考虑时域约束的线性系统非脆弱H∞控制

doi:10.11772/j.issn.1001-9081.2014.07.2140

计算机应用 ›› 2014, Vol. 34 ›› Issue (7): 2140-2144.DOI: 10.11772/j.issn.1001-9081.2014.07.2140

• 行业与领域应用 • 上一篇

考虑时域约束的线性系统非脆弱H∞控制

高兴泉¹,胡云峰²

1. 吉林化工学院信息与控制工程学院，吉林吉林 132022
2. 吉林大学通信工程学院，长春 130025

收稿日期:2014-01-14 修回日期:2014-02-27 出版日期:2014-07-01 发布日期:2014-08-01
通讯作者: 高兴泉
作者简介:高兴泉(1976-)，男，吉林吉林人，副教授，博士，主要研究方向：鲁棒控制、非线性系统控制；胡云峰(1983-)，男，吉林长春人，讲师，博士，主要研究方向：发动机控制、汽车电子。
基金资助:
国家自然科学基金资助项目;吉林省教育厅项目;吉林省科技发展计划项目

Non-fragile H∞ control of linear system with time-domain constraints

GAO Xingquan¹,HU Yunfeng²

1. College of Information and Control Engineering, Jilin University of Chemical Technology，Jilin Jilin 132022，China;
2. College of Communication Engineering, Jilin University, Changchun Jilin 130025, China

Received:2014-01-14 Revised:2014-02-27 Online:2014-07-01 Published:2014-08-01
Contact: GAO Xingquan

摘要/Abstract

摘要：

针对带有时域约束(包含控制输入约束、状态约束或两者的混合约束)的线性系统，在线性矩阵不等式(LMI)优化框架下，提出了一种非脆弱H∞状态反馈控制器设计方法。首先通过初始条件和外部干扰能量的假设确定一个能包含系统所有可能状态的固定椭圆域，然后得到控制器增益在一定范围内摄动情况下确保闭环系统满足时域约束的充分条件，进而转化为相应的矩阵不等式，详细地给出了推导过程。最终时域约束线性系统的非脆弱H∞控制问题可转化为求解多目标的LMI优化问题。将该方法用于质量-弹簧-阻尼系统的干扰抑制控制。仿真实验结果表明：利用该方法设计的控制器能够在满足时域约束的条件下，提高闭环系统对控制器增益摄动的鲁棒性。

Abstract:

For linear system with time-domain constraints including control input constraints, state constraints or their mixed constraints, an H∞ control scheme via Linear Matrix Inequalities (LMI) optimization was proposed in this paper. First, by assumption of initial states and the energy of external disturbance, a fixed ellipsoid containing all perturbed feasible trajectories was confirmed. Then, sufficient conditions of the closed-loop system satisfying time-domain constraints with the controller gain varying during a certain scope were derived and converted to LMI, and the derivation process was given in detail. Finally, the non-fragile H∞ controller design with time-domain constraints was led to solving an optimization problem with LMI constraints. Simulation results for application in the disturbance reject problem of mass-spring-damper system were discussed. The simulation application results show that the designed controller can improve the robustness of the closed-cloop system with controller gain variations while the time-domain constraints are respected.

中图分类号:

TP 273

高兴泉胡云峰. 考虑时域约束的线性系统非脆弱H∞控制[J]. 计算机应用, 2014, 34(7): 2140-2144.

GAO Xingquan HU Yunfeng. Non-fragile H∞ control of linear system with time-domain constraints[J]. Journal of Computer Applications, 2014, 34(7): 2140-2144.

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考虑时域约束的线性系统非脆弱H∞控制

Non-fragile H∞ control of linear system with time-domain constraints

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