Extras Index
This section contains a list of the pages that are not in
the main flow of the which are not in the main flow of the tutorials, but
which provide important reference information. Short descriptions of each
Extra page are provided.
The Conversions page explains how to use MATLAB to convert between
three different types of representations of a control system. The three
forms are the transfer function form, the state space form, and the
zero-pole-gain form which can be represented using vectrors, matrices, or
MATLAB's 'sys' formats.
The Commands page contains a list of the commands used in Controls
Tutorials for MATLAB. Commands are standard
MATLAB Commands, commands from
the Controls Systems Toolbox, or customized commands written for the
tutorials.
The Difference Equations page describes the difference equation
description of discrete-time systems and how to derive transfer functions
and state space representations from them.
The Discrete Lead-Lag page covers the design of discrete-time lead
and lag controllers using root locus methods.
The Digital Steady State Error page explains the Final Value
Theorem for discrete time systems and how to use it to calculate the steady
state error of a system for a step input or an impulse input.
The Discrete Transient Response page shows more analysis of the
relationship between the transient response of a discrete-time system and
the locations of the dominant poles.
The Function page gives an introduction on how to write your own
functions in MATLAB.
Links to files containing functions written for
Controls to Tutorials for MATLAB are provided.
The function lnyquist.m is a variation of nyquist1.m below which
plots the polar plot of a transfer function using log2 | G(jw) + 1| as the
radius instead of | G(jw) +1|. The same algorithm is used to shape the
Nyquist contour around the poles on the imaginary axis and the origin. The
page contains an explanation and code listing for the function.
The function nyquist1.m contains a special contour shaping
algorithm to handle poles on the imaginary axis and at the origin, for
which MATLAB's
nyquist command frequently gives erroneous results. The
page contains an explanation and code listing for the function.
This function will find the scale factor for a full-state feedback
system to eliminate the steady-state error in response to a step reference
input. The page contains an explanation and code listing for the function.
This function will plot a vertical line through a point on the real
axis of a graph generated by another plotting function, such as rlocus. The
function is useful for plotting a bound of the real parts of poles on a
root locus plot. The page contains an explanation and code listing for the
function.
This page contains an explanation and a code listing of the
function wbw.m which returns the approximate closed loop bandwidth
frequency given the desired damping ratio of the dominant closed loop poles
and desired the peak time or settling time of the closed loop step response.
This page discusses the time lag effect caused by using a
zero-order hold with a discrete control system response.
The Lead and Lag Compensators page shows how to design
continuous-time lead, lag, and lead-lag compensators in MATLAB using root
locus and frequency response techniques.
The Lsim page explains the MATLAB command lsim, which simulates the
time response of a linear time invariant system (continuous-time or
discrete-time) to arbitrary inputs and initial conditions.
The Introduction to M-files page describes how to use files called
m-files or script files which contain MATLAB commands. M-files serve as
MATLAB programs and MATLAB
executes the commands exactly as if the commands
had been executed at the MATLAB prompt.
The Notch Filter page explains how to design a compensator that
will place zeroes to approximately cancel lightly damped complex conjugate
poles of a system with a resonance.
The PID Bilinear page shows how to design a discrete-time PID
compensator using a bilinear transformation substitution for the Laplace
variable in a continuous-time PID transfer function.
This page explains the basics of using MATLAB's
plot command
including how to plot different line styles and different colors. Other
topics covered include the subplot command, changing the axes, and adding
text to a plot.
This page discusses the problem with attempting to cancel a
right-half plane pole with a zero at the same location and shows why a
designer should never do this.
This page explains the functionality of the blocks appearing in the
Sources, Sinks, Linear, Discrete, Nonlinear, and Connections Simulink Block
Libraries.
This page examines the three of the ways in which Simulink can
interact with MATLAB. These are
The Steady State Error page explains the concept of steady state
error and how to calculate steady state error for various standard test
inputs. The page covers relationship between system type (the number of
free integrators) and the steady state error for the step, ramp, and
parabolic test inputs. The page also shows how to design a compensator to
reduce or eliminate steady state error.
The Step page describes the use of the step command which is one
of most useful functions in the MATLAB Control Systems Toolbox for control
system design. The step command plots the response of a system represented
in either transfer function, state space, or zero/pole format to a
continuous or discrete step input.
- Tutorials
-
MATLAB Basics |
MATLAB Modeling |
PID |
Root Locus |
Frequency Response |
State Space |
Digital Control |
Simulink Basics |
Simulink Modeling |
Examples
