Course Outline
Semester 1
2015
MMAN3200
Linear Systems and Control
MMAN3200 Linear Systems and Control
Contents
1.
Course Staff
2
2.
Course Details
2
3.
Rationale for inclusion of content and teaching approach
5
4.
Teaching Strategies
5
5.
Assessment
6
6.
Bode Diagrams  Tutorial and Exercise
Contents
1 Bode plots
1
2 Frequency domain performance criteria
2
3 Gain and Phases Margin
2
4 Example 1
4
5 Example 2
6
6 Exercise
7
A Appendix  Matlab Code
7
1
Bode plots
A method for obtaining and presenting syste
Bode Diagrams  Supplementary
Reading for Quadratic Terms
Consider a general quadratic term in sdomain
G(s) =
s2
2
n
.
2
+ 2n s + n
(1)
In the jdomain, we have
2
n
2
+ j2n + n
2
n
= 2
.
2 + j2
n
n
G(j) =
(2)
(j)2
(3)
2
Divide numerator and denominator
State Space Model
Contents
1 Overview
1.1 Modern Control Theory . . . . . . . . . . . . . . . . . . . . . . .
1.2 Modern Control Theory Versus Conventional Control Theory . .
1
1
2
2 Notations
2.1 State . . . . . .
2.2 State Variables
2.3 State Vector . .
StateSpace Solutions
Contents
1 Laplace Transform Approach to the Solution of Homogeneous
State Equations
1
2 Solution of Homogeneous State Equations
2
3 StateTransition Matrix
4
4 Properties of StateTransition Matrices
5
5 Example
5
6 Laplace Transfor
State Space Analysis Eigenvalue and Eigenvector
Contents
1 System Characteristic Equation and Eigenvalues
1
2 Similarity Transformation
2
3 Eigenvalues of n n Matrix
3
4 Diagonalization of n n Matrix
4.1 Example . . . . . . . . . . . . . . . . . . . . . .
StateSpace Design
Statespace design methods are discussed on the basis of the poleplacement
method. The poleplacement method is somewhat similar to the rootlocus
method in that we place closedloop poles at desired locations. The basic difference is
ROOT LOCUS
PROBLEM A:
Given ﬂre open loop transfer function
K
s(s+ b)
draw the complete root locus for applying unity gain negative feedback. Deﬁne the
value of K at signiﬁcant points on each locus. What characteristics in terms of
stability will the clos
Lecture 11  THE ROOT LOCUS TECHNIQUE
We now deal with one of several analysis techniques for studying the movement of s roots
as functions of system variables in feedback loops.
Root locus concentrates on a SISO system using unity gain negative feedback.
LECTURE NOTES FOR
MMAN 3200
MODULE A  LINEAR SYSTEMS ANALYSIS
Written by R. Willgoss
Modified by Z. Vulovic
These notes consist of lectures 1 to 10 covering the syllabus taught.
There may be some differences of text and examples compared to what is
offer
LECTURE 4 THE DERIVATION OF SYSTEM EQUATIONS
To MODEL a physical system into a LINEAR system, we must describe each of the
components of the system with its governing mathematical equation. Then we combine the
equations into a complete system specifying t
LECTURE 5 MORE COMPLEX SYSTEMS
5.
For the electrical circuit, derive
the transfer function.
We have
But
by differentiation.
Since
Then
all currents are eliminated.
Rearranging
Let
LECTURE 8 PERFORMANCE PARAMETERS
One often used measure of how well a system responds to driving signals is to look at the
response to a unit step input in terms of the shape of the output.
Here are the parameters that will be looked at.
 the time to the
LECTURE 3 ELEMENTARY BUILDING BLOCKS
The formulation of the equations to describe commonly used engineering components
included in electrical, mechanical, fluidic and thermal systems. A discussion of methods of
transduction is also given.
1.
