Control System Toolbox For Use with MATLAB Computation Visualization Programming The MATH WORKS Inc. Using the Control System Toolbox Version 1
Computation Visualization Programming For Use with MATLAB® Using the Control System Toolbox Version 1 Control System Toolbox
Contents Introduction LTI Models LTI Models Using LTI Models in the Control System Toolbox LTI Objects Precedence rules 2-5 Viewing LTI Systems As Matrices 2-5 Command Summary 2-6 Creating LTI Model 2-8 Transfer Function Models Zero-Pole- Gain Models 2-12 State-Space Models 2-14 Descriptor State-Space Models 2-16 Frequency Response Data(FRD) Models 2-17 Discrete-Time models 2-19 Data Retrieval 2-23 LTI Properties Generic Properties Model-Specific Properties Setting Lti Properties Accessing Property Values Using get Direct Property Referencing Additional Insight into LTI Properties 2-32 Model Conversion Explicit Conversion 2-40 Automatic Conversion 2-41 Caution about Model conversions 2-41
i Contents 1 Introduction 2 LTI Models LTI Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2 Using LTI Models in the Control System Toolbox . . . . . . . . . . . 2-3 LTI Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 Precedence Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5 Viewing LTI Systems As Matrices . . . . . . . . . . . . . . . . . . . . . . . 2-5 Command Summary . . . ............................... 2-6 Creating LTI Models .................................. 2-8 Transfer Function Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8 Zero-Pole-Gain Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12 State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14 Descriptor State-Space Models . . . . . . . . . . . . . . . . . . . . . . . . . 2-16 Frequency Response Data (FRD) Models . . . . . . . . . . . . . . . . . 2-17 Discrete-Time Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19 Data Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23 LTI Properties ....................................... 2-25 Generic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-25 Model-Specific Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Setting LTI Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28 Accessing Property Values Using get . . . . . . . . . . . . . . . . . . . . 2-30 Direct Property Referencing . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31 Additional Insight into LTI Properties . . . . . . . . . . . . . . . . . . 2-32 Model Conversion ................................... 2-40 Explicit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40 Automatic Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41 Caution About Model Conversions . . . . . . . . . . . . . . . . . . . . . . 2-41
Time Delays Supported Functionality Specifying Input/Output Delays Specifying Delays on the Inputs or Outputs 2-48 Specifying Delays in Discrete-Time Models 2-50 Retrieving Information About Delays 2-51 Pade Approximation of Time Delays 2-52 Simulink Block for LTI Systems 2-54 References 2-56 Operations on Lti Models 3 Precedence and Property Inheritance Extracting and Modifying Subsystems Referencing FRD Models Through Frequencies 3-7 Referencing Channels by Name -8 Resizing lti systems∴ 3-9 Arithmetic Operations Addition and Subtraction 3-11 Multiplication Inversion and Related Operations Transposition 3-14 Pertransposition 3-14 Model interconnection functions Concatenation of LTI Models Feedback and Other Interconnection Functions 3-18 Continuous/Discrete Conversions of lTi Models Zero-Order hold 3-20 First-Order hold Tustin Approximation
ii Time Delays ......................................... 2-43 Supported Functionality . . . ........................... 2-43 Specifying Input/Output Delays . . . . . . . . . . . . . . . . . . . . . . . . 2-44 Specifying Delays on the Inputs or Outputs . . . . . . . . . . . . . . . 2-48 Specifying Delays in Discrete-Time Models . . . . . . . . . . . . . . . 2-50 Retrieving Information About Delays . . . . . . . . . . . . . . . . . . . . 2-51 Padé Approximation of Time Delays . . . . . . . . . . . . . . . . . . . . . 2-52 Simulink Block for LTI Systems ....................... 2-54 References .......................................... 2-56 3 Operations on LTI Models Precedence and Property Inheritance .................. 3-3 Extracting and Modifying Subsystems .................. 3-5 Referencing FRD Models Through Frequencies . . . . . . . . . . . . . 3-7 Referencing Channels by Name . . . . . . . . . . . . . . . . . . . . . . . . . 3-8 Resizing LTI Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-9 Arithmetic Operations ................................ 3-11 Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11 Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-13 Inversion and Related Operations . . . . . . . . . . . . . . . . . . . . . . 3-13 Transposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 Pertransposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 Model Interconnection Functions ..................... 3-16 Concatenation of LTI Models . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16 Feedback and Other Interconnection Functions . . . . . . . . . . . 3-18 Continuous/Discrete Conversions of LTI Models ........ 3-20 Zero-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-20 First-Order Hold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22 Tustin Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22
