Control System Toolbox Getting Started What Is the Control System Toolbox? Introduction Installation Demos Using the Documentation Building Models Linear Models Linear Model Representations SISO Example: the DC Motor Constructing SISO Models Discrete Time Systems Adding Delays to Linear Models LTI Objects MIMO Models MIMO Example: Jet Transport Aircraft Constructing MIMO Transfer Functions Accessing I/O Pairs in MIMO Systems Arrays of Linear Models Model Characteristics Interconnecting Linear Models Feedback Interconnection Continuous/Discrete Conversions Discrete DC Motor Model Model Order Reduction Example: Gasifier Model Analyzing Models LTI Viewer Example: Time and Frequency Responses of the DC Motor Right-Click Menus Displaying Response Characteristics on a Plot Changing Plot Type Showing Multiple Response Types Comparing Multiple Models Functions for Time and Frequency Response Time and Frequency Responses Plotting MIMO Model Responses Data Markers Plotting and Comparing Multiple Systems Creating Custom Plots Designing Compensators The SISO Design Tool Opening the SISO Design Tool Importing Models into the SISO Design Tool Feedback Structure Loop Responses Bode Diagram Design Example: DC Motor Adjusting the Compensator Gain Right-Click Menus Adjusting the Bandwidth Adding an Integrator Adding a Lead Network Moving Compensator Poles and Zeros Changing Units on a Plot Adding a Notch Filter Adding a Prefilter Root Locus Design Example: Electrohydraulic Servomechanism Changing the Compensator Gain Adding Poles and Zeros to the Compensator Editing Compensator Pole and Zero Locations Viewing Damping Ratios Exporting the Compensator and Models Storing and Retrieving Intermediate Designs Nichols Plot Design DC Motor Example Opening a Nichols Plot Adjusting the Compensator Gain Adding an Integrator Adding a Lead Network Functions for Compensator Design Root Locus Design Pole Placement Linear-Quadratic-Gaussian (LQG) Design Example: LQG Design Example: LQG Design for Set Point Tracking Learning More Demos Online Help Setting Plot Preferences and Properties The MathWorks Online Examples Creating and Manipulating Models LTI Models Linear, Time-Invariant Models LTI Model Formats Using LTI Models LTI Objects Precedence Rules Viewing LTI Systems As Matrices LTI Command Summary Creating LTI Models Transfer Function Models Zero-Pole-Gain Models State-Space Models Descriptor State-Space Models Frequency Response Data (FRD) Models Discrete-Time Models Data Retrieval LTI Properties Generic LTI Properties Model-Specific Properties Setting LTI Properties Accessing Property Values Using get Direct Property Referencing Using Dot Notation Additional Insight into LTI Properties Model Conversion Explicit Conversion Automatic Conversion Caution About Model Conversions Time Delays Functions that Support Time Delays Specifying Input/Output Delays Distillation Column Example Specifying Delays on the Inputs or Outputs Specifying Delays in Discrete-Time Models Retrieving Information About Delays Padé Approximation of Time Delays Simulink Block for LTI Systems References Operations on LTI Models Overview Precedence and Property Inheritance Extracting and Modifying Subsystems Basic Subsystem Concepts Referencing FRD Models Through Frequencies Referencing Channels by Name Resizing LTI Systems Arithmetic Operations on LTI Models Addition and Subtraction Multiplication Inversion and Related Operations Transposition Pertransposition Model Interconnection Functions Concatenation of LTI Models Feedback and Other Interconnection Functions Continuous/Discrete Conversions of LTI Models Zero-Order Hold First-Order Hold Tustin Approximation Tustin with Frequency Prewarping Matched Poles and Zeros Discretization of Systems with Delays Resampling of Discrete-Time Models References Model Analysis Tools General Model Characteristics Model Dynamics State-Space Realizations Arrays of LTI Models The Concept of an LTI Array When to Use an LTI Array When to Collect a Set of Models in an LTI Array Restrictions for LTI Models Collected in an Array Where to Find Information on LTI Arrays Visualizing LTI Arrays Higher Dimensional Arrays of LTI Models Dimensions, Size, and Shape of an LTI Array I/O and Array Dimensions of LTI Arrays Accessing the Dimensions of an LTI Array Using size and ndims Using reshape to Rearrange an LTI Array Building LTI Arrays Building LTI Arrays Using for Loops Building LTI Arrays Using the stack Function Building LTI Arrays Using tf, zpk, ss, and frd Generating Random LTI Arrays Using rss Indexing Into LTI Arrays Accessing Particular Models in an LTI Array Extracting LTI Arrays of Subsystems Reassigning Parts of an LTI Array Deleting Parts of an LTI Array Operations on LTI Arrays Example: Addition of Two LTI Arrays Dimension Requirements Special Cases for Operations on LTI Arrays Other Operations on LTI Arrays Customization Preliminaries Terminology The Property and Preferences Hierarchy Setting Toolbox Preferences Toolbox Preferences Editor Opening the Toolbox Preferences Editor Units Pane