EEL4657 - Dr. Haniph Latchman
Chapter 2 Solutions
1.
L
d2 y
s2 Y (s)
dt2
2. Derive the Laplace Transform pairs from Table 2.1, page 33 of the text
*Note that the Laplace Equation is given as: X (s) = 0 x(t)est dt
(a)
x(t) = (t)
(t)est
X (s) =
0
(since
H W IZ Scimitar-13
(D XHJ =[2 33] 7<H) r[o']ul+)
guy-U 037M)
s gem is confrontablc
(0 8: [B 951%): ame W IS a 2x2.
NW4 1 (me earl
IE l =9 mnK = 2 Hull rank) Inaagendemro waif/column.
m I (chiral/05m; mafnv
c _ l o sffm II amenable.
(b) 8: [CA] '[01] $5: a
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Note: All negative exponents should be
positive for problem 3b.
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Linear Systems Theory
A Neo-Classical Approach
Haniph A. Latchman
ii
Modern Control Systems A State Variables Approach
Contents
1 Control Objectives - A Classical Perspective
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The
Control Systems Theory and Practice
- A Laboratory Manual and Handbook
Haniph A. Latchman
Rami Okasha
Ghaith Alnadi
ii
Control Systems Theory and Practice Lab Manual
Contents
Preface
vii
SECTION I: LAB MODULES
2
Module 1: System Modeling
Objective . . . .
EEL4657 - Dr. Haniph Latchman
Chapter 3: Example Problems
1. Given the signal ow diagram in Figure 1, use Masons rule to nd the transY
fer function T (s) = X(s)
( s)
Figure 1: Signal ow diagram for example problem 1, where X (s) is the input
and Y (s) is
EEL4657 - Dr. Haniph Latchman
Chapter 4: Example Problems
1. The transfer function for a system with unity negative feedback is given
by:
1
G(s) =
(s + 1)(s + 3)
( s)
a) Find the closed-loop transfer function T (s) = Y (s) .
R
b) Find the time response y
EEL4657 - Dr. Haniph Latchman
Chapter 4 Solutions
1. The second order system is given by:
G(s) =
2
n
2
s2 + 2s + n
The impulse response is determined by:
G(s) =
=
g (t) =
=
s2
2
n
2
+ sn s + n
n
1 2
n
1
2
n 1 2
2
(s + n )2 + n (1 2 )
en t sin(n
1 2 t)
n n
EEL4657 - Dr. Haniph Latchman
Chapter 6: Lead and Lag Compensator Design Examples: - Domain Analysis
I. Design a lead compensator for the system:
1
(s)(1 + 0.3s)
where the compensator is given by the form:
G(s) =
C (s) =
k (1 + s)
1 + s
Which meets the fo
Solutions to Midterm
1)
Alternatively recognize the new block diagram:
(Note: the negative sign in the first diagram carries through to D(s) input)
Final value theorem:
2)
With
Sensitivity is found by using quotient rule:
3)
Examine the denominator of the
Introduction
In this lab, we are going to model the systems using SRV02 and Micro-Pad control
platform in order to obtain a good transfer function. We are looking to find parameters
that will help us control the transfer function, such as DC gain (k) and
and
3T z 4 .
Eu 1 + KlKaG(3)
(b) The tracking error, E(3) : 6,;(3) 6(3) 2 6(3), since 6d(3) I 0. The
transfer function from the wave disturbance to the output 6(3) is
0(3)
6(8) : 1 + romeo)
1131(8) .
Consider a step disturbance input for the open and clos