is:

wherein the content of the first and second substances,for a desired output trajectory sequence of the piezoelectric motor,is the actual output position sequence of the piezoelectric motor, G is the system relativity, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

6. The open-close loop iterative learning control method for the high-relative-degree piezoelectric motor according to claim 1, wherein the open-loop iterative learning control gain is required to satisfy the following convergence condition:

||I-LCA^G-1B||<1；

wherein L is the open loop iterative learning control gain,C＝[1 0]g is the system contrast, K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_SIs the sampling period of the piezoelectric motor, T_dThe time during which the motor is running is,representing the moving mass.

7. The open-close loop iterative learning control method for the high-relative-degree piezoelectric motor according to claim 1, wherein the iterative learning control law is as follows:

wherein the content of the first and second substances,representing the input control voltage sequence of the system at the kth iteration, L is the open loop iterative learning control gain, R is the closed loop iterative learning control gain,for the error sequence of the system at the kth iteration,the error sequence for the system at iteration k + 1.

8. The iterative learning control method for the open-close loop of the high-relative-degree piezoelectric motor according to claim 1, wherein the control input voltage of the next iteration is:

the range of iteration times is k ∈ [1, 2. - ∞ ];

wherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

Technical Field

The invention relates to the technical field of piezoelectric motor control, in particular to an open-close loop iterative learning control method for a high-relativity piezoelectric motor.

Background

In some engineering applications with high-precision control, the controlled system is not only required to be able to repeat the same control task in a limited interval, but also required that its output must strictly track the desired output trajectory. Precise control of high speed motors is a challenging engineering task. There are many difficulties in controlling a motor operating at a high speed due to a certain response time lag after a control input due to a delayed response of a motor system. If the accurate model of the system cannot be obtained, most mainstream control algorithms based on time domain information cannot complete high-speed accurate tracking control, and in practical application, external interference which cannot be effectively processed by the traditional control algorithm also exists.

The piezoelectric motor utilizes the piezoelectric body to vibrate under the action of voltage to drive the moving part to rotate or linearly move. Aiming at the problem of motion trail tracking control of the piezoelectric motor, the existing iterative learning control algorithm can effectively overcome the problem of response time lag in high-speed motor control, does not need accurate motor models and parameters, and has the capability of resisting external interference and external noise. However, most of the existing iterative learning control algorithms require that the system relative degree of a controlled system is 1, and are not suitable for a system with high relative degree, so that the application range of the algorithm is greatly limited. In addition, in the iterative learning control process, the more iterations are required to achieve error convergence, the more time is consumed, most iterative learning control algorithms can enable the system output to meet the requirements after a certain number of iterations, the excessive number of iterations makes the algorithm difficult to be applied to occasions needing to complete the track tracking task quickly, and energy waste is caused due to the fact that the learning process is too long.

Disclosure of Invention

The invention aims to provide an open-close loop iterative learning control method for a high-relativity piezoelectric motor, which is not limited by high relativity, reduces iteration times on the basis of achieving accurate tracking control and saves energy consumption.

In order to solve the above technical problem, an embodiment of the present invention provides an open-close loop iterative learning control method for a high-relative piezoelectric motor, including:

step 1, obtaining an expected output track of a piezoelectric motor, and sampling the expected output track of the piezoelectric motor according to a sampling period of the piezoelectric motor to obtain an expected output track sequence of the piezoelectric motor;

step 2, applying a control input voltage to the piezoelectric motor to obtain an actual output position of the piezoelectric motor;

step 3, sampling the actual output position of the piezoelectric motor according to the sampling period to obtain an actual output position sequence of the piezoelectric motor;

step 4, forming an error sequence according to the actual output position sequence of the piezoelectric motor and the expected output track sequence of the piezoelectric motor;

step 5, forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain;

step 6, updating the control input voltage of the next iteration according to the iterative learning control law;

and 7, repeatedly executing the steps 2-6 until the error index is smaller than the allowable range, and stopping iteration.

Preferably, the model of the piezoelectric motor is as follows:

wherein x is_1,k(t) and x_2,k(t) is the motor position and motor speed, y_k(t) is the position of the motor,representative shiftDynamic mass, K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_dThe time for which the motor is running;

the model of the piezoelectric motor can be modeled as a discrete system as follows:

wherein the content of the first and second substances,C＝[1 0]。

preferably, the initial control input voltage is:

wherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

Preferably, the actual output position sequence of the piezoelectric motor is as follows:

wherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time of operation of the piezoelectric motor is G, and the system relativity is G.

