Robust controller design by linear programming with application to a double-axis positioning system

被引：53
|
作者：
Karimi, Alireza [1 ]
Kunze, Marc [1 ]
Longchamp, Roland [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Lab Automat, STI, CH-1015 Lausanne, Switzerland
来源：
CONTROL ENGINEERING PRACTICE | 2007年 / 15卷 / 02期
关键词：
linear programming; convex optimization; PID controller; robustness margin;
D O I：
10.1016/j.conengprac.2006.06.002
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A linear programming approach is proposed to tune fixed-order linearly parameterized controllers for stable LTI plants. The method is based on the shaping of the open-loop transfer function in the Nyquist diagram. A lower bound on the crossover frequency and a new linear stability margin which guarantees lower bounds for the classical robustness margins are defined. Two optimization problems are proposed and solved by linear programming. In the first one the robustness margin is maximized for a given lower bound on the crossover frequency, whereas in the second one the closed-loop performance in terms of the load disturbance rejection is optimized with constraints on the new stability margin. The method can directly consider multi-model as well as frequency-domain uncertainties. An application to a high-precision double-axis positioning system illustrates the effectiveness of the proposed approach. (c) 2006 Elsevier Ltd. All rights reserved.
引用
收藏
页码：197 / 208
页数：12
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