CN114625008A - Self-tuning nonlinear iterative learning control method - Google Patents

Abstract

A self-tuning nonlinear iterative learning control method belongs to the field of ultra-precise motion control. The method is mainly characterized in that a self-tuning nonlinear learning coefficient is additionally added in the learning gain of the existing robust inverse model iterative learning control method. Compared with the prior art, the invention has the beneficial effects that: compared with a robust inverse model iterative learning control method, the method disclosed by the invention can better inhibit the accumulation of non-repetitive errors; compared with a Kalman filtering iterative learning control method, the nonlinear learning coefficient in the method disclosed by the invention is related to errors, so that the learning efficiency is improved; in addition, compared with the traditional nonlinear iterative learning method, the method disclosed by the invention adopts a self-tuning method to determine the combined delimitation of noise and uncertainty, and avoids the problem of control performance reduction caused by overhigh or overlow delimitation.

Description

Self-tuning nonlinear iterative learning control method

Technical Field

The invention belongs to the field of ultra-precise motion control, and particularly relates to a self-tuning nonlinear iterative learning control method.

Background

Iterative learning control is widely applied to modern industrial applications such as wafer exposure and ultra-precision machining, so as to meet the ever-increasing requirements of the applications on motion control performance. In practical application, the iterative learning control mainly has two aims of compensating repeatability errors and inhibiting non-repeatability error accumulation. At present, a widely used robust inverse model iterative learning control method has the advantage of quickly compensating for repetitive errors, but has poor performance in the aspect of inhibiting non-repetitive error accumulation; the Kalman filtering iterative learning control method can well inhibit the accumulation of non-repetitive errors, but the learning efficiency is poor due to the influence of modeling errors. In addition, the performance of the traditional nonlinear iterative learning control method depends on the accuracy of noise-uncertainty joint delimitation, and the control performance is influenced by over-high or over-low delimitation. At present, an iterative learning control method which can well meet the performance requirements of the two aspects is still lacked.

Disclosure of Invention

The invention aims to solve the problem that the conventional iterative learning control method cannot give consideration to the two aims of compensating the repetitive errors and inhibiting the accumulation of the non-repetitive errors, and provides a self-tuning nonlinear iterative learning control method which can simultaneously realize the two aims of rapidly compensating the repetitive errors and effectively inhibiting the accumulation of the non-repetitive errors.

In order to achieve the purpose, the technical scheme adopted by the invention is as follows:

a self-tuning nonlinear iterative learning control method, the learning gain of the method is additionally provided with a self-tuning nonlinear learning coefficient on the basis of the learning gain of a robust inverse model;

the self-tuning nonlinear learning coefficient tau of the method_iThe form is as follows:

wherein the content of the first and second substances,

e_i[k]representing the servo error of the ith test at the moment when T is kT, wherein a positive integer i is an iteration test serial number, T is a continuous time variable, k is a natural number, and T is a sampling period of a control system;

is the servo error e_i[k]Filtered signal after low pass filter H (z), z representing the systemA z operator of a discrete transfer function; lambda [ alpha ]_iJointly delimiting the noise-uncertainty; n represents the number of sampling points contained in each test;

the method described noise-uncertainty joint bounding lambda_iThe update is performed using the following iterative expression:

wherein the content of the first and second substances,

further, the specific algorithm form of the method is as follows:

wherein u is_i+1[k]Represents the feedforward control input of the i +1 test at the moment t-kT; u. u_i[k]Represents the feedforward control input of the ith test at the time t-kT;

learning gain for robust inverse model, h (z) is a low pass filter; for control structures in which the feedforward control input is injected into the closed-loop system before the feedback controller, G₀(z) is a known nominal model of a closed loop system.

Further, the method applies with the provisos that: g₀(z) and H (z) satisfy the following constraint

Wherein G (z) is a real model of the closed-loop system.

Compared with the prior art, the invention has the beneficial effects that: compared with a robust inverse model iterative learning control method, the method can better inhibit the accumulation of non-repeatability errors; compared with a Kalman filtering iterative learning control method, the nonlinear learning coefficient in the method disclosed by the invention is related to errors, so that the learning efficiency is improved; compared with the traditional nonlinear iterative learning control method, the method disclosed by the invention adopts a self-tuning method to determine the combined delimitation of noise and uncertainty, and avoids the problem of control performance reduction caused by overhigh or overlow delimitation.

Drawings

FIG. 1 is a schematic view of a two-degree-of-freedom motion control structure employed in embodiment 1;

FIG. 2 is a graph of the amplitude-frequency characteristics of the controlled object in example 1;

FIG. 3 is a diagram of a reference trajectory to be tracked in example 1;

FIG. 4 is a diagram of the method disclosed in the present invention and the conventional nonlinear iterative learning control method (including noise-uncertainty joint bounding λ)_iSetting two conditions of too high and too low) control effect comparison graph;

FIG. 5 is a diagram of the method disclosed in the present invention and the conventional nonlinear iterative learning control method (including noise-uncertainty joint bounding λ)_iSet both too high and too low cases) of lambda_iComparing the images;

FIG. 6 is a comparison graph of the control effect of the disclosed method and the robust inverse model iterative learning control method and the Kalman filtering iterative learning control method.