Preferably, the error sequence is:

wherein the content of the first and second substances,for a desired output trajectory sequence of the piezoelectric motor,for the actual output position sequence of the piezo-electric motor,g is the system relative degree, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

As a preferred solution, the open-loop iterative learning control gain needs to satisfy the following convergence condition:

||I-LCA^G-1B||＜1；

wherein L the open loop iterative learning controls the gain,C＝[1 0]g is the system contrast, K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_SIs the sampling period of the piezoelectric motor, T_dThe time during which the motor is running is,representing the moving mass.

As a preferred scheme, the iterative learning control law is as follows:

wherein the content of the first and second substances,representing the input control voltage of the system at the kth iteration, L is the open loop iterative learning control gain, R is the closed loop iterative learning control gain,for the error sequence of the system at the kth iteration,the error sequence for the system at iteration k + 1.

As a preferred scheme, the control input voltage of the next iteration is:

the number of iterations ranges from k ∈ [1, 2.. infinity ].

Wherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

In summary, the embodiment of the invention has the following beneficial effects:

according to the iterative learning control method for the open-close loop of the high-relativity piezoelectric motor, which is provided by the embodiment of the invention, the expected output track sequence of the piezoelectric motor is obtained by acquiring the expected output track of the piezoelectric motor and sampling the expected output track of the piezoelectric motor according to the sampling period of the piezoelectric motor; applying a control input voltage to the piezoelectric motor to obtain an actual output position of the piezoelectric motor; sampling the actual output position of the piezoelectric motor according to the sampling period to obtain an actual output position sequence of the piezoelectric motor; forming an error sequence according to the actual output position sequence of the piezoelectric motor and the expected output track sequence of the piezoelectric motor; forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain; and updating the control input voltage of the next iteration according to the iterative learning control law, reapplying the updated voltage to the piezoelectric motor, and stopping iteration until the error index is smaller than the allowable range, so that the motor system is not limited by high relativity, the iteration times can be reduced on the basis of achieving accurate tracking control, and the energy consumption is saved.

Drawings

In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

Fig. 1 is a flowchart of an open-close loop iterative learning control method for a high-relative-degree piezoelectric motor according to an embodiment of the present invention.

FIG. 2 is a graph comparing the output error of an example of a high-contrast piezoelectric motor model with the output error of a conventional iterative control method.

FIG. 3 is a diagram of the system output of the expected trajectory and different iteration numbers under an example of a high-contrast piezoelectric motor model.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be understood that the step numbers used herein are for convenience of description only and are not intended as limitations on the order in which the steps are performed.

It is to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.

The terms "comprises" and "comprising" indicate the presence of the described features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

The term "and/or" refers to and includes any and all possible combinations of one or more of the associated listed items.

One type of piezoelectric motor is a motor that converts electromechanical energy using the piezoelectric reverse effect of a piezoelectric body. The piezoelectric body is used for driving a moving part to rotate or linearly move by utilizing the vibration of the piezoelectric body under the action of voltage.

One type of piezoelectric motor is modeled as follows:

wherein x is_1,k(t) and x_2,k(t) is the motor position and motor speed, y_kAnd (t) is the motor position.Representing moving masses, K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_dThe time the motor is running.

The piezoelectric motor model can be modeled as a discrete system as follows:

wherein the content of the first and second substances,

C＝[1 0]。

the embodiment of the invention provides an iterative learning control method for an open-close ring of a high-relativity piezoelectric motor, which can be applied to the piezoelectric motor model and comprises the steps 1-7.

Wherein, before step 1 is implemented, the sampling period T of the piezoelectric motor system needs to be set_SThe discrete sequence of samples is:the corresponding discrete time sequence isWherein, T_SIs the sampling period of the piezoelectric motor, T_dThe time the piezoelectric motor is running.

Step 1: obtaining a desired output trajectory y of a piezoelectric motor_d(T) and according to the sampling period T of the piezoelectric motor_SSampling a desired output trajectory of the piezoelectric motor,obtaining the expected output track sequence y of the piezoelectric motor_d(n·T_S)，Defining a desired output trajectory sequence y of the motor_d(n·T_S) Is composed of

Step 2: will control the input voltage u_k(t) acting on the piezoelectric motor to obtain the actual output position y of the piezoelectric motor_k(t)。

In step 2, the first input control input voltage is the initial control input voltage u₀(t), the initial control input voltage is:

and step 3: according to the sampling period T_SFor actual output position y of piezoelectric motor_k(t) sampling to obtain the actual output position sequence y of the piezoelectric motor_k(n·T_S)，Defining the sequence asThe concrete formula is as follows:

according to the definition of the system relativity, additionally defining:

wherein G is the system relative degree.

It is understood here that when G is 1, i.e.That is to sayIs the output position sequence adopted by most systems with the relative degree of 1, while the relative degree in the piezoelectric motor model used by the invention is 2, namely the high relative degree, therefore, the output position sequence formed by the inventionShould be deformed intoNamely, it isThe calculation is performed using the formula.