MECHANICAL CO
LECTURE 7 ANALYSIS IN THE TIME DOMAIN
This section attempts to build up a consistent picture of how systems of various complexities
will respond to standard inputs driving them.
We recall
where
is the numerator polynomial in s and the denominator. If w
LECTURE 6 ANALYSIS USING BLOCK DIAGRAMS
Block diagrams are a means to displaying graphically the connections between various
components of a system. There are rules for reducing any block diagram down to just one
box with an input and output. That box rep
LECTURE 10 STEADY STATE ERRORS
There is a need to know how closely the output of a system follows the input driving
function. So we will
Calculate offsets that occur
Comment on trends that are inherent in a system
Look for common characteristics expressed
MMAN3200
Frequency Domain
As we have seen in Linear Systems in this course, a LTI (Linear Timeinvariant) system
can be represented in the Laplace Domain by its Transfer Function.
Another useful transformation is the Fourier transform. This transformation
Principles of Control
Lecture 1 Introduction
ljl the Laplace domain, by just analyzing the roots of the transfer function’s denominator
we are able to evaluate the behavior of the system in terms of stability, presence of
oscillations and convergence.
F o
MMAN3200
BODE (part 2)
Bode plot of Quadratic Factors
Consider the case of a second order system modeled by the following TF
1
H :
2
1+2éi +[ 5]
w,l w"
1:)“ _ I. I z 2
l+2§iH—+(ﬂi] l—(‘1]+2§*“—j
w" w" w” u”
Then its frequency response is
HUH'} : H(s)
MMAN2300 Engineering Mechanics 2
Unit 2 Instant Centre Method
Question 1
When crank OA passes the horizontal position as shown in Figure Q1, determine the velocity of
the centre G of link AB using the method of instant centres.
Figure Q1
Question 2
Horizo
MMAN3200 LINEAR SYSTEMS ANALYSIS
Midsession Test
April 2008
Time allowed: 90 minutes
No literature permitted
Answer each question in a separate booklet
Question 1 (15 marks)
F
A
B
Figure 11
F

Figure 12
A brake block of mass M and variable temperature
MMAN3200  LINEAR SYSTEMS ANALYSIS
Midsession test
April 2011
Time allowed: 1 hour 40 minutes
Reading time: 5 minutes
No literature permitted
Answer each question in a separate booklet
Question 1 (14 marks)
Conveyor
Figure 1
A schematic of a coal l
Course Outline
Semester 1 2017
MMAN3200
LINEAR SYSTEMS AND CONTROL
Contents
1.
Staff Contact Details. 2
Contact details and consultation times for course convenor . 2
Contact details and consultation times for additional lecturers. 2
2.
Course details . 2
1
MMAN3200  LINEAR SYSTEMS AND CONTROL
Midsession test
April 2012
Time allowed: 100 minutes
No literature permitted
Answer each question in a separate booklet
Question 1 (14 marks)
F
A
B
Figure 11
!
F

Figure 12
A brake block of mass M and variable t
r
MMAN3200 LINEAR sYsTEMs ANALVsIs
d semester test
ApriI2017
Tirne aHOwed:1hour40I inutes
NoI"erature pe"itted
TOtaI marks:25
Reading tirne:5 inutes
Question1(13marks)
9tA
&1
Figure1
A schematic of a coal oader,which is automatica"y cOntro"ed to f
particu
MMAN3200 LINEAR SYSTEMS AND CONTROL
QUIZ March 2016
Total Marks: 10
Time allowed: 55 minutes
No literature permitted
Question 1 (4 marks)
A crate is delivered from an aircraft using a parachute (Figure 1). The transient period
of its motion that consists
TUTORIAL
SET I LINEARISATION
1.
2.
Linearise the following equations for small variations about the operating points
indicated.
+2
(a)
=3
(b)
=
+2
(c)
=
+2
+4
+4
;
=1
;
,
= 1,1
;
,
= 1,1
The volume of a sphere is:
=
Determine the linear approximation of
w