1 Introduction Related products The MathWorks provides several associated products that are especially relevant to the kinds of tasks you can perform with the Control System Toolbox. For more information about any of these products, see either: The online documentation for that product, if it is installed or if you are reading the documentation from the CD TheMathworksWebsiteathttp://www.mathworks.comseethe"products section The table below lists MathWorks products that complement the functionality of the Control System Toolbox Product Description Fuzzy Logic Toolbox Tools for developing fuzzy logic algorithms Linear Matrix Inequality Convex optimization algorithms for solving linear matrix inequalities(LMi), with application to robust control, multi-objective control, and gain scheduling Model Predictive Control A complete set of tools for implementing model Toolbox predictive control strategies u-Analysis and Synthesis Computational algorithms for the structured singular value, u, applicable to robustness and performance analysis for systems with modeling and parameter uncertainties Nonlinear Control An optimization-based approach to control Design Blockset system design that tunes parameters based on user-defined time-domain performance constraint Robust Control Toolbox Tools for modeling, analysis, and design of "robust"multivariable feedback control systems using H techniques 1-6
1 Introduction 1-6 Related Products The MathWorks provides several associated products that are especially relevant to the kinds of tasks you can perform with the Control System Toolbox. For more information about any of these products, see either: • The online documentation for that product, if it is installed or if you are reading the documentation from the CD • The MathWorks Web site, at http://www.mathworks.com; see the “products” section The table below lists MathWorks products that complement the functionality of the Control System Toolbox. Product Description Fuzzy Logic Toolbox Tools for developing fuzzy logic algorithms Linear Matrix Inequality Toolbox Convex optimization algorithms for solving linear matrix inequalities (LMI), with application to robust control, multi-objective control, and gain scheduling Model Predictive Control Toolbox A complete set of tools for implementing model predictive control strategies. µ-Analysis and Synthesis Toolbox Computational algorithms for the structured singular value, µ, applicable to robustness and performance analysis for systems with modeling and parameter uncertainties Nonlinear Control Design Blockset An optimization-based approach to control system design that tunes parameters based on user-defined time-domain performance constraints Robust Control Toolbox Tools for modeling, analysis, and design of “robust” multivariable feedback control systems using H∞ techniques
Related Products Product Description Simulink A comprehensive environment for modeling, simulating, and analyzing dynamical systems in block diagram format System Identification Tool for building linear models of dynamical Toolbox systems from noisy time series (input-output
Related Products 1-7 Simulink A comprehensive environment for modeling, simulating, and analyzing dynamical systems in block diagram format System Identification Toolbox Tool for building linear models of dynamical systems from noisy time series (input-output data) Product Description
1 Introduction Typographic Conventions This manual uses some or all of these conventions Item Convention to use Examp Example code Monospace font To assign the value 5 to A Function names/syntax Monospace font The cos function finds the ne of each Syntax line example is MLGet Var M var name Keys Boldface with an initial Press the return key. pital lette Literal strings (in syntax e bold fo f freespace(n, ' whole') descriptions in Referenc chapters Mathematical Italics for variables This vector represents the expressions Standard text font for polynomial functions,operators,and p=x+2x+3 MATLAB output Monospace font MATLAB nds with A Menu names, menu items, and Boldface with an initial Choose the File menu controls capital letter New terms Italics n array is an ordered String variables(from a finite Monose i italics sysc =d2c(sys, 'method') list) 1-8
1 Introduction 1-8 Typographic Conventions This manual uses some or all of these conventions. Item Convention to Use Example Example code Monospace font To assign the value 5 to A, enter A = 5 Function names/syntax Monospace font The cos function finds the cosine of each array element. Syntax line example is MLGetVar ML_var_name Keys Boldface with an initial capital letter Press the Return key. Literal strings (in syntax descriptions in Reference chapters) Monospace bold for literals f = freqspace(n,'whole') Mathematical expressions Italics for variables Standard text font for functions, operators, and constants This vector represents the polynomial p = x2 + 2x + 3 MATLAB output Monospace font MATLAB responds with A = 5 Menu names, menu items, and controls Boldface with an initial capital letter Choose the File menu. New terms Italics An array is an ordered collection of information. String variables (from a finite list) Monospace italics sysc = d2c(sysd, 'method')
Building models Introduction 2-2 Linear models 2-3 MIMO Models Arrays of Linear Models Model Characteristics Interconnecting Linear Models ContinuousDiscrete conversions Model order reduction 2-26
2 Building Models Introduction . . . . . . . . . . . . . . . . . . . . 2-2 Linear Models . . . . . . . . . . . . . . . . . . . 2-3 MIMO Models . . . . . . . . . . . . . . . . . . . 2-13 Arrays of Linear Models . . . . . . . . . . . . . . 2-18 Model Characteristics . . . . . . . . . . . . . . . 2-21 Interconnecting Linear Models . . . . . . . . . . . 2-22 Continuous/Discrete Conversions . . . . . . . . . . 2-24 Model Order Reduction . . . . . . . . . . . . . . . 2-26
2 Building Models Introduction This chapter discusses how to build models of linear, time invariant (LTD) dynamical systems using functions from the Control System Toolbox. It begins by developing a simple single-input, single-output(SISO)model of a DC motor and describes the various model representations possible, including: Transfer functions Frequency response data This chapter then describes how to build multiple-input multiple-output (MIMO)models by presenting a jet transport model. It also discusses topics related to creating general LTi models, including How to access model characteristics Conversions between model representation Building larger models from smaller ones Accessing and manipulating I/O pairs LTI objects, which are MATLAB objects that store multiple linear models in a single variable This chapter also discusses discrete-time systems, including analog to discrete-time conversion, sample time specification, and how to introduce time delays in your linear system. The last section describes functions that perform model order reduction and presents an example of how to perform a model 2-2
2 Building Models 2-2 Introduction This chapter discusses how to build models of linear, time invariant (LTI) dynamical systems using functions from the Control System Toolbox. It begins by developing a simple single-input, single-output (SISO) model of a DC motor and describes the various model representations possible, including: • Transfer functions • State-space • Zero/pole/gain • Frequency response data This chapter then describes how to build multiple-input multiple-output (MIMO) models by presenting a jet transport model. It also discusses topics related to creating general LTI models, including: • How to access model characteristics • Conversions between model representations • Building larger models from smaller ones • Accessing and manipulating I/O pairs • LTI objects, which are MATLAB objects that store multiple linear models in a single variable This chapter also discusses discrete-time systems, including analog to discrete-time conversion, sample time specification, and how to introduce time delays in your linear system. The last section describes functions that perform model order reduction and presents an example of how to perform a model order reduction