a brief introduction to the siso design toolusers.auth.gr/lazarosm/sisodesigntool.pdf · a brief...
Post on 28-Jun-2018
219 Views
Preview:
TRANSCRIPT
A Brief
Introduction To
The SISO Design
Tool Lecture notes for the seminars ‘An Introduction
to Matlab & Examples from Control Theory’ Aristotle University of Thessaloniki, Faculty of Sciences, Department of Mathematics
2012
Moysis Lazaros
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
For any questions, corrections or comments feel free to contact me:
Moysis Lazaros
M.Sc. student ‘Theoretical Informatics & Control Systems and Theory’.
Department of Mathematics, AUTH.
E-mail: moysis.lazaros@hotmail.com
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
3
An Introduction To The SISO Design Tool
The single input single output design tool is part of Matlab’s Control Systems Toolbox that enables us to analyse simple SISO system interconnections. The optimal tool for this task is Simulink,
but this toolbox helps us understand the basic capabilities of Matlab, so we can then proceed to Simulink.
This will be a simple introduction to the toolbox, so it is assumed that the reader is familiar with the theory behind transfer functions (and consequently zero-pole-gain, simple transfer functions or state-
space commands) and system interconnections (series, parallel and feedback).
We open the toolbox from:
Start ToolboxesControl SystemSISO Design Tool
This will open up two windows, the main toolbox window (Control and Estimation Tools
Manager) where we make all the design c hanges and another one with figures (SISO Design for SISO
Design Task) that displays different system characteristics, like Root Locus & Bode.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
We will now see the basic capabilities of the design tool.
Control Architecture
In Control Architecture we choose
among ready block architectures the
model we desire.
In Signs & Blocks and Signals we
change the feedback signs and give
the names we want to each block.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
5
System Data
The System Data window allows us
to change the values of the different
blocks.
The big bonus of this tool is that it
allows us to import data from the
workplace or a Mat file.
Choosing Browse opens the Model
Import window.
Here, we choose block G and import
the transfer function G that we
previously defined in the Command
Window. In this example the tf we
used is:
>>G=zpk([],[-1 -2 -3],1)
G
Zero/pole/gain:
1
-----------------
(s+1) (s+2) (s+3)
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
Compensator Editor
In Compensator Editor we can
manipulate the compensator
characteristics.
We can change the gain, but
we can also add poles and
zeros by right clicking in the
Pole/Zero window.
We will see later that we can
also change the compensator
from the Automated Tuning
options.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
7
Graphical Tuning
Analysis Plots
In Graphical Tuning we
choose which plots we want
to be displayed on our
figure.
We can choose between
Root Locus, Bode and
Nichols, as well as make the
choice between open or
closed loop system.
In Analysis Plots we can
choose Step Response,
Impulse Response, Bode
Diagram, Nyquist, Nichols
or Pole/Zero plots to be
displayed.
Here, we choose the
closed loop system from r
to y, (If we go back to
Control Architecture we
can see which is which)
and plot the Step and
Impulse Responses.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
We see that a new figure is displayed, containing the step and impulse responses.
By right clicking we can see characteristics such as the rise time and the peak response.
Changing the compensator value automatically changes the plotted responses.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
9
A good question is which is the transfer function for the whole feedback system. We know that
Matlab has probably computed it, but it is not displayed. This is no problem, because this toolbox also
allows us to export data to the workspace. So by choosing FileExport, this window pops up
So if we have the system architecture also displayed, we can easily find that the transfer function
we are looking for is the Closed Loop from r to y. We press export to workspace and a new system
named anadrasis is created in the form of state space.
>> anadrasis
a =
x1 x2 x3
x1 -1 1 0
x2 0 -2 1
x3 -1 0 -3
b =
r
x1 0
x2 0
x3 1
c =
x1 x2 x3
y 1 0 0
d =
r
y 0
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
Or in the form of transfer function:
>> t f(anadrasis)
Transfer function from input "r" to output "y":
1
----------------------
s^3 + 6 s^2 + 11 s + 7
Automated Tuning
In Automated Tuning we can
change the type of Compensator.
For example we choose PID
Tuning and a PI controller. When
we press Update Compensator we
get the new form for the
compensator C.
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
11
This concludes our basic analysis of the Control Systems Toolbox. There are some features we
did not dive into, yet we covered all the basic parts and features one needs to know. The next big step
from here is to get to know Simulink, an environment capable of designing all kinds of systems and real-
time applications.
As an exercise, you can study the case of C=-6. Check out the step and impulse responses. Do
you find the result unexpected? In order to understand this result, take a look at the closed loop transfer
function and it’s solution. Is this system stable? Is it BIBO (bounded- input bounded-output) stable?
A Brief Introduction To the SISO Design Tool – Moysis Lazaros
References 1. Mathworks Control System Toolbox videos & examples
http://www.mathworks.com/products/control/examples.html.
2. N. Karampetakis. Lecture notes for MSc course Computer Aided Control Systems, Dept. of
Mathematics AUTH.
3. A.I. Vardulakis, Εισαγωγή στη Μαθηματική Θεωρία Σημάτων, Συστημάτων και Ελέγχου Τόμος
Α΄. Εκδόσεις Τζιόλα 2012.
top related