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Contents

Index

• Getting Started

Example: ACC Benchmark Problem

Example: ACC Two-Cart Benchmark Problem

Example: Designing a Controller with LOOPSYN

Example: NASA HiMAT Controller Order Reduction

Norms and Singular Values

Singular Values

Guaranteed Gain/Phase Margins in MIMO Systems

Example: NASA HiMAT Loop Shaping

Design Specifications

MATLAB Commands for a LOOPSYN Design

Example: NASA HiMAT Design Using MIXSYN

Hankel Singular Values

Rigid Body Dynamics

Creating Uncertain Models of Dynamic Systems

Creating Uncertain Parameters

Quantifying Unmodeled Dynamics

Adding Independent Input Uncertainty toEachChannel

Closed-Loop Robustness Analysis

Nominal Stability Margins

Robustness of Stability Model Uncertainty

Norms of Signals and Systems

Using Weighted Norms to Characterize Performance

Performance as Generalized Disturbance Rejection

Robustness in the H-Infinity Framework

Quarter Car Suspension Model

Linear H-Infinity Controller Design

H-Infinity Control Design 1

H-Infinity Control Design 2

Control Design via Mu Synthesis

What is a Fixed-Structure Control System?

Choosing an Approach to Fixed Control Structure Tuning

Difference Between Fixed-Structure Tuning and Traditional H-Infinity Synthesis

How looptune Sees Your Control System

Setting Up Your Control System in MATLAB

Setting Up Your Control System in Simulink

Performance and Robustness Specifications

Tune a MIMO Control System for a Specified Bandwidth

Tune a Two-Loop Control System to Meet Specific Design Requirements

Tune a MIMO Control System in Simulink

What is hinfstruct?

Structured H-Infinity Synthesis Workflow

Formulating Design Requirements as H-Infinity Constraints

Building a Tunable Closed-Loop Model

Tuning the Controller Parameters

Interpreting the Outputs of hinfstruct

Validating the Controller Design

Application Examples

Tuning Unsupported Blocks

• User's Guide

• Uncertain Elements

• Uncertain Matrices and Systems

• Manipulation of Uncertain Models

• Interconnection of Uncertain Models

• Model Order Reduction

• Robustness and Worst-Case Analysis

• Robustness Analysis for Parameter-Dependent Systems (P-Systems)

• Controller Synthesis and Tuning

• µ-Synthesis

• Sampled-Data Systems

• Gain Scheduling

• Frequency-Response Data (FRD) Models

• Supporting Utilities

• LMIs

• Release Notes

aff2pol - Convert affine parameter-dependent models to polytopic models

Syntax

polsys = aff2pol(affsys)

Description

aff2pol derives a polytopic representation polsys of the affine parameter-dependent system

(3-1)

(3-2)

where p = (p₁, . . . , p_n) is a vector of uncertain or time-varying real parameters taking values in a box or a polytope. The description affsys of this system should be specified with psys.

The vertex systems of polsys are the instances of Equation 3-1 and Equation 3-2 at the vertices p_ex of the parameter range, i.e., the SYSTEM matrices

for all corners p_ex of the parameter box or all vertices p_ex of the polytope of parameter values.

See Also

psys | pvec | uss

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