MATLAB Control Sytem Toolbox™ User's Guide

Linear System Modeling
	Linear System Model Objects
		What Are Model Objects?
			Model Objects Represent Linear Systems
			About Model Data
		Control System Modeling with Model Objects
		Types of Model Objects
		Dynamic System Models
		Static Models
		Numeric Models
			Numeric Linear Time Invariant (LTI) Models
			Identified LTI Models
			Identified Nonlinear Models
		Generalized Models
			Generalized and Uncertain LTI Models
			Control Design Blocks
			Generalized Matrices
		Models with Tunable Coefficients
			Tunable Generalized LTI Models
			Modeling Tunable Components
			Modeling Control Systems with Tunable Components
			Internal Structure of Generalized Models
		Using Model Objects
		References
	Model Creation
		Transfer Functions
			Transfer Function Representations
			Commands for Creating Transfer Functions
			Create Transfer Function Using Numerator and Denominator Coefficients
			Create Transfer Function Model Using Zeros, Poles, and Gain
		State-Space Models
			State-Space Model Representations
			Explicit State-Space Models
			Descriptor (Implicit) State-Space Models
			Commands for Creating State-Space Models
			Create State-Space Model From Matrices
		Frequency Response Data (FRD) Models
			Frequency Response Data
			Commands for Creating FRD Models
			Create Frequency-Response Model from Data
		Proportional-Integral-Derivative (PID) Controllers
			Continuous-Time PID Controller Representations
			Create Continuous-Time Parallel-Form PID Controller
			Create Continuous-Time Standard-Form PID Controller
		Two-Degree-of-Freedom PID Controllers
			Continuous-Time 2-DOF PID Controller Representations
			2-DOF Control Architectures
		Discrete-Time Numeric Models
			Create Discrete-Time Transfer Function Model
			Other Model Types in Discrete Time Representations
		Discrete-Time Proportional-Integral-Derivative (PID) Controllers
			Discrete-Time PID Controller Representations
			Create Discrete-Time Standard-Form PID Controller
			Discrete-Time 2-DOF PI Controller in Standard Form
		MIMO Transfer Functions
			Concatenation of SISO Models
			Using the tf Function with Cell Arrays
		MIMO State-Space Models
			MIMO Explicit State-Space Models
			MIMO Descriptor State-Space Models
			State-Space Model of Jet Transport Aircraft
		MIMO Frequency Response Data Models
		Select Input/Output Pairs in MIMO Models
		Time Delays in Linear Systems
			First Order Plus Dead Time Model
			Input and Output Delay in State-Space Model
			Transport Delay in MIMO Transfer Function
			Discrete-Time Transfer Function with Time Delay
		Closing Feedback Loops with Time Delays
		Time-Delay Approximation
			Time-Delay Approximation in Discrete-Time Models
		Time-Delay Approximation in Continuous-Time Open-Loop Model
		Time-Delay Approximation in Continuous-Time Closed-Loop Model
		Approximate Different Delays with Different Approximation Orders
		Convert Time Delay in Discrete-Time Model to Factors of 1/z
		Frequency Response Data (FRD) Model with Time Delay
		Internal Delays
			Why Internal Delays Are Necessary
			Behavior of Models With Internal Delays
			Inside Time Delay Models
			Functions That Support Internal Time Delays
			Functions That Do Not Support Internal Time Delays
			References
		Tunable Low-Pass Filter
		Create Tunable Second-Order Filter
		Create State-Space Model with Both Fixed and Tunable Parameters
		Control System with Tunable Components
		Control System with Multichannel Analysis Points
		Mark Signals of Interest for Control System Analysis and Design
			Analysis Points
			Specify Analysis Points for MATLAB Models
			Specify Analysis Points for Simulink Models
			Refer to Analysis Points for Analysis and Tuning
		Model Arrays
			What Are Model Arrays?
			Uses of Model Arrays
			Visualizing Model Arrays
			Visualizing Selection of Models From Model Arrays
		Select Models from Array
		Query Array Size and Characteristics
		Linear Parameter-Varying Models
			What are Linear Parameter-Varying Models?
