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) =
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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) .
Osamah Y. Alharbi
UFID# 11608464
Osamah Y. Alharbi
UFID# 11608464
Osamah Y. Alharbi
UFID# 11608464
Osamah Y. Alharbi
UFID# 11608464
Osamah Y. Alharbi
UFID# 11608464
Suresh Sookraj
EEL 4657C
Lab Module 1
System Modeling
Introduction
The objective of this module is to utilize the systems in lab to retrieve transfer functions
characterized by the SRV02 and uPAD Cont
Linear Control Systems Assignment #7
Due Thursday, October 12, 2017
Problem 1:
(a) Prove the root locus consists of n branches which start at the n poles of the open loop system
and approach the zeroe
Linear Control Systems Assignment #4
Due Thursday, September 21, 2017
Problem 1:
(a) Using a partial fraction decomposition (or otherwise), calculate the impulse response of
() =
1
( + 5)( + 8)
(b) As
Linear Control Systems Assignment #2
Due Tuesday, September 5, 2017
Problem 1: Classify the following systems in terms of the property indicated. Namely, state whether the
given property is satisfied
Linear Control Systems Assignment #6 Solution
Problem 1:
For the automotive cruise control system with open loop transfer function
1
() =
(3 + 1)(0.4 + 1)
Design a lag compensator in the s-domain to g
Linear Control Systems Assignment #1
Due Tuesday, August 29, 2017
Problem 1:
Prove that the quadratic formula for obtaining all solutions (possibly complex) of the second
order polynomial equation
2
Linear Control Systems Assignment #2 Solution
Problem 1: Classify the following systems in terms of the property indicated. Namely, state whether the
given property is satisfied and clearly explain th
Linear Control Systems Assignment #5 Solution
Problem 1:
Find an expression for the step response, y(t), of the standard second order system whose transfer
function is given by
2
() = 2
+ 2 + 2
2
()
Linear Control Systems Assignment #1 Solution
Problem 1: Prove that the quadratic formula for obtaining all solutions (possibly complex) of the second
order polynomial equation
2 + + = 0
is given by
Linear Control Systems Assignment #7 Solution
Problem 1:
(a) Prove the root locus consists of n branches which start at the n poles of the open loop system
and approach the zeroes of the open loop sys
Linear Control Systems Assignment #3 Solution
Problem 1: Calculate the transfer function and zero input response of the following system, if the initial
3
condition, x(0) is given by [ ]
4
1
7 15
()
Linear Control Systems Assignment #4 Solution
Problem 1:
(a) Using a partial fraction decomposition (or otherwise), calculate the impulse response of
() =
1
( + 5)( + 8)
Solution:
() =
1
= +
+
( + 5)(
Linear Control Systems Assignment #6
Due Thursday, October 5, 2017
Problem 1:
For the automotive cruise control system with open loop transfer function
1
() =
(3 + 1)(0.4 + 1)
Design a lag compensator
Linear Control Systems Assignment #5
Due Thursday, September 28, 2017
Problem 1:
Find an expression for the step response, y(t), of the standard second order system whose transfer
function is given by
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Note: All negative exponents should be
positive for problem 3b.
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(D XHJ =[2 33] 7<H) r[o']ul+)
guy-U 037M)
s gem is confrontablc
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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 ex
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
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
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
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
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
Linear Control Systems Assignment #3
Due Thursday, September 14, 2017
Problem 1: Calculate the transfer function and zero input response of the following system, if the initial
3
condition, x(0) is gi