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Contents

Index

• Getting Started

What Is a Plant?

Linear Model Representations

SISO Example: The DC Motor

Building SISO Models

Constructing Discrete Time Systems

Adding Delays to Linear Models

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

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

Linear-Quadratic-Gaussian (LQG) Design

Design an LQG Regulator

Design an LQG Servo Controller

Design an LQR Servo Controller in Simulink

• User's Guide

• GUIs

• Numeric Linear Models

• Generalized Linear Models

• Data Extraction

• Conversions

• System Interconnections

• System Gain and Dynamics

• Time Domain Analysis

• Frequency Domain Analysis

getGainCrossover

• 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

• Release Notes

allmargin - Gain margin, phase margin, delay margin and crossover frequencies

Syntax

S = allmargin(sys) S = allmargin(mag,phase,w,ts)

Description

S = allmargin(sys)

allmargin computes the gain margin, phase margin, delay margin and the corresponding crossover frequencies of the SISO open-loop model sys. The allmargin command is applicable to any SISO model, including models with delays.

The output S is a structure with the following fields:

GMFrequency — All –180° (modulo 360°) crossover frequencies in rad/TimeUnit, where TimeUnit is the time units of the input dynamic system, specified in the TimeUnit property of sys.
GainMargin — Corresponding gain margins, defined as 1/G, where G is the gain at the –180° crossover frequency. Gain margins are in absolute units.
PMFrequency — All 0 dB crossover frequencies in rad/TimeUnit, where TimeUnit is the time units of the input dynamic system, specified in the TimeUnit property of sys).
PhaseMargin — Corresponding phase margins in degrees.
DMFrequency and DelayMargin — Critical frequencies and the corresponding delay margins. Delay margins are specified in the time units of the system for continuous-time systems and multiples of the sample time for discrete-time systems.
Stable — 1 if the nominal closed-loop system is stable, 0 otherwise.
Where stability cannot be assessed, Stable is set to NaN. In general, stability cannot be assessed for an frd system.

S = allmargin(mag,phase,w,ts) computes the stability margins from the frequency response data mag, phase, w, and the sampling time, ts. Provide magnitude values mag in absolute units, and phase values phase in degrees. You can provide the frequency vector w in any units; allmargin returns frequencies in the same units. allmargin interpolates between frequency points to approximate the true stability margins.

See Also

ltiview | margin

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