Tustin with Frequency Prewarping 3-23 Matched poles and zeros 3-23 Discretization of Systems with delays Resampling of Discrete-Time Models References 3-27 Model analysis Tools General Model Characteristics 4-2 Model Dynamics State-Space Realizations 47 Arrays of LTi Models 5 Introduction 5-2 When to Collect a Set of Models in an LTI Array Restrictions for LTI Models Collected in an Array 22 Where to find information on lti array 5-3 The Concept of an LTI Array 5-4 Higher Dimensional Arrays of LTI Model 5-6 Dimensions, Size, and Shape of an LTI Array size and dims 5-9 Building LTI Arrays. 5-12 Generating LTI Arrays Using rss 5-12
iii Tustin with Frequency Prewarping . . . . . . . . . . . . . . . . . . . . . 3-23 Matched Poles and Zeros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 Discretization of Systems with Delays . . . . . . . . . . . . . . . . . . . 3-23 Resampling of Discrete-Time Models ................... 3-26 References .......................................... 3-27 4 Model Analysis Tools General Model Characteristics ......................... 4-2 Model Dynamics ...................................... 4-4 State-Space Realizations ............................... 4-7 5 Arrays of LTI Models Introduction .......................................... 5-2 When to Collect a Set of Models in an LTI Array . . . . . . . . . . . 5-2 Restrictions for LTI Models Collected in an Array . . . . . . . . . . 5-2 Where to Find Information on LTI Arrays . . . . . . . . . . . . . . . . . 5-3 The Concept of an LTI Array ........................... 5-4 Higher Dimensional Arrays of LTI Models . . . . . . . . . . . . . . . . 5-6 Dimensions, Size, and Shape of an LTI Array ............ 5-7 size and ndims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9 reshape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-11 Building LTI Arrays .................................. 5-12 Generating LTI Arrays Using rss . . . . . . . . . . . . . . . . . . . . . . . 5-12
Building LTI Arrays Using for Loops 5-12 Building LTI Arrays Using the stack Function 5-15 uilding Lti arrays Using tf, zpk, ss, and frd Indexing Into LTI Arrays Accessing Particular Models in an LTI Array Extracting LTI Arrays of Subsystems 5-21 Reassigning Parts of an LTI Array 5-22 Deleting Parts of an LTI Array 5-23 Operations on LTI Arrays 5-24 Example: Addition of Two LTI Arrays Dimension Requirements 5-26 Special Cases for Operations on LTI Arrays Other operations on LTi arrays Customization 6 The Property and Preferences Hierarchy Setting Toolbox Preferences 7「 Opening the Toolbox Preferences Editor 6-2 Units Page 6-3 Style Page Characteristics Page SISO Tool Page Setting Tool Preferences 8 Opening the Lti Viewer Preferences Editor 82 8-3
iv Building LTI Arrays Using for Loops . . . . . . . . . . . . . . . . . . . . 5-12 Building LTI Arrays Using the stack Function . . . . . . . . . . . . 5-15 Building LTI Arrays Using tf, zpk, ss, and frd . . . . . . . . . . . . . 5-17 Indexing Into LTI Arrays ............................. 5-20 Accessing Particular Models in an LTI Array . . . . . . . . . . . . . 5-20 Extracting LTI Arrays of Subsystems . . . . . . . . . . . . . . . . . . . 5-21 Reassigning Parts of an LTI Array . . . . . . . . . . . . . . . . . . . . . . 5-22 Deleting Parts of an LTI Array . . . . . . . . . . . . . . . . . . . . . . . . . 5-23 Operations on LTI Arrays ............................. 5-24 Example: Addition of Two LTI Arrays . . . . . . . . . . . . . . . . . . . 5-25 Dimension Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-26 Special Cases for Operations on LTI Arrays . . . . . . . . . . . . . . 5-26 Other Operations on LTI Arrays . . . . . . . . . . . . . . . . . . . . . . . . 5-29 6 Customization The Property and Preferences Hierarchy . . . . . . . . . . . . . . . . . . 6-3 7 Setting Toolbox Preferences Opening the Toolbox Preferences Editor . . . . . . . . . . . . . . . . . . 6-2 Units Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3 Style Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3 Characteristics Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4 SISO Tool Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5 8 Setting Tool Preferences Opening the LTI Viewer Preferences Editor . . . . . . . . . . . . . . . 8-2 Units Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-3