			Regular vs. Irregular Grids
			Use Model Arrays to Create Linear Parameter-Varying Models
			Approximate Nonlinear Systems using LPV Models
			Applications of Linear Parameter-Varying Models
		Using LTI Arrays for Simulating Multi-Mode Dynamics
Working with Linear Models
	Data Manipulation
		Store and Retrieve Model Data
			Model Properties
			Specify Model Properties at Model Creation
			Examine and Change Properties of an Existing Model
		Extract Model Coefficients
			Functions for Extracting Model Coefficients
			Extracting Coefficients of Different Model Type
			Extract Numeric Model Data and Time Delay
			Extract PID Gains from Transfer Function
		Attach Metadata to Models
			Specify Model Time Units
			Interconnect Models with Different Time Units
			Specify Frequency Units of Frequency-Response Data Model
			Extract Subsystems of Multi-Input, Multi-Output (MIMO) Models
			Specify and Select Input and Output Groups
		Query Model Characteristics
		Customize Model Display
			Configure Transfer Function Display Variable
			Configure Display Format of Transfer Function in Factorized Form
	Model Interconnections
		Why Interconnect Models?
		Catalog of Model Interconnections
			Model Interconnection Commands
			Arithmetic Operations
		Numeric Model of SISO Feedback Loop
		Control System Model With Both Numeric and Tunable Components
		Multi-Loop Control System
		Mark Analysis Points in Closed-Loop Models
		MIMO Control System
		MIMO Feedback Loop
		How the Software Determines Properties of Connected Models
		Rules That Determine Model Type
		Recommended Model Type for Building Block Diagrams
	Model Transformation
		Conversion Between Model Types
			Explicit Conversion Between Model Types
			Automatic Conversion Between Model Types
			Recommended Working Representation
		Convert From One Model Type to Another
		Get Current Value of Generalized Model by Model Conversion
		Decompose a 2-DOF PID Controller into SISO Components
		Discretize a Compensator
		Improve Accuracy of Discretized System with Time Delay
		Convert Discrete-Time System to Continuous Time
		Continuous-Discrete Conversion Methods
			Zero-Order Hold
			First-Order Hold
			Impulse-Invariant Mapping
			Tustin Approximation
			Zero-Pole Matching Equivalents
			Least Squares
		Upsample Discrete-Time System
		Choosing a Resampling Command
	Model Simplification
		Model Reduction Basics
			When to Reduce Model Order
			Model Reduction Tools
			Choosing a Model Reduction Method
		Reduce Model Order Using the Model Reducer App
		Balanced Truncation Model Reduction
			Balanced Truncation in the Model Reducer App
			Balanced Truncation in Other Environments
		Approximate Model by Balanced Truncation at the Command Line
		Compare Truncated and DC Matched Low-Order Model Approximations
		Approximate Model with Unstable or Near-Unstable Pole
		Frequency-Limited Balanced Truncation
		Model Reduction in the Live Editor
		Pole-Zero Simplification
			Pole-Zero Simplification in the Model Reducer App
			Pole-Zero Cancellation at the Command Line
		Mode-Selection Model Reduction
			Mode Selection in the Model Reducer App
			Mode Selection at the Command Line
		Visualize Reduced-Order Models in the Model Reducer App
			Error Plots
			Response Plots
			Plot Characteristics
			Plot Tools
Linear Analysis
	Time Domain Analysis
		Plotting System Responses
		Time-Domain Responses
		Time-Domain Response Data and Plots
		Time-Domain Characteristics on Response Plots
		Numeric Values of Time-Domain System Characteristics
		Time-Domain Responses of Discrete-Time Model
		Time-Domain Responses of MIMO Model
		Time-Domain Responses of Multiple Models
		Joint Time-Domain and Frequency-Domain Analysis
		Response from Initial Conditions
		Import LTI Model Objects into Simulink
			Simulate LTI Model in Simulink
			Import MIMO LTI Model into Simulink
		Analysis of Systems with Time Delays
