Robust Control Toolbox Getting Started Introduction What Is the Robust Control Toolbox? Required Software Modeling Uncertainty Example: ACC Benchmark Problem Worst Case Performance Example: ACC Two Cart Benchmark Problem Synthesis of Robust MIMO Controllers Example: Designing a Controller with LOOPSYN Model Reduction and Approximation Example: NASA HIMAT Controller Order Reduction LMI Solvers Extends Control System Toolbox About the Authors Bibliography Multivariable Loop Shaping Tradeoff between Performance and Robustness Norms and Singular Values Typical loop shapes, S and T Design Singular Values Guaranteed Gain/Phase Margins in MIMO Systems Using LOOPSYN to do H-Infinity Loop Shaping Example: NASA HiMAT loop-shaping Design Specifications MATLAB Commands for a LOOPSYN design Using MIXSYN for H-Infinity Loop Shaping Example: NASA HiMAT design using MIXSYN Loop Shaping Commands Model Reduction for Robust Control Introduction Hankel Singular Values Overview of Model Reduction Techniques Approximating Plant Models -- Additive Error Methods Approximating Plant Models -- Multiplicative Error Method Using Modal Algorithms Rigid Body Dynamics Reducing Large Scale Models Using Normalized Coprime Factor Methods References Robustness Analysis Uncertainty Modeling Creating Uncertain Models of Dynamic Systems Creating Uncertain Parameters Quantifying Unmodeled Dynamics Robustness Analysis Multi-Input, Multi-Output Robustness Analysis Adding Independent Input Uncertainty to Each Channel Closed-Loop Robustness Analysis Nominal Stability Margins Robustness of Stability Model Uncertainty Worst-Case Gain Analysis Summary of Robustness Analysis Tools H-Infinity and Mu Synthesis H-Infinity Performance Performance as Generalized Disturbance Rejection Robustness in the H Application of H Quarter Car Suspension Model Linear H Controller Design H Control Design 1 H Control Design 2 Control Design via m-Synthesis Functions for Control Design Appendix: Interpretation of H-Infinity norm Norms of Signals and Systems Using Weighted Norms to Characterize Performance References Building Uncertain Models Introduction to Uncertain Atoms Uncertain Real Parameters Uncertain LTI Dynamics Atoms Complex Parameter Atoms Complex Matrix Atoms Unstructured Uncertain Dynamic Systems Uncertain Matrices Creating Uncertain Matrices from Uncertain Atoms Accessing Properties of a umat Row and Column Referencing Matrix Operation on umat Objects Substituting for Uncertain Atoms Uncertain State-Space Systems (uss) Creating Uncertain Systems Properties of uss Objects Sampling Uncertain Systems Feedback Around Uncertain Plant Interpreting Uncertainty in Discrete Time Lifting a ss to a uss Handling Delays in uss Uncertain frd Creating Uncertain Frequency Response Objects Properties of ufrd objects Interpreting Uncertainty in Discrete Time Lifting an frd to a ufrd Handling Delays in ufrd Basic Control System Toolbox Interconnections Simplifying Representation of Uncertain Objects Effect of AutoSimplify Property Direct Use of simplify Sampling Uncertain Objects Generating One Sample Generating Many Samples Sampling ultidyn Atoms Substitution by usubs Specifying the Substitution with Structures Nominal and Random Values Array Management for Uncertain Objects Referencing Arrays Creating Arrays with stack, cat Creating Arrays by Assignment Binary Operations with Arrays Creating Arrays With usample Creating Arrays With usubs Creating Arrays with gridureal Creating Arrays with repmat Creating Arrays with repsys Using permute and ipermute Decomposing Uncertain Objects (for Advanced Users) Normalizing Functions for Uncertain Atoms Properties of the Decomposition Syntax of lftdata Advanced Syntax of lftdata Generalized Robustness Analysis Introduction to Generalized Robustness Analysis Robust Stability Margin Robust Performance Margin Worst-Case Gain Measure LMI Introduction to Linear Matrix Inequalities Linear Matrix Inequalities LMI Features LMIs and LMI Problems The Three Generic LMI Problems Further Mathematical Background References The LMI Lab Introduction Some Terminology Overview of the LMI Lab Specifying a System of LMIs A Simple Example Initializing the LMI System Specifying the LMI Variables Specifying Individual LMIs Specifying LMIs With the LMI Editor How It All Works Querying the LMI System Description lmiinfo lminbr and matnbr LMI Solvers From Decision to Matrix Variables and Vice Versa Validating Results Modifying a System of LMIs Deleting an LMI Deleting a Matrix Variable Instantiating a Matrix Variable Advanced Topics Structured Matrix Variables Complex-Valued LMIs Specifying cTx Objectives for mincx Feasibility Radius Well-Posedness Issues Semi-Definite B(x) in gevp Problems Efficiency and Complexity Issues Solving M + PTXQ + QTXTP < 0 References Function Reference Functions--Categorical List 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 m-Synthesis Sampled-Data Systems Gain Scheduling Supporting Utilities Specification of Systems of LMIs LMI Characteristics LMI Solvers Validation of Results Modification of Systems of LMIs Functions -- Alphabetical List Release Notes Robust Control Toolbox 3.0.1 Release Notes New Functions Renamed Functions Printable Documentation (PDF) Product Page (Web)