﻿ 基于弹性能量函数的非线性不确定系统控制方法
 控制与决策  2019, Vol. 34 Issue (6): 1247-1252 0

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TAN Yong-hong, ZENG Zhe-zhao. Nonlinear uncertain system control method based on elastic energy function[J]. Control and Decision, 2019, 34(6): 1247-1252. DOI: 10.13195/j.kzyjc.2017.1545.
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### 文章历史

1. 湖南科技学院 电子与信息工程学院，湖南 永州 425199;
2. 长沙理工大学 电气与信息工程学院，长沙 410076

Nonlinear uncertain system control method based on elastic energy function
TAN Yong-hong 1, ZENG Zhe-zhao 2
1. School of Electronics and Information Engineering, Hu'nan University of Science and Engineering, Yongzhou 425199, China;
2. College of Electric and Information Engineering, Changsha University of Science and Technology, Changsha 410076, China
Abstract: For the control problem of a nonlinear uncertain system, a disturbance observation method and an elastic tracking control method are proposed based on the elastic energy function. The elastic energy function is applied to design the disturbance observer, virtual tracking instruction and elastic tracking controller, respectively, as the core technology. The prominent advantage of the proposed control method is only according to the error to eliminate the error, does not involve the differential operators of the error, and the controller gain parameters are determined completely by the integral step. Theory research show that the proposed elastic tracking control method not only guarantees the stability of various sub-controller theoretically, and effectively solves the control problem of higher-order SISO nonlinear uncertain systems, but also effectively avoids the differential explosion problem of the back stepping control method. In addition, each sub-controller has only one gain parameter which can be tunned by the integral step, so the controller has simple structure and small calculation. Simulation results show that the proposed elastic tracking control method not only has fast response speed, high control precision and strong ability to resist disturbance, but also is not dependent on the controlled object model, therefore has wide application prospect in the field of nonlinear uncertain systems control.
Keywords: elastic tracking control    elastic energy function    disturbance observer    nonlinear uncertain system    robust stability    parameter-free tuning
0 引言

1 弹性能量函数及其特性分析 1.1 弹性能量函数定义

 (1)

 图 1 fee(x, δ)图形(δ=1)
1.2 弹性能量函数特性分析

1) 时域特性.

ⅰ) fee(0, δ)=0, fee(±∞, δ)=0;

ⅱ) 当xδ时, fee(x, δ)取极大、极小值: fee , 其中e为自然对数的底.

2) 能量特性.

 (2)

2 弹性跟踪控制器设计 2.1 问题描述

 (3)

2.2 虚拟递推控制器设计

x2的虚拟跟踪指令为x2d, 且有

 (4)

 (5)

 (6)

i=n时, 由式(6)可得虚拟跟踪指令

 (7)

 (8)

2.3 基于扰动观测器的弹性跟踪控制器设计

 (9)

 (10)

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 图 2 弹性跟踪控制系统
2.4 控制系统稳定性分析

 (12)

 (13)

 (14)

 (15)

 (16)

 (17)

 (18)

 (19)

3 仿真结果与分析

 (20)

 (21)

 图 3 例1仿真结果

 (22)

 (23)

 图 4 例2仿真结果

4 结论

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