EXAMPLE OF LINEARISATION
Consider a tank commonly used to store liquid to be processed as shown in Figure 1. The
aim is to study the control of the level H(t) of liquid in the tank of constant crosssectional area A such that it remains constant at a desir
FUNDAMENTALS OF CONTROL AND
MECHATRONICS FOR ENGINEERS
R. PAUROBALLY
(AUGUST 2011)
SCHOOL OF MECHANICAL ENGINEERING
THE UNIVERSITY OF WESTERN AUSTRALIA
CHAPTER 1
GENERAL INTRODUCTION
1.1 CONTROL SYSTEM
Control can be described as a study of the theory and
For the LeadLag compensators the following applies. You can derive the following
expressions.
The maximum/minimum phase is given by
sin max =
b a b a 1
=
b + a b a +1
or
b a
1 b a 1
= sin b a + 1
b + a
max = sin 1
The frequency at which this occurs
TABLE OF COMMON LAPLACE TRANSFORMS
Time Function f (t )
Unit Impulse
(t )
Delayed Impulse (t T )
Unit Step
u (t )
Unit Ramp
t
Polynomial
tn
Exponential
e at
Sine
sin t
Sin
sin(t + )
Sinh
sinh t
Cosine
cost
Cosine
cos(t + )
Cosh
cosh t
Damped sine
e at si
T HE UNIVERSITY OF WESTERN AUSTRALIA
SCHOOL OF MECHANICAL AND CHEMICAL E NGINEERING
MCTX3421 LABORATORY 2
SEPTEMBER 2011
ACTIVE EAR DEF ENDER
Submit r epor t in box M 4
Demonstrator: to be advised
Email: to be advised
Active Ear Defender
1. AIM OF LAB
The
L aboratory 1  FEEDBACK POSITION CONTROL
1
I NTRODUCTION
The aims of this laboratory are to:
Demonstrate practical steps involved in developing a feedback control system.
Introduce devices used to accomplish theoretical block diagrams.
Compare the dif
Control & Mechatronics
Lecture 35 Frequency domain, summary
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Aims are to:
 explain classical control theory and its applications
 analyse linear control systems

Control & Mechatronics
Lecture 34 Time domain, summary
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Aims are to:
 explain classical control theory and its applications
 analyse linear control systems
 expla
Control and Mechatronics
&
Process Dynamics and Control
Lecture 33 Process Design example , cont
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
OVEN TEMPERATURE CONTROL SYSTEM
heating element
+u(t)
Oven contain
Control and Mechatronics
&
Process Dynamics and Control
Lecture 32 Process Design example 1
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
OVEN TEMPERATURE CONTROL SYSTEM
heating element
+u(t)
Oven contains 100
Control and Mechatronics
&
Process Dynamics and Control
Lecture 31  Case study, Eardefender 2
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
FEEDBACK CONTROL EAR DEFENDER
P
o
Za
L
M
C
P, P
uc
CLOSEDLOOP STABI
Control and Mechatronics
&
Process Dynamics and Control
Lecture 30 Case study, Eardefender 1
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
AIM OF USING CONTROL IN PASSIVE EAR DEFENDERS
Ear defenders have poor
Control and Mechatronics
&
Process Dynamics and Control
Lecture 29  Realisation of compensators
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Realisation of phase compensators
1
Cs
1
s 1 R1C
Vo
1
+
( s)
Vi
Control and Mechatronics
&
Process Dynamics and Control
Lecture 28  Compensation techniques
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
SUMMARYCLOSED LOOP
Mp
1
2 1 2
P.O. (e
BW
p n 1 2 2
1 2
) 100
n 1 2
Control and Mechatronics
&
Process Dynamics and Control
Lecture 27  Frequency domain specifications
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
TRANSIENT PERFORMANCE CRITERIA
Three important criteria commonl
Control and Mechatronics
&
Process Dynamics and Control
Lecture 26  Nyquist stability criterion
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
NON MINIMUMPHASE SYSTEM
Im
Im
zeros
poles
X
10
XOO
3 2 1
O
5(
Control and Mechatronics
&
Process Dynamics and Control
Lecture 25 positive feedback, pure time
delay & nonminimum phase systems
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
SUMMARY OF STABILITY MARGINS
GM
g
Control and Mechatronics
&
Process Dynamics and Control
Lecture 24  Stability margins
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Schematic of acoustic feedback problem
Microphone
preamplifier
Microphone
Lou
Control and Mechatronics
&
Process Dynamics and Control
Lecture 23  Acoustic feedback and stability
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Controller in feedback path
U(j) +
E(j)
_
V(j)
G(j)
Y(j)
Plant
Control and Mechatronics
&
Process Dynamics and Control
Lecture 22 Stability, Process Control Example
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
StirredTank Heat Exchanger (STHE)
see Lecture 18
Flow rate, F
Control and Mechatronics
&
Process Dynamics and Control
Lecture 21  Stability from Frequency Response
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Openloop frequency response of robot arm
G ( j )
2
2
n
n
2
Control and Mechatronics
&
Process Dynamics and Control
Lecture 20  Bode Diagram
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
FREQUENCY RESPONSE FUNCTION
Transfer function
(s)
i
H(s)
o(s)
Definition of frequ
Control and Mechatronics
&
Process Dynamics and Control
Lecture 19  Frequency response methods
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
FREQUENCY RESPONSE (FR) METHODS
So far step input has been considere
Control and Mechatronics
&
Process Dynamics and Control
Lecture 18 PI Example
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
StirredTank Heat Exchanger (STHE)
Flow rate, F
Temperature, To
Temperature
controller
Control and Mechatronics
&
Process Dynamics and Control
Lecture 17  PI, PD, PID Controllers
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
Cascade Controller
U(s) +
E(s)
_
C(s)
V(s)
Controller
G(s)
Plant
Closed
Control and Mechatronics
&
Process Dynamics and Control
Lecture 16  P, I Controllers
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
EXAMPLE: ROBOT ARM
Varying K1 from 0 to K varies from 0 to
K
K 0
K
K
K 0.64
Control and Mechatronics
&
Process Dynamics and Control
Lecture 15  Root Locus Method
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
CONSTRUCTION OF ROUTHHURWITZ TABLE
j
i
1
2
3
4
3
2
1
a
an
sn
n2
n 1 a
a
s
n
Control and Mechatronics
&
Process Dynamics and Control
Lecture 14 RouthHurwitz Stability
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
ROUTHHURWITZ METHOD FOR STABILITY
AIM:
TO JUDGE IF A CONTROL SYSTEM IS S
Control and Mechatronics
&
Process Dynamics and Control
Lecture 13 closedloop poles, stability
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
TRANSIENT PERFORMANCE CRITERIA
There are 3 basic criteria most commo
Control and Mechatronics
&
Process Dynamics and Control
Lecture 12  dynamic performance, analytical solution
Dr. Roshun Paurobally
School of Mechanical Engineering
The University of Western Australia
EXAMPLE OF DYNAMIC PERFORMANCE
0.1, n 8rad / s =30
io