Robustness and Worst-Case Analysis

Worst-case effect of uncertainty on stability, margins, and overshoot

A robust control system meets stability and performance requirements for all possible values of uncertain parameters. Although Monte-Carlo parameter sampling can yield a general idea of system performance across all uncertainty ranges, it cannot produce a guaranteed analysis of the worst-case parameter combination. The robustness analysis commands in this category directly calculate the upper and lower bounds on worst-case performance without random sampling. You can also calculate robustness margins that tell you how much variation in uncertain parameters the system can tolerate while maintaining stability or desired performance.

Functions

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 robstab Robust stability of uncertain system robgain Robust performance of uncertain system uscale Scale uncertainty of block or system robOptions Option set for robustness analysis gapmetric Gap metric and Vinnicombe (nu-gap) metric for distance between two systems lncf Left normalized coprime factorization rncf Right normalized coprime factorization ncfmargin Calculate normalized coprime stability margin of plant-controller feedback loop loopsens Sensitivity functions of plant-controller feedback loop sdhinfnorm Compute L2 norm of continuous-time system in feedback with discrete-time system sdlsim Time response of sampled-data feedback system
 wcgain Worst-case gain of uncertain system wcsigmaplot Plot worst-case gain of uncertain system wcnorm Worst-case norm of uncertain matrix wcOptions Option set for worst-case analysis
 mussv Compute bounds on structured singular value (µ) mussvextract Extract muinfo structure returned by mussv

Topics

Robustness Analysis

Robustness and Worst-Case Analysis

Understand the relationships among measures of robust stability, robust performance, and worst-case gain.

Robust Stability and Worst-Case Gain of Uncertain System

Calculate the robust stability and examine the worst-case gain of a closed-loop uncertain system.

Worst-Case Sensitivity Functions of Feedback Loops

Use wcgain to compute the worst-case sensitivity and complementary sensitivity functions of feedback control structures.

Robust Stability, Robust Performance and Mu Analysis

Analyze and quantify the robustness of feedback control systems with uncertainty, and understand the relationship between robustness and the structured singular value, μ.

MIMO Robustness Analysis

Create a MIMO system with parametric uncertainty and analyze it for robust stability and worst-case performance.

Getting Reliable Estimates of Robustness Margins

Systems with only real uncertain parameters can have discontinuities in the structured singular value μ that hide robustness issues.

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