Control System Toolbox For Use with MATLAB' Computation Visualization Programming The MATH WORKS Getting Started Inc. Version 5
Computation Visualization Programming For Use with MATLAB® Getting Started Version 5 Control System Toolbox
Contents Introduction What Is the Control System Toolbox? 1-2 Installation Using the Documentation Related Products Typographic Conventions Building models Introduction Linear models 2-3 Linear Model Representations SISO Example: the DC Motor 2-4 Constructing SISO Models Discrete Time Systems 2-10 Adding Delays to Linear Models 2-11 LTI Object 2-11 MIMO Models 2-13 MIMO Example: Jet Transport Aircraft 2-13 Constructing MIMO Transfer Functions 2-15 Accessing I/O Pairs in MIMO Systems 2-17 Arrays of Linear models 2-18 Model characteristics 2-21
i Contents 1 Introduction What Is the Control System Toolbox? ................... 1-2 Installation ........................................... 1-3 Using the Documentation .............................. 1-4 Related Products ..................................... 1-6 Typographic Conventions ............................. 1-8 2 Building Models Introduction ......................................... 2-2 Linear Models ........................................ 2-3 Linear Model Representations . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 SISO Example: the DC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4 Constructing SISO Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6 Discrete Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Adding Delays to Linear Models . . . . . . . . . . . . . . . . . . . . . . . . 2-11 LTI Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11 MIMO Models ....................................... 2-13 MIMO Example: Jet Transport Aircraft ................. 2-13 Constructing MIMO Transfer Functions . . . . . . . . . . . . . . . . . 2-15 Accessing I/O Pairs in MIMO Systems . . . . . . . . . . . . . . . . . . 2-17 Arrays of Linear Models .............................. 2-18 Model Characteristics ................................ 2-21
Interconnecting Linear Models Feedback Interconnection ContinuousDiscrete conversions 2-24 Discrete dc motor model 2-24 Model Order reduction 2-26 Example: Gasifier Model Analyzing models 3 Introduction 3-2 LTI Viewer 3-4 Example: Time and Frequency Response f the Dc motor Right-Click Menus 3-6 Displaying Response Characteristics on a Plot 3-8 Changing Plot Type 3-11 Showing Multiple Response Types 3-13 Comparing Multiple Models 3-14 Functions for Time and Frequency Response 3-18 Time and Frequency Responses 3-18 Plotting MIMO Model Responses 3-20 Data markers 3-23 Plotting and Comparing Multiple Systems Creating Custom Plots .......3-27 Simulink lti viewer Using the Simulink LTI Viewer 3-30 Comparing Linear and Nonlinear Models Bode plots of linearized models Specifying Operating Conditions 1 Contents
ii Contents Interconnecting Linear Models ........................ 2-22 Feedback Interconnection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23 Continuous/Discrete Conversions ..................... 2-24 Discrete DC Motor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-24 Model Order Reduction ............................... 2-26 Example: Gasifier Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 3 Analyzing Models Introduction .......................................... 3-2 LTI Viewer ........................................... 3-4 Example: Time and Frequency Responses of the DC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4 Right-Click Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6 Displaying Response Characteristics on a Plot . . . . . . . . . . . . . 3-8 Changing Plot Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-11 Showing Multiple Response Types . . . . . . . . . . . . . . . . . . . . . . 3-13 Comparing Multiple Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-14 Functions for Time and Frequency Response ........... 3-18 Time and Frequency Responses . . . . . . . . . . . . . . . . . . . . . . . . 3-18 Plotting MIMO Model Responses . . . . . . . . . . . . . . . . . . . . . . . 3-20 Data Markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23 Plotting and Comparing Multiple Systems . . . . . . . . . . . . . . . 3-24 Creating Custom Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-27 Simulink LTI Viewer ................................. 3-30 Using the Simulink LTI Viewer . . . . . . . . . . . . . . . . . . . . . . . . 3-30 Comparing Linear and Nonlinear Models . . . . . . . . . . . . . . . . 3-31 Bode Plots of Linearized Models . . . . . . . . . . . . . . . . . . . . . . . . 3-38 Specifying Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . 3-43
Designing Compensators 4 Introduction 4-2 The SIsO Design Tool Opening the SISO Design Tool 3 Importing Models into the SISO Design Tool 4-5 Feedback Structure 4-6 Bode Diagram Design 4-8 Example: DC Motor 4-8 Adjusting the Compensator gain Right-Click Menus 4-9 djusting the Bandwidth 4-9 Adding an Integra 4-12 Adding a Lead Network 4-14 Moving Compensator Poles and Zeros Changing Units on a Plot 4-19 Adding a Notch Filter 4-20 Root Locus Design 4-24 Example: Electrohydraulic Servomechanism 4-25 Changing the Compensator Gain Adding Poles and Zeros to the Compensator 4-31 Editing Compensator Pole and Zero Locations Exporting the Compensator and Models 439 Storing and Retrieving Intermediate Designs 4-40 Functions For Compensator Design Root Locus design 4-42 ceme 4-42 Linear-Quadratic-Gaussian (LQG) Design......... 4-46 Example: LQG Design 4-51 Example: LQG Design for Set Point Tracking 4-55
iii 4 Designing Compensators Introduction .......................................... 4-2 The SISO Design Tool ................................. 4-3 Opening the SISO Design Tool . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3 Importing Models into the SISO Design Tool . . . . . . . . . . . . . . . 4-5 Feedback Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6 Loop Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7 Bode Diagram Design ................................. 4-8 Example: DC Motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Adjusting the Compensator Gain . . . . . . . . . . . . . . . . . . . . . . . . 4-8 Right-Click Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9 Adjusting the Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9 Adding an Integrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12 Adding a Lead Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14 Moving Compensator Poles and Zeros . . . . . . . . . . . . . . . . . . . 4-17 Changing Units on a Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19 Adding a Notch Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20 Root Locus Design ................................... 4-24 Example: Electrohydraulic Servomechanism . . . . . . . . . . . . . . 4-25 Changing the Compensator Gain . . . . . . . . . . . . . . . . . . . . . . . 4-30 Adding Poles and Zeros to the Compensator . . . . . . . . . . . . . . 4-31 Editing Compensator Pole and Zero Locations . . . . . . . . . . . . 4-36 Exporting the Compensator and Models . . . . . . . . . . . . . . . . . 4-39 Storing and Retrieving Intermediate Designs . . . . . . . . . . . . . 4-40 Functions For Compensator Design ................... 4-42 Root Locus Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 Pole Placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 Linear-Quadratic-Gaussian (LQG) Design . . . . . . . . . . . . . . . . 4-46 Example: LQG Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-51 Example: LQG Design for Set Point Tracking . . . . . . . . . . . . . 4-55
Learning More 5「 Demos Online Help Setting Plot Preferences and Properties 223 The mathWorks Online Contents
iv Contents 5 Learning More Demos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 Online Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2 Setting Plot Preferences and Properties . . . . . . . . . . . . . . . . . . . 5-3 The MathWorks Online . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4