Exam 1, 2014 Control Theory, ENGR 058 Page 1 of 9
Name:A\lF—,5 7’11" [bl 10 pts
Problem 1) A variety of topic
a) All other things being equal, is a system faster if its poles are closer to, or further from, the origin?
Brieﬂy justify your answer.
Cf“ o/I‘

JUST THE MATHS
SLIDES NUMBER
16.6
LAPLACE TRANSFORMS 6
(The Dirac unit impulse function)
by
A.J.Hobson
16.6.1 The denition of the Dirac unit impulse function
16.6.2 The Laplace Transform of the Dirac unit impulse
function
16.6.3 Transfer functions
16.6.4

JUST THE MATHS
SLIDES NUMBER
16.5
LAPLACE TRANSFORMS 5
(The Heaviside step function)
by
A.J.Hobson
16.5.1
16.5.2
16.5.3
16.5.4
The denition of the Heaviside step function
The Laplace Transform of H(t T )
Pulse functions
The second shifting theorem
UNIT 16

JUST THE MATHS
SLIDES NUMBER
16.4
LAPLACE TRANSFORMS 4
(Simultaneous dierential equations)
by
A.J.Hobson
16.4.1 An example of solving simultaneous linear dierential
equations
UNIT 16.4 - LAPLACE TRANSFORMS 4
16.4.1 AN EXAMPLE OF SOLVING
SIMULTANEOUS LINEA

JUST THE MATHS
SLIDES NUMBER
16.2
LAPLACE TRANSFORMS 2
(Inverse Laplace Transforms)
by
A.J.Hobson
16.2.1 The denition of an inverse Laplace Transform
16.2.2 Methods of determining an inverse Laplace Transform
UNIT 16.2 - LAPLACE TRANSFORMS 2
16.2.1 THE DE

JUST THE MATHS
SLIDES NUMBER
16.1
LAPLACE TRANSFORMS 1
(Denitions and rules)
by
A.J.Hobson
16.1.1
16.1.2
16.1.3
16.1.4
Introduction
Laplace Transforms of simple functions
Elementary Laplace Transform rules
Further Laplace Transform rules
UNIT 16.1 - LAPLA

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Introduction. 1
Performance Objective . 1
The Importance of Process Control . 1
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. I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, "How many arbitrary parameters did you use for your calculations?" I thought for a moment about ou

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We also want the initial condition of its derivative.
Last, we want to find its final value.
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Dr Mustafa M Aziz (2013)
_
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3. Second-Order Systems
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JUST THE MATHS
SLIDES NUMBER
16.7
LAPLACE TRANSFORMS 7
(An appendix)
by
A.J.Hobson
One view of how Laplace Transforms might have arisen
UNIT 16.7 - LAPLACE TRANSFORMS 7
(AN APPENDIX)
ONE VIEW OF HOW LAPLACE
TRANSFORMS MIGHT HAVE ARISEN.
(i) The problem is

JUST THE MATHS
SLIDES NUMBER
16.3
LAPLACE TRANSFORMS 3
(Dierential equations)
by
A.J.Hobson
16.3.1 Examples of solving dierential equations
16.3.2 The general solution of a dierential equation
UNIT 16.3 - LAPLACE TRANSFORMS 3
DIFFERENTIAL EQUATIONS
16.3.1

E58 Exam 2, 2014 Page 1 of 11
E58 Exam 2, 2014
The ground rules for the exam follow:
0 The exam is due Monday, April 7th at 12:30 pm.
0 You must turn in the exam to either myself or Cassy Burnett in person (don’t just slide under my
door, or leave in mail

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12:20
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5.2 State-Variable Models 260
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Appl
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An Introduction to Mathematical
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Version 0.2
By
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Department of Mathematics
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Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
1:
2:
3:
4:
5:
6:
7:
Introduction
Controllability,

22
The z-Transform
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Sheet number 1 Page number 1
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Department of Electrical Engineering
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Spring 2012
1. Verify the following facts regarding the H2 system performance.
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Homework 1
Due on Monday, February 13 by 11:15 AM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
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Homework 2
Due on Friday, March 16 by 11:15 AM
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Spring 2012
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20 The Laplace Transform
Solutions to
Recommended Problems
S20.1
(a) The Fourier transform of the signal does not exist because of the presence of
growing exponentials. In other words, x(t) is not absolutely integrable.
For the case a = 1, we have that