And 4, step 4: according to the actual output position sequence of the piezoelectric motorAnd a desired output trajectory sequence of the piezoelectric motorForming an error sequence

According to the definition of the system relativity, additionally defining:

it is understood here that when G is 1, i.e.That is to sayIs the error sequence adopted by most systems with the relative degree of 1, while the relative degree in the piezoelectric motor model used by the invention is 2, namely the high relative degree, therefore, the error sequence formed by the inventionShould be deformed intoReady to useAnd (4) calculating the formula.

And 5: and forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain.

In step 5, the open-loop iterative learning control gain L should satisfy the following condition:

||I-LCA^G-1B||＜1；

wherein L is the open loop iterative learning control gain,C＝[1 0]g is the system relative degree K_vAs a velocity damping factor, K_fIs the force constant, T, of the motor_SIs the sampling period of the piezoelectric motor, T_dThe time during which the motor is running is,representing the moving mass.

Further, in step 5, the iterative learning control law is:

wherein the content of the first and second substances,representing the control input voltage sequence of the motor system at the kth iteration, L is the open loop iterative learning control gain, R is the closed loop iterative learning control gain,for the error sequence of the system at the kth iteration,the error sequence for the system at iteration k + 1.

Step 6: and updating the control input voltage of the next iteration according to the iterative learning control law. The control input voltage of the next iteration is:

the number of iterations ranges from k ∈ [1, 2.. infinity ].

And 7: and repeating the steps 2-6 until the error index is smaller than the allowable range, and stopping iteration.

According to the embodiment of the invention, an expected output track sequence of a piezoelectric motor is obtained by acquiring the expected output track of the piezoelectric motor and sampling the expected output track of the piezoelectric motor according to the sampling period of the piezoelectric motor; applying a control input voltage to the piezoelectric motor to obtain an actual output position of the piezoelectric motor; sampling the actual output position of the piezoelectric motor according to the sampling period to obtain an actual output position sequence of the piezoelectric motor; forming an error sequence according to the actual output position sequence of the piezoelectric motor and the expected output track sequence of the piezoelectric motor; forming an iterative learning control law according to the error sequence, the open-loop iterative learning control gain and the closed-loop iterative learning control gain; and updating the control input voltage of the next iteration according to the iterative learning control law, reapplying the updated voltage to the piezoelectric motor, and stopping iteration until the error index is smaller than the allowable range, so that the motor system is not limited by high relativity, the iteration times can be reduced on the basis of achieving accurate tracking control, and the energy consumption is saved.

Referring to fig. 2 and fig. 3, fig. 2 is a graph comparing an output error of a high-contrast piezoelectric motor model according to the present invention with an output error of a conventional iterative control. FIG. 3 is a diagram of the system output of the expected trajectory and different iteration numbers under an example of a high-contrast piezoelectric motor model. The piezoelectric motor system model adopted in fig. 2 and 3 is:

whereinC＝[1 0]。

Representing the control input voltage sequence of the system at the kth iteration.

The output track of the piezoelectric motor system model is as follows:

y_d(t)＝0.0002t[1+cos(0.005πt-π)],t∈[0,3]。

andrespectively sampling values of the motor position and the motor speed, setting the motor position to be 0m and the motor speed to be 0m/s at the initial moment of each iteration,representing the moving mass, and taking the value of 1kg, K_vIs a velocity damping factor with the value of 80N, K_fIs the force constant of the motor, is 6N/V,C＝[1 0]. Sampling period T_S0.01s, the iteration running time T of the system_d3s, the system relativity is 2 according to the motor system model, I-L CA according to the convergence condition^G-1If B | | < 1, the open-loop iterative learning control gain L is set to 20, and the closed-loop iterative learning control gain R is set to 10.

As can be seen from FIG. 2, under the control of an embodiment of the present invention, the error indicator function ME_k(ME_k＝max|y_d(n)-y_k(n)|,) Converge quickly and converge to within a tolerable error range at iteration 60 (i.e., the output trajectory of the motor nearly matches the desired output trajectory). Under the control of the traditional P-type iterative learning control method, the error index function converges to the tolerance error after the 100 th iteration. It can be seen that, in the present embodiment, the number of iterations is reduced by about 40 times when the output error reaches the acceptable range, thereby confirming that the present invention can accelerate the convergence rate, reduce the system operation time, and avoid unnecessary energy consumption on the basis of ensuring that the tracking error is reduced.

Fig. 3 is a graph of the output trajectory of the piezoelectric motor and the expected output trajectory for 8 th, 12 th and 20 th iterations, and it can be seen from fig. 3 that the output trajectory of the piezoelectric motor gradually tracks the expected output trajectory as the number of iterations increases.

It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a computer-readable storage medium, and can include the processes of the embodiments of the methods described above when the computer program is executed. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), or the like.

While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.

While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.