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‘
1
Homework 2 (Attendance 3) for Statistics 513
Statistical Control Theory
Material Covered: Chapter 4 Montgomery and Kuhn
This homework is worth 5% and marked out of 5 points. Homework assignments
are to be handed in using Vista on the Internet before 4am
Igor Zelenko, Fall 2011
1
Homework Assignment 3 in Geometric Control Theory, MATH666
due to Oct 21, 2011
Problem 1 Consider the control of angular momentum M of a rigid body with
a xed point by two torques in the direction of two axis of inertia. It is de
EE 584: Robust Control Theory
Homework 3
Due on Friday, April 6 by 11:15 AM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
1. Address the following problems regarding the balanced truncation approach.
(a) [Exercise 4.6] Fin
EE 584: Robust Control Theory
Homework 4
Due on Wednesday, April 25 by 11:15 AM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
1. Verify the following facts regarding the H2 system performance.
(a) [Exercise 6.1] The H2 nor
EE 584: Robust Control Theory
Final Exam
Due on Friday, May 4 by 1:00 PM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
1. Impulse Response Regulation. A servomotor that drives a load is described by
(t) + (t) = u(t) + d1 (
EE 584: Robust Control Theory
Homework 1
Due on Monday, February 13 by 11:15 AM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
1. Suppose A Rnn represents a linear map in L(Cn , Cn ).
(a) [Exercise 1.6] Show that Ker A and
EE 584: Robust Control Theory
Homework 2
Due on Friday, March 16 by 11:15 AM
Department of Electrical Engineering
Pennsylvania State University
Spring 2012
1. Let V, Y, and Z be vector spaces over C.
(a) [Exercise 3.1] Suppose V is a Hilbert space equippe
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
Control Theory 1
Homework Assignment Number 5
We will consider a problem of designing a ship steering control system. The transfer function of
the ship is
Y (s)
0.25(s + 0.3)(s + 0.42)
G(s) =
= 2
(s)
s (s + 0.35)(s 0.006)
where Y (s) is the Laplace transf
ESE 617: Nonlinear Control Theory (S14)
Homework 6
Due on 4/2/14
1. Consider the system
x1 = x1 + x2 x3 ,
x2 = x1 x3 x2 + u,
x3 = x1 + u,
y = x3 .
(a) Show that the system is inputoutput linearizable.
(b) Transform the system into normal form and specify
Homework AssignmentsLinear Systems and Control Theory
Semester I
Fall 2015 2016
Howeworks are due one week after they are assigned. All assignments are
from A Mathematical Introduction to Control Theory, 2nd ed., unless
otherwise noted.
1. (To be Assigned
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
1
Homework 3 (Attendance 5) for Statistics 513
Statistical Control Theory
Material Covered: Chapter 6 Montgomery and Kuhn
This homework is worth 5% and marked out of 5 points. Homework assignments
are to be handed in using Vista on the Internet before 4am
1
Homework 1 (Attendance 1) for Statistics 513
Statistical Control Theory
Material Covered: Chapters 1,2 and Kuhn
This homework is worth 5% and marked out of 5 points. Homework assignments
are to be handed in using Vista on the Internet before 4am (West L
An Introduction to Mathematical
Optimal Control Theory
Version 0.2
By
Lawrence C. Evans
Department of Mathematics
University of California, Berkeley
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
Chapter
1:
2:
3:
4:
5:
6:
7:
Introduction
Controllability,
22
The zTransform
In Lecture 20, we developed the Laplace transform as a generalization of the
continuoustime Fourier transform. In this lecture, we introduce the corresponding generalization of the discretetime Fourier transform. The resulting
transfo
25 Feedback
Recommended
Problems
P25.1
Consider the two feedback systems in Figures P25.11 and P25.12.
y(t)
H(s)
x(t)
K (s)
Figure P25.11
(a) Express the overall system functions
Q(s)
Q Y(s)

X(S)
and
Q(z)
=
Y(z)
X(z)
in terms of the system functio
22 The zTransform
Recommended
Problems
P22.1
An LTI system has an impulse response h[n] for which the ztransform is
H(z) =
h[n]z
z1 ,

(a) Plot the polezero pattern for H(z).
(b) Using the fact that signals of the form z" are eigenfunctions of LT
20 The Laplace Transform
Recommended
Problems
P20.1
Consider the signal x(t) = 3e 2'u(t) + 4e 3 'u(t).
(a) Does the Fourier transform of this signal converge?
(b) For which of the following values of a does the Fourier transform of x(t)e "
converge?
Lecture 1
Introduction  Course mechanics
History
Modern control engineering
EE392m  Winter 2003
Control Engineering
11
Introduction  Course Mechanics
What this course is about?
Prerequisites & course place in the curriculum
Course mechanics
Outline
Control Theory
Homework 7
Due 9 Nov 2012
1. Consider the system x(t) = 10x(t) + u(t). Using the HamiltonJacobi
Bellman equation, nd the control that minimizes the cost
J=
1 2
x (T ) +
2
T
1 2
1
x (t) + u2 (t) dt.
4
2
0
2. Consider the system x1 (t) = x2
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
16.6
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
Here well find the initial value of capacitor voltage, or vc(0).
We also want the initial condition of its derivative.
Last, we want to find its final value.
Part of our answer is already given: the initial value is 0 V.
When finding the initial value of
ECM2105  Control Engineering
Dr Mustafa M Aziz (2013)
_
SYSTEM RESPONSE
1. Introduction
2. Response Analysis of FirstOrder Systems
3. SecondOrder Systems
4. Sinusoidal Response of the System
5. Bode Diagrams
6. Basic Facts About Engineering Systems
1.
June 21, 2001 09:40
hay83645_ch19
Sheet number 1 Page number 1
black
Chapter
19
StateVariable
Analysis
Specic goals and objectives of this chapter include:
s Introducing the concept of state variables and normalform equations
s Learning how to write a c
1
A control theory perspective on conguration
management and cfengine
Mark Burgess
Oslo University College, Norway
Abstract Cfengine is an autonomous agent for the conguration
of Unixlike operating systems. It works by implementing a hybrid
feedback loop