Detailed Description

The technical solution of the present invention is further described below with reference to the drawings and the embodiments, but the present invention is not limited thereto, and modifications or equivalent substitutions may be made to the technical solution of the present invention without departing from the spirit of the technical solution of the present invention, and the technical solution of the present invention is covered by the protection scope of the present invention.

Example 1:

the two-degree-of-freedom control scheme shown in figure 1 is adopted to carry out trajectory tracking control on the Y degree of freedom of a certain six-degree-of-freedom micro-motion stage, and the feedforward control input is generated by adopting the method disclosed by the invention. Meanwhile, other degrees of freedom of the micropositioner keep zero servo under the action of feedback control. The frequency characteristics of the controlled object with the Y degree of freedom are shown in FIG. 2, and the reference trajectory to be tracked is shown in FIG. 3.

As shown in fig. 2, the controlled object p (z) can be approximated as a rigid body as follows:

wherein, P₀(z) is the nominal model of P (z); z represents the z operator of the system discrete transfer function; b is equivalent mass related to the micro-motion stage mass, the motor output coefficient, the motor driver voltage-current conversion coefficient and the digital-to-analog conversion coefficient, and can be obtained by calculation according to the intermediate frequency range amplitude-frequency characteristic shown in FIG. 2; t2 × 10^-4Seconds is the sampling period of the control system in this embodiment.

For the controlled object shown in fig. 2, a feedback controller is designed in the form of:

where s represents the laplacian of the continuous transfer function. It should be noted that in practical applications, the controller c(s) in the form of a continuous transfer function needs to be converted into the controller c (z) in the form of a discrete transfer function to be used in the digital control system. In the present embodiment, a bilinear transformation is employed.

Selecting

Selecting

Similarly, in practical applications, the filter h(s) in the form of a continuous transfer function needs to be converted into the filter h (z) in the form of a discrete transfer function to be used in the digital control system. In the present embodiment, a bilinear transformation is employed.

Here, it is to be noted that G₀(z) and H (z) the convergence condition of the existing robust inverse model iterative learning control needs to be satisfied

Wherein the content of the first and second substances,

a real model of a closed loop system;

the self-tuning nonlinear learning coefficient τ is given below_iThe calculating method of (2):

step 1: set the feedforward control input for trial 1 to 0, i.e., u₁[k]After the test, the servo error e of the 1 st test was obtained as 0₁[k]。

Step 2: setting of lambda₁When it is equal to 0, τ is calculated₁。

And step 3: updated to obtain u₂[k]Obtaining the servo error e of the 2 nd test after the test₂[k]。

And 4, step 4: updated to obtain lambda₂Calculating to obtain tau₂。

And (4) repeating the steps 3-4, continuously carrying out the iterative test, and stopping the test when the iterative process is judged to enter a steady state.

In this example, 30 iterative experiments were performed. FIG. 4 shows a method (λ) disclosed in the present invention_iSelf-tuning) and traditional nonlinear iterative learning control method in noise-uncertainty joint delimitation lambda_iSet too high (lambda)_i＝2.5×10^-11) And too low (lambda)_i＝1×10^-11) Control effect in the case is compared with the graph. FIG. 5 shows the noise-uncertainty joint bounding λ for three cases_iThe variation of (2). As is apparent from fig. 4, the control effect of the method disclosed by the present invention is the best. In addition, FIG. 6 shows the iterative learning control method (τ) of the robust inverse model and the method disclosed in the present invention_i1) and Kalman Filter iterationsLearning control method (tau)_iThe control effect of 1/i) was compared. As can be seen, the control effect of the method disclosed by the invention is better than that of a robust inverse model iterative learning control method in a steady state stage, and the convergence speed is higher than that of a Kalman filtering iterative learning control method in a transient state stage.

Claims (3)

1. A self-tuning nonlinear iterative learning control method is characterized in that: the learning gain of the method is additionally provided with a self-tuning nonlinear learning coefficient on the basis of the learning gain of the robust inverse model;

the self-tuning nonlinear learning coefficient tau of the method_iThe form is as follows:

wherein the content of the first and second substances,

e_i[k]representing the servo error of the ith test at the moment when T is kT, wherein a positive integer i is an iteration test serial number, T is a continuous time variable, k is a natural number, and T is a sampling period of a control system;

is the servo error e_i[k]Filtered signal after low pass filter h (z), z representing the z operator of the system discrete transfer function; lambda [ alpha ]_iJointly delimiting noise-uncertainty; n represents the number of sampling points contained in each test;

the method described noise-uncertainty joint bounding lambda_iThe update is performed using the following iterative expression:

wherein the content of the first and second substances,

2. the self-tuning nonlinear iterative learning control method according to claim 1, characterized in that: the specific algorithm form of the method is as follows:

wherein u is_i+1[k]Represents the feedforward control input of the i +1 test at the moment t-kT; u. of_i[k]Represents the feedforward control input of the ith test at the time t-kT;

learning gain for robust inverse model, h (z) is a low pass filter; for control structures in which the feedforward control input is injected into the closed-loop system before the feedback controller, G₀(z) is a known nominal model of a closed loop system.

3. The self-tuning nonlinear iterative learning control method according to claim 1 or 2, characterized in that: the method is applied with the precondition that: g₀(z) and H (z) satisfy the following constraint

Wherein G (z) is a real model of the closed-loop system.

Images