			Considerations to Keep in Mind when Analyzing Systems with Internal Time Delays
	Frequency Domain Analysis
		Frequency-Domain Responses
		Frequency Response of a SISO System
		Frequency Response of a MIMO System
		Frequency-Domain Characteristics on Response Plots
		Numeric Values of Frequency-Domain Characteristics of SISO Model
		Pole and Zero Locations
		Assessing Gain and Phase Margins
		Analyzing Control Systems with Delays
		Analyzing the Response of an RLC Circuit
	Sensitivity Analysis
		Model Array with Single Parameter Variation
		Model Array with Variations in Two Parameters
		Study Parameter Variation by Sampling Tunable Model
		Sensitivity of Control System to Time Delays
	Passivity and Conic Sectors
		About Passivity and Passivity Indices
		About Sector Bounds and Sector Indices
		Passivity Indices
		Parallel Interconnection of Passive Systems
		Series Interconnection of Passive Systems
		Feedback Interconnection of Passive Systems
Control Design
	PID Controller Design
		PID Controller Design at the Command Line
		Designing Cascade Control System with PI Controllers
		Tune 2-DOF PID Controller (Command Line)
		Tune 2-DOF PID Controller (PID Tuner)
		PID Controller Types for Tuning
			Specifying PID Controller Type
			1-DOF Controllers
			2-DOF Controllers
			2-DOF Controllers with Fixed Setpoint Weights
		PID Controller Tuning in Simulink
		Design PID Controller Using Estimated Frequency Response
		Design Family of PID Controllers for Multiple Operating Points
		Design PID Controller Using Simulated I/O Data
		PID Controller Design in the Live Editor
		Tune PID Controller from Measured Plant Data Using Live Editor Tasks
	Classical Control Design
		Choosing a Control Design Approach
		Control System Designer Tuning Methods
			Graphical Tuning Methods
			Automated Tuning Methods
			Effective Plant for Tuning
			Select a Tuning Method
		Design Requirements
			Add Design Requirements
			Edit Design Requirements
			Root Locus and Pole-Zero Plot Requirements
			Open-Loop and Closed-Loop Bode Diagram Requirements
			Open-Loop Nichols Plot Requirements
			Step and Impulse Response Requirements
		Feedback Control Architectures
		Design Multiloop Control System
		Multimodel Control Design
			Control Design Overview
			Model Arrays
			Nominal Model
			Frequency Grid
			Design Controller for Multiple Plant Models
		Bode Diagram Design
			Tune Compensator For DC Motor Using Bode Diagram Graphical Tuning
		Root Locus Design
			Tune Electrohydraulic Servomechanism Using Root Locus Graphical Tuning
		Nichols Plot Design
			Tune Compensator For DC Motor Using Nichols Plot Graphical Design
		Edit Compensator Dynamics
			Compensator Editor
			Graphical Compensator Editing
			Poles and Zeros
			Lead and Lag Networks
			Notch Filters
		Design Compensator Using Automated Tuning Methods
			Select Tuning Method
			Select Compensator and Loop to Tune
			PID Tuning
			Optimization-Based Tuning
			LQG Synthesis
			Loop Shaping
			Internal Model Control Tuning
		Analyze Designs Using Response Plots
			Analysis Plots
			Editor Plots
			Plot Characteristics
			Plot Tools
			Design Requirements
		Compare Performance of Multiple Designs
		Design Hard-Disk Read/Write Head Controller
		Design Compensator for Plant Model with Time Delays
		Design Compensator for Systems Represented by Frequency Response Data
		Design Internal Model Controller for Chemical Reactor Plant
		Design LQG Tracker Using Control System Designer
		Export Design to MATLAB Workspace
		Generate Simulink Model for Control Architecture
		Tune Simulink Blocks Using Compensator Editor
		Single Loop Feedback/Prefilter Compensator Design
		Cascaded Multiloop Feedback Design
		Reference Tracking of DC Motor with Parameter Variations
	State-Space Control Design
		Extended and Unscented Kalman Filter Algorithms for Online State Estimation
			Extended Kalman Filter Algorithm
			Unscented Kalman Filter Algorithm
		Generate Code for Online State Estimation in MATLAB
			Tunable and Nontunable Object Properties
		Validate Online State Estimation at the Command Line
			Examine Output Estimation Error
			Examine State Estimation Error for Simulated Data
		Validate Online State Estimation in Simulink
			Examine Residuals
			Examine State Estimation Error for Simulated Data
			Compute Residuals and State Estimation Errors
		Troubleshoot Online State Estimation
		Nonlinear State Estimation Using Unscented Kalman Filter and Particle Filter
		Estimate States of Nonlinear System with Multiple, Multirate Sensors
		Regulate Pressure in Drum Boiler
Control System Tuning
	Control System Tuning
		Automated Tuning Overview
		Choosing an Automated Tuning Approach
		Automated Tuning Workflow
		Specify Control Architecture in Control System Tuner
			About Control Architecture
			Predefined Feedback Architecture
			Arbitrary Feedback Control Architecture
			Control System Architecture in Simulink
		Open Control System Tuner for Tuning Simulink Model
			Command-Line Equivalents
		Specify Operating Points for Tuning in Control System Tuner
			About Operating Points in Control System Tuner
			Linearize at Simulation Snapshot Times
			Compute Operating Points at Simulation Snapshot Times
			Compute Steady-State Operating Points
		Specify Blocks to Tune in Control System Tuner
		View and Change Block Parameterization in Control System Tuner
			View Block Parameterization
			Fix Parameter Values or Limit Tuning Range
			Custom Parameterization
			Block Rate Conversion
		Setup for Tuning Control System Modeled in MATLAB
		How Tuned Simulink Blocks Are Parameterized
			Blocks With Predefined Parameterization
			Blocks Without Predefined Parameterization
			View and Change Block Parameterization
		Specify Goals for Interactive Tuning
		Quick Loop Tuning of Feedback Loops in Control System Tuner
		Quick Loop Tuning
			Purpose
			Description
			Feedback Loop Selection
			Desired Goals
			Options
			Algorithms
		Step Tracking Goal
			Purpose
			Description
			Step Response Selection
			Desired Response
			Options
			Algorithms
		Step Rejection Goal
			Purpose
			Description
			Step Disturbance Response Selection
			Desired Response to Step Disturbance
			Options
			Algorithms
		Transient Goal
			Purpose
			Description
			Response Selection
			Initial Signal Selection
			Desired Transient Response
			Options
			Tips
			Algorithms
		LQR/LQG Goal
			Purpose
			Description
			Signal Selection
			LQG Objective
			Options
			Tips
			Algorithms
		Gain Goal
			Purpose
			Description
			I/O Transfer Selection
			Options
			Algorithms
		Variance Goal
			Purpose
			Description
			I/O Transfer Selection
			Options
			Tips
			Algorithms
		Reference Tracking Goal
			Purpose
			Description
			Response Selection
			Tracking Performance
			Options
			Algorithms
		Overshoot Goal
			Purpose
			Description
			Response Selection
			Options
			Algorithms
		Disturbance Rejection Goal
			Purpose
			Description
			Disturbance Scenario
			Rejection Performance
			Options
			Algorithms
		Sensitivity Goal
			Purpose
			Description
			Sensitivity Evaluation
			Sensitivity Bound
			Options
			Algorithms
		Weighted Gain Goal
			Purpose
			Description
			I/O Transfer Selection
			Weights
			Options
			Algorithms
		Weighted Variance Goal
			Purpose
			Description
			I/O Transfer Selection
			Weights
			Options
			Tips
			Algorithms
		Minimum Loop Gain Goal
			Purpose
			Description
			Open-Loop Response Selection
			Desired Loop Gain
			Options
			Algorithms
		Maximum Loop Gain Goal
			Purpose
			Description
			Open-Loop Response Selection
			Desired Loop Gain
			Options
			Algorithms
		Loop Shape Goal
			Purpose
			Description
			Open-Loop Response Selection
			Desired Loop Shape
			Options
			Algorithms
		Margins Goal
			Purpose
			Description
			Feedback Loop Selection
			Desired Margins
			Options
			Algorithms
