MATLAB鲁棒控制工具箱：计算、可视化与编程指南

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"鲁棒控制工具箱"是一款专为MATLAB®设计的软件，其目标是提供计算、可视化和编程功能，支持用户在处理复杂的动态系统时实现稳健控制。该工具箱在设计过程中考虑了各种不确定性因素，确保控制策略在面对外界干扰或模型不精确时仍能保持性能稳定。 "Computation"部分强调了工具箱的计算能力，它可能包括高级算法和优化技术，如H∞控制、滑模控制等，这些方法旨在设计出对参数变化和模型不确定性具有鲁棒性的控制器。 "Visualization"功能使得用户能够通过图表和图形直观地分析系统的动态特性，帮助理解控制策略的效果和性能。这可能包括Bode图、根轨迹图和灵敏度分析等图形工具，有助于系统设计者评估和调整控制系统的响应特性。 "Programming"意味着该工具箱提供了丰富的接口和API，用户可以直接编写代码来定制控制算法，或者调用预置的函数库，从而快速构建和测试控制解决方案。联系MathWorks的方式多种多样，包括官方网站www.mathworks.com获取最新技术支持，访问comp.soft-sys.matlab新闻组进行交流，或者通过电子邮件(support@mathworks.com)、(suggest@mathworks.com)、(bugs@mathworks.com)报告问题和建议产品改进。此外，对于文档错误、销售咨询、订单状态等其他需求，用户也可以找到相应的联系方式。版权信息表明，鲁棒控制工具箱是由The MathWorks, Inc.于1992年至2001年期间开发并受版权保护的，用户只能按照许可协议的条款使用和复制软件，未经该公司书面同意，禁止任何形式的复制或再生产。联邦采购方面，该工具箱的使用须遵循适用于所有程序的特定采购条款，确保在政府机构的购买和使用中符合相关规定。鲁棒控制工具箱是一款强大的 MATLAB 工具，旨在提升动态系统控制设计的鲁棒性和效率，同时提供了丰富的技术支持和易用的界面，以便工程师们能够在实际工程应用中充分利用。

1 Tutorial

1-10

The Robust Control Problem

In the past two decades there have been great advances in the theory for the

design of robustly uncertainty-tolerant multivariable feedback control systems

[8, 9]. Many of the questions that created the much lamented “gap” of the

1970’s between the theory and practice of control design have been resolved, at

least partially, in the wake of the renewed concern of control theorists with

such feedback issues such as stability margin, sensitivity, disturbance

attenuation and so forth. Out of this renewed concern has emerged the singular

value Bode plot as a key indicator of multivariable feedback system

performance (e.g., [12, 29]). The singular value thus joins such previously used

measures of multivariable feedback system performance as dominant pole

locations (related to disturbance rejection bandwidth and transient response),

transmission zeros (related to steady-state response and “internal models”)

and rms error of control signals (from the

Wiener-Hopf/LQG optimal control

theory, [1, 45, 46]).

The real problem in robust multivariable feedback control system design is to

synthesize a control law which maintains system response and error signals to

within prespecified tolerances despite the effects of uncertainty on the system.

Uncertainty may take many forms but among the most significant are noise/

disturbance signals and transfer function modeling errors. Another source of

uncertainty is unmodeled nonlinear distortion. Uncertainty in any form is no

doubt the major issue in most control system designs. Consequently people

have adopted a standard quantitative measure for the size of the uncertainty,

viz., the

∞

norm.

The general robust control problem is described mathematically as follows (See

Figure 1-2, Canonical Robust Control Problem):

Given a multivariable plant P(s), find a stabilizing controller F(s) such that the

closed-loop transfer function satisfies

where

jω()()

--------------------------------------

()

def

inf

∆

σ∆() det IT

–()∆()0={}=

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