Style Pane Options Pane SISO Tool Pane Setting Tool Preferences Introduction LTI Viewer Preferences Editor Units Pane Style Pane Options Pane Parameters Pane SISO Design Tool Preferences Editor Units Pane Style Pane Options Pane Line Colors Pane Customizing Response Plot Properties Introduction Response Plots Property Editor Labels Pane Limits Pane Units Pane Style Pane Options Pane Property Editing for Subplots Customizing Plots Inside the SISO Design Tool Root Locus Property Editor Labels Pane Limits Pane Options Pane Open-Loop Bode Property Editor Labels Pane Limits Pane Open-Loop Nichols Property Editor Labels Pane Limits Pane Prefilter Bode Property Editor Customizing Plots from the Command Line Introduction Using Plot and Plot Options Handles Obtaining Plot Handles Obtaining Plot Options Handles Retrieving a Handle Creating a Handle Which Properties Can You Modify? Examples Changing Plot Units Create Plots Using Existing Plot Options Handle Creating a Default Plot Options Handle Using Dot Notation Like a Structure Setting Property Pairs in setoptions Properties and Values Reference Property/Value Pairs Common to All Response Plots Bode Plots Hankel Singular Values Nichols Plots Nyquist Charts Pole/Zero Maps Sigma Plots Time Response Plots Property Organization Reference Design Case Studies Yaw Damper for a 747 Jet Transport Computing Open-Loop Eigenvalues Open-Loop Analysis Root Locus Design Washout Filter Design Hard-Disk Read/Write Head Controller Deriving the Model Model Discretization Adding a Compensator Gain Adding a Lead Network Design Analysis LQG Regulation: Rolling Mill Example Process and Disturbance Models LQG Design for the x-Axis LQG Design for the y-Axis Cross-Coupling Between Axes MIMO LQG Design Kalman Filtering Discrete Kalman Filter Steady-State Design Time-Varying Kalman Filter Time-Varying Design References Reliable Computations Introduction Conditioning and Numerical Stability Conditioning Numerical Stability Choice of LTI Model State Space Transfer Function Zero-Pole-Gain Models Scaling Summary References Using the SISO Design Tool and the LTI Viewer SISO Design Tool Overview Importing and Exporting Models Importing Models Exporting Models Exporting to Disk Exporting Multiple Models Tuning Compensators Root-Locus Open-Loop Bode Diagram Open-Loop Nichols Plot Prefilter Bode Diagram Using the Right-Click Menu to Design Compensators Adding Dynamics to Your Compensator Example: Adding a Complex Pair of Poles Viewing Loop Responses and System Data Viewing Specialized Loop Responses Viewing System Data Storing and Retrieving Designs Creating and Editing Design Constraints Design Constraints for the Root Locus Example: Adding Damping Ratio Constraints Design Constraints for Open-Loop and Prefilter Bode Diagrams Example: Adding Upper Gain Limits Design Constraints for Open-Loop Nichols Plots Example: Adding a Closed-Loop Peak Gain Constraint Editing Constraints Edit Constraint(s) Dialog Deleting Constraints Current Compensator Customizing the SISO Design Tool LTI Viewer Basic LTI Viewer Tasks Using the Right-Click Menu Setting Characteristics of Response Plots Importing and Exporting Models Exporting Models Selecting Response Types Right Click Menu: Plot Type Plot Configurations Window Analyzing MIMO Models I/O Grouping for MIMO Models Selecting I/O Pairs Customizing the LTI Viewer Functions -- Categorical List General Creating Linear Models Data Extraction Conversions System Interconnections System Gain and Dynamics Time Domain Analysis Frequency Domain Analysis Classical Design Pole Placement LQR/LQG Design State-Space Models Time Delays Model Dimensions and Characteristics Overloaded and Arithmetic Operators Matrix Equation Solvers Command-Line Plot Customization Functions -- Alphabetical List Block Reference Introduction LTI System Release Notes Control System Toolbox 6.2 Release Notes New Features New Command-Line API for Customizing Plots New SISO Design Constraint Types New Bode and Nichols Plot Options New Commands for Model Approximation and Order Reduction Major Bug Fixes Known Software and Documentation Problems Control System Toolbox 6.1 Release Notes Major Bug Fixes Platform Limitations for HP Preference and Property Editors SISO Design Tool Control System Toolbox 6.0 Release Notes New Features Linearization Tools Moved to Simulink Control Design Enhanced Numerical Algorithms Improved Support for Model Order Reduction New Commands for Modal Decompositions Major Bug Fixes Platform Limitations for HP Preference and Property Editors SISO Design Tool Control System Toolbox 5.2 Release Notes New Features Response Plots LTI Viewer SISO Design Tool Enhancements to the c2d Function Major Bug Fixes allmargin dlinmod place Control System Toolbox 5.1 Release Notes New Features SISO Design Tool Enhancements Algorithmic Enhancements Control System Toolbox 5.0 Release Notes New Features SISO Design Tool LTI Viewer Property and Preference Editors Algorithmic Enhancements New Demo Suite Documentation Printable Documentation (PDF) Product Page (Web)