		Passivity Goal
			Purpose
			Description
			I/O Transfer Selection
			Options
			Algorithms
		Conic Sector Goal
			Purpose
			Description
			I/O Transfer Selection
			Options
			Tips
			Algorithms
		Weighted Passivity Goal
			Purpose
			Description
			I/O Transfer Selection
			Weights
			Options
			Algorithms
		Poles Goal
			Purpose
			Description
			Feedback Configuration
			Pole Location
			Options
			Algorithms
		Controller Poles Goal
			Purpose
			Description
			Constrain Dynamics of Tuned Block
			Keep Poles Inside the Following Region
			Algorithms
		Manage Tuning Goals
		Generate MATLAB Code from Control System Tuner for Command-Line Tuning
		Interpret Numeric Tuning Results
			Tuning-Goal Scalar Values
			Tuning Results at the Command Line
			Tuning Results in Control System Tuner
			Improve Tuning Results
		Visualize Tuning Goals
			Tuning-Goal Plots
			Difference Between Dashed Line and Shaded Region
			Improve Tuning Results
		Create Response Plots in Control System Tuner
		Examine Tuned Controller Parameters in Control System Tuner
		Compare Performance of Multiple Tuned Controllers
		Create and Configure slTuner Interface to Simulink Model
		Stability Margins in Control System Tuning
			Gain and Phase Margins
			Combined Gain and Phase Variations
			Interpreting the Gain and Phase Margin Plot
			Algorithm
		Tune Control System at the Command Line
		Speed Up Tuning with Parallel Computing Toolbox Software
		Validate Tuned Control System
			Extract and Plot System Responses
			Validate Design in Simulink Model
		Extract Responses from Tuned MATLAB Model at the Command Line
	Loop-Shaping Design
		Structure of Control System for Tuning With looptune
		Set Up Your Control System for Tuning with looptune
			Set Up Your Control System for looptunein MATLAB
			Set Up Your Control System for looptune in Simulink
		Tune MIMO Control System for Specified Bandwidth
		Tuning Feedback Loops with LOOPTUNE
		Decoupling Controller for a Distillation Column
		Tuning of a Digital Motion Control System
	Gain-Scheduled Controllers
		Gain Scheduling Basics
			Gain Scheduling in Simulink
			Tune Gain Schedules
		Model Gain-Scheduled Control Systems in Simulink
			Model Scheduled Gains
			Gain-Scheduled Equivalents for Commonly Used Control Elements
			Custom Gain-Scheduled Control Structures
			Tunability of Gain Schedules
		Tune Gain Schedules in Simulink
			Workflow for Tuning Gain Schedules
		Plant Models for Gain-Scheduled Controller Tuning
			Obtaining the Family of Linear Models
			Set Up for Gain Scheduling by Linearizing at Design Points
			Sample System at Simulation Snapshots
			Sample System at Varying Parameter Values
			Eliminate Samples at Unneeded Design Points
			LPV Plants in MATLAB
		Multiple Design Points in slTuner Interface
			Block Substitution for Plant
			Multiple Block Substitutions
			Substituting Blocks that Depend on the Scheduling Variables
			Resolving Mismatches Between a Block and its Substitution
			Block Substitution for LPV Blocks
		Parameterize Gain Schedules
			Basis Function Parameterization
			Tunable Gain Surfaces
			Tunable Gain with Two Independent Scheduling Variables
			Tunable Surfaces in Simulink
			Tunable Surfaces in MATLAB
		Change Requirements with Operating Condition
			Define Variable Tuning Goal
			Enforce Tuning Goal at Subset of Design Points
			Exclude Design Points from systune Run
		Validate Gain-Scheduled Control Systems
			Examine Tuned Gain Surfaces
			Visualize Tuning Goals
			Check Linear Performance
			Validate Gain Schedules in Nonlinear System
		Gain-Scheduled Control of a Chemical Reactor
		Tuning of Gain-Scheduled Three-Loop Autopilot
		Trimming and Linearization of the HL-20 Airframe
		Angular Rate Control in the HL-20 Autopilot
		Attitude Control in the HL-20 Autopilot - SISO Design
		Attitude Control in the HL-20 Autopilot - MIMO Design
		MATLAB Workflow for Tuning the HL-20 Autopilot
	Control System Tuning Examples - Generalized LTI Models
		Tuning Control Systems with SYSTUNE
		Building Tunable Models
		Active Vibration Control in Three-Story Building
		Vibration Control in Flexible Beam
		Passive Control with Communication Delays
	Control System Tuning Examples
		Tuning Multiloop Control Systems
		PID Tuning for Setpoint Tracking vs. Disturbance Rejection
		Time-Domain Specifications
		Frequency-Domain Specifications
		Loop Shape and Stability Margin Specifications
		System Dynamics Specifications
		Configuring Design Requirements
		Validating Results
		Tune Control Systems in Simulink
		Tune a Control System Using Control System Tuner
		Using Parallel Computing to Accelerate Tuning
		Control of a Linear Electric Actuator
		Control of a Linear Electric Actuator Using Control System Tuner
		Multi-Loop PI Control of a Robotic Arm
		Control of an Inverted Pendulum on a Cart
		Digital Control of Power Stage Voltage
		MIMO Control of Diesel Engine
		Tuning of a Two-Loop Autopilot
		Multiloop Control of a Helicopter
		Fixed-Structure Autopilot for a Passenger Jet
		Fault-Tolerant Control of a Passenger Jet
		Passive Control of Water Tank Level
		Tuning for Multiple Values of Plant Parameters
Customization
	Preliminaries
		Terminology
		Property and Preferences Hierarchy
		Ways to Customize Plots
	Setting Toolbox Preferences
		Toolbox Preferences Editor
			Overview of the Toolbox Preferences Editor
			Opening the Toolbox Preferences Editor
			Units Pane
			Style Pane
			Options Pane
			SISO Tool Pane
	Setting Tool Preferences
		Linear System Analyzer Preferences Editor
			Opening the Linear System Analyzer Preference Editor
			Units Pane
			Style Pane
			Options Pane
			Parameters Pane
	Customizing Response Plot Properties
		Customize Response Plots Using the Response Plots Property Editor
			Opening the Property Editor
			Overview of Response Plots Property Editor
			Labels Pane
			Limits Pane
			Units Pane
			Style Pane
			Options Pane
			Editing Subplots Using the Property Editor
		Customizing Response Plots Using Plot Tools
			Properties You Can Customize Using Plot Tools
			Opening and Working with Plot Tools
			Example of Changing Line Color Using Plot Tools
		Customizing Response Plots from the Command Line
			Overview of Customizing Plots from the Command Line
			Obtaining Plot Handles
			Obtaining Plot Options Handles
			Examples of Customizing Plots from the Command Line
			Properties and Values Reference
		Build GUI With Interactive Response-Plot Updates
Design Case Studies
	Design Yaw Damper for Jet Transport
		Overview of this Case Study
		Creating the Jet Model
		Computing Open-Loop Poles
		Open-Loop Analysis
		Root Locus Design
		Washout Filter Design
	LQG Regulation: Rolling Mill Case Study
		Overview of this Case Study
		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
Canonical State-Space Realizations
	Canonical State-Space Realizations
		Modal Canonical Form
		Companion Canonical Form
		Observable Canonical Form
		Controllable Canonical Form
Reliable Computations
	Scaling State-Space Models
		Why Scaling Is Important
		When to Scale Your Model
		Manually Scale Your Model
Linear System Analyzer
	Linear System Analyzer Overview
	Using the Right-Click Menu in the Linear System Analyzer
		Overview of the Right-Click Menu
		Setting Characteristics of Response Plots
	Importing, Exporting, and Deleting Models in the Linear System Analyzer
		Importing Models
		Exporting Models
		Deleting Models
	Selecting Response Types
		Methods for Selecting Response Types
		Right Click Menu: Plot Type
		Plot Configurations Window
		Line Styles Editor
	Analyzing MIMO Models
		Overview of Analyzing MIMO Models
		Array Selector
		I/O Grouping for MIMO Models
		Selecting I/O Pairs
	Customizing the Linear System Analyzer
		Overview of Customizing the Linear System Analyzer
		Linear System Analyzer Preferences Editor