GNU Octave 语言 控制系统设计实战 鲁棒控制

GNU Octave 语言控制系统设计实战：鲁棒控制技术解析

鲁棒控制是控制系统设计中的一个重要分支，它关注于系统在面临外部扰动和内部参数不确定性时的稳定性和性能。GNU Octave 是一个功能强大的数学计算软件，它提供了丰富的工具和函数，非常适合进行控制系统设计。本文将围绕鲁棒控制这一主题，使用 GNU Octave 语言进行实战操作，解析相关技术。

鲁棒控制概述

鲁棒控制的核心思想是设计控制器，使得系统在参数不确定性和外部扰动下仍能保持稳定。鲁棒控制器的设计方法有很多，如H∞控制、μ综合、LMI（线性矩阵不等式）方法等。本文将重点介绍H∞控制和LMI方法在GNU Octave中的实现。

H∞控制

H∞控制是一种基于H∞范数的鲁棒控制方法，它通过最小化系统对不确定性的敏感度来实现鲁棒性。在GNU Octave中，我们可以使用 `hinf` 函数来实现H∞控制器的设计。

示例：H∞控制器设计

```octave

% 定义系统模型

A = [1 0 0; 0 1 0; 0 0 1];

B = [1 0 0];

C = [1 0 0];

D = [0];

E = [0];

F = [0];

% 定义不确定性模型

A1 = [1.1 0 0; 0 1.1 0; 0 0 1.1];

B1 = [1.2 0 0];

C1 = [1.3 0 0];

D1 = [0];

E1 = [0];

F1 = [0];

% 设计H∞控制器

K = hinf(A, B, C, D, A1, B1, C1, D1, E1, F1);

% 验证控制器性能

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