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R2012a Documentation → Control System Toolbox
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Contents

Index

• Getting Started

Key Features

What Is a Plant?

Linear Model Representations

SISO Example: The DC Motor

Building SISO Models

Constructing Discrete Time Systems

Adding Delays to Linear Models

LTI Objects

MIMO Example: State-Space Model of Jet Transport Aircraft

Constructing MIMO Transfer Functions

Accessing I/O Pairs in MIMO Systems

Arithmetic Operations for Interconnecting Models

Feedback Interconnections

Available Commands for Continuous/Discrete Conversion

Available Methods for Continuous/Discrete Conversion

Digitizing the Discrete DC Motor Model

Model Order Reduction Commands

Techniques for Reducing Model Order

Example: Gasifier Model

Plot Types Available in the 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

What is the Linear Simulation Tool?

Opening the Linear Simulation Tool

Working with the Linear Simulation Tool

Importing Input Signals

Example: Loading Inputs from a Microsoft Excel Spreadsheet

Example: Importing Inputs from the Workspace

Designing Input Signals

Specifying Initial Conditions

When to Use Functions for Time and Frequency Response

Time and Frequency Response Functions

Plotting MIMO Model Responses

Data Markers

Plotting and Comparing Multiple Systems

Creating Custom Plots

Choosing a PID Controller Design Tool

Designing PID Controllers with the PID Tuner GUI

PID Controller Design for Fast Reference Tracking

Designing PID Controllers at the Command Line

Tune Compensator Parameters Using the SISO Design Tool

Components of the SISO Tool

Design Options in the SISO Tool

Opening the SISO Design Tool

Using the SISO Design Task Node in the Control and Estimation Tools Manager

Importing Models into the SISO Design Tool

Feedback Structure

Analysis Plots for Loop Responses

Using the Graphical Tuning Window

Exporting the Compensator and Models

Storing and Retrieving Intermediate Designs

What Is Bode Diagram Design?

Bode Diagram Design for DC Motor

Adjusting the Compensator Gain

Adjusting the Bandwidth

Adding an Integrator

Adding a Lead Network

Moving Compensator Poles and Zeros

Adding a Notch Filter

Modifying a Prefilter

What Is Root Locus Design?

Root Locus Design for Electrohydraulic Servomechanism

Changing the Compensator Gain

Adding Poles and Zeros to the Compensator

Editing Compensator Pole and Zero Locations

Viewing Damping Ratios

What Is Nichols Plot Design?

Nichols Plot Design for DC Motor

Opening a Nichols Plot

Adjusting the Compensator Gain

Adding an Integrator

Adding a Lead Network

Supported Automated Tuning Methods

Loading and Displaying the DC Motor Example for Automated Tuning

Applying Automated PID Tuning

When to Use Multi-Loop Compensator Design

Workflow for Multi-Loop Compensator Design

Position Control of a DC Motor

Multiple Models Represent System Variations

Control Design Analysis Using the SISO Design Tool

Specifying a Nominal Model

Frequency Grid for Multimodel Computations

How to Analyze the Controller Design for Multiple Models

When to Use Functions for Compensator Design

Root Locus Design

Pole Placement

Linear-Quadratic-Gaussian (LQG) Design

Design an LQG Regulator

Design an LQG Servo Controller

Design an LQR Servo Controller in Simulink

• User's Guide

• Blocks

• Functions

• GUIs

• Numeric Linear Models

• Generalized Linear Models

• Data Extraction

• Conversions

• System Interconnections

• System Gain and Dynamics

• Time Domain Analysis

• Frequency Domain Analysis

• Model Simplification

• Compensator Design

• LQR/LQG Design

• State-Space Models

• Frequency Response Data Models

• Time Delays

• Model Dimensions and Characteristics

• Overloaded and Arithmetic Operators

• Matrix Equation Solvers

• Preferences

• Visualization of Model Dynamics and Responses

• Plot Customization

Examples

• Release Notes

c2dOptions - Create option set for continuous- to discrete-time conversions

Syntax

opts = c2dOptions opts = c2dOptions('OptionName', OptionValue)

Description

opts = c2dOptions returns the default options for c2d.

opts = c2dOptions('OptionName', OptionValue) accepts one or more comma-separated name/value pairs that specify options for the c2d command. Specify OptionName inside single quotes.

Input Arguments

Name-Value Pair Arguments

'Method'

Discretization method, specified as one of the following values:

'zoh' Zero-order hold, where c2d assumes the control inputs are piecewise constant over the sampling period Ts.

'foh' Triangle approximation (modified first-order hold), where c2d assumes the control inputs are piecewise linear over the sampling period Ts. (See [1], p. 228.)

'impulse' Impulse-invariant discretization.

'tustin' Bilinear (Tustin) approximation. By default, c2d discretizes with no prewarp and rounds any fractional time delays to the nearest multiple of the sample time. To include prewarp, use the PrewarpFrequency option. To approximate fractional time delays, use theFractDelayApproxOrder option.

'matched' Zero-pole matching method. (See [1], p. 224.) By default, c2d rounds any fractional time delays to the nearest multiple of the sample time. To approximate fractional time delays, use the FractDelayApproxOrder option.

Default: 'zoh'

'PrewarpFrequency'

Prewarp frequency for 'tustin' method, specified in rad/TimeUnit, where TimeUnit is the time units, specified in the TimeUnit property, of the discretized system. Takes positive scalar values. A value of 0 corresponds to the standard 'tustin' method without prewarp.

Default: 0

'FractDelayApproxOrder'

Maximum order of the Thiran filter used to approximate fractional delays in the 'tustin' and 'matched' methods. Takes integer values. A value of 0 means that c2d rounds fractional delays to the nearest integer multiple of the sample time.

Default: 0

Examples

Discretize two models using identical discretization options.

% generate two arbitrary continuous-time state-space models
sys1 = rss(3, 2, 2);
sys2 = rss(4, 4, 1);

Use c2dOptions to create a set of discretization options.

opt = c2dOptions('Method', 'tustin', 'PrewarpFrequency', 3.4);

Then, discretize both models using the option set.

dsys1 = c2d(sys1, 0.1, opt);  % 0.1s sampling time
dsys2 = c2d(sys2, 0.2, opt);  % 0.2s sampling time

The c2dOptions option set does not include the sampling time Ts. You can use the same discretization options to discretize systems using a different sampling time.