Complex nonlinear system learning control method based on problem of non-strict repetition

A nonlinear system, learning control technology, applied in the field of learning control of complex nonlinear systems based on non-strictly repetitive problems

Active Publication Date: 2019-06-28
JIANGSU INST OF ECONOMIC & TRADE TECH
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] Purpose of the invention: For the problems existing in the prior art, the purpose of the invention is to provide a learning control method for complex nonlinear systems based on non-strictly repeated problems, so as to solve the problem of how to solve the problem of unknown variables, control gains and disturbances in the system. Make full use of the known boundary conditions and non-strictly repetitive laws of unknown variables in the actual system, combine the classic adaptive iterative learning control method with known boundary conditions, design a learning control method, and simultaneously solve a variety of non-strictly repetitive problems in the system , to achieve robust asymptotic tracking of the target trajectory

Method used

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  • Complex nonlinear system learning control method based on problem of non-strict repetition
  • Complex nonlinear system learning control method based on problem of non-strict repetition
  • Complex nonlinear system learning control method based on problem of non-strict repetition

Examples

Experimental program
Comparison scheme
Effect test

Embodiment 1

[0091] Embodiment one: the system equation of the controlled nonlinear system is as follows:

[0092]

[0093] in, i=1, 2, 3 are unknown parameters that are not strictly repeated, and the change law satisfies the high-order internal model;

[0094]

[0095] Linearly growing vector of system functions. unknown parameters Bounded variation in the interval [-1.4,+1.4]; The bounded change interval of is [-3,+3]; The bounded change interval of is [-0.1,+0.1]; the bounded change interval of external disturbance is [-0.1,+0.1]. The system runs iteratively in the discrete time interval {0,1,…,100}.

[0096] The iterative change laws of i=1, 2, and 3 respectively satisfy different high-order internal models, as shown in the following formula:

[0097]

[0098] It can be seen from the above formula that the unknown parameter with respectively satisfy the second-order internal model, and Then satisfy the first-order internal model, that is, the unknown paramete...

Embodiment 2

[0119] Embodiment 2: In order to better investigate the scope of application of the proposed learning control method for complex nonlinear systems based on non-strictly repetitive problems, considering that strict repetition in the iterative domain is a special case of non-strict repetition, the designed learning control The method is applied to the following control problem of a permanent magnet linear motor:

[0120]

[0121] Among them, v k (t) represents the stator angular velocity of the permanent magnet linear motor, and the nonlinear functions of the system are with The iteration domain of unknown parameters of the system is strictly repeated, as follows: θ (1) =0.8237, θ (2) = θ (3) = θ (4) =-0.014, control gain b=0.0014, disturbance d(t)=-0.07sin(0.001πt). The system tracking reference trajectory is where coefficient Randomly takes values ​​in the interval (0,1] as the iteration changes.

[0122] At this time, the boundary of the unknown parameters o...

Embodiment 3

[0124] Embodiment 3: For a single-input single-output system with multiple non-strictly repeated problems, the system equation is considered as follows:

[0125]

[0126] Among them, the unknown parameter θ k (t) changes with the time domain-iterative domain, and the range of change is known, and the change law is the same as that in Embodiment 1 Unknown control gain B(t)=(1+sin(0.5t)), disturbance d(t)=0.1cos(0.05t). System tracking reference trajectory is the same as that in Embodiment 1 The controlled system runs iteratively within a finite time interval t∈{0,1,…,100}.

[0127] According to the formula, take the initial value of the learning gain matrix A complex nonlinear system learning control method based on non-strictly repetitive problems is run iteratively 100 times in the discrete time interval {0,1,...,100}, and the learning convergence of the maximum absolute value error of state tracking as table 1 and Figure 4 shown.

[0128] Table 1. The maximum ab...

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Abstract

The invention discloses a complex nonlinear system learning control method based on the problem of non-strict repetition. Unknown variables, control gain and disturbance in a complex nonlinear systemthat can be operated repeatedly are taken into consideration, the known boundary condition of the unknown variables and non-strict repletion rules in the practical system are fully used, a classic adaptive iterative learning control method is combined with the known boundary condition, and thus, the learning control method is designed to solve the problems of non-strict repetition in the sytem. Thus, such kind of the complex nonlinear systems can be converged into the target track of non-strict repetition asymptotically within limited time, and the method has certain robustness.

Description

technical field [0001] The invention relates to a method in the field of learning control, in particular to a learning control method for complex nonlinear systems based on non-strictly repeated problems. Background technique [0002] The non-strictly repetitive problem refers to the problem that some states of the system are not strictly consistent in each iteration in a repeatable system. Since the main purpose of iterative learning control theory is to make full use of the repeatable operation characteristics of the controlled system, by comparing the measured error with the ideal value, continuous self-learning and error correction are carried out in the iteration, so the problem of non-strict repetition is seriously shackles. The development of iterative learning control theory. At present, the discussions on non-strictly repetitive problems in the system mainly include non-strictly repetitive initial states, non-strictly repetitive reference trajectories, and non-stri...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G05B13/04
Inventor 周伟刘保彬于淼
Owner JIANGSU INST OF ECONOMIC & TRADE TECH
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