University of Illinois at UrbanaChampaign
Department of Electrical and Computer Engineering
ECE486
Homework 7 solutions
Fall 2014
Problem1
1
2
Problem2
3
Problem3
4
5
ECE 486
Assignment # 8
Issued: April 10
Due: April 17, 2014
Reading Assignment:
FPE, Sections 6.3, 6.7.16.7.6.
Problems:
1. Consider the transfer function
H(s) =
1
,
s+a
where a > 0. Prove that the Nyquist plot of H is a circle of radius
point
1
,0 .
2a
1
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
Homework 5 Solutions
Spring 2014
Problem 1
Sketch the root loci below by hand, applying rules AF.
1
+ 2s + 10
OL zeros: None
OL poles: 1
University of Illinois at UrbanaChampaign
Department of Electrical and Computer Engineering
ECE486
Homework 1 solutions
Fall 2014
Problem1
a)
A B =
b)
2 1
5 4
8 1
A B = 1 1
3 0
c)A B is not dened because the number of columns of A is not equal
to the nu
Problem Set # 6
ECE 486: Control Systems
Instructor:M.A. Belabbas, [email protected], CSL 166
Homework TA :Yuan Yao, [email protected]
Due date: Tue Oct 28 2014
Reading Assignment:
FPE (6th ed.), Sections 5.1 to 5.6,Sections 6.1 to 6.2
Problems:
University of Illinois at UrbanaChampaign
Department of Electrical and Computer Engineering
ECE486
Homework 8 solutions
Fall 2014
Problem1
P M = 60 < 90 c BW 2c BW = 10 choose c = 5
1
 = 1 we get K 25
Solve K
s(s + 1)
z p c
after slight adjustion we ge
Problem Set # 4
ECE 486: Control Systems
Instructor:M.A. Belabbas, [email protected], CSL 166
Homework TA :Yuan Yao, [email protected]
Due date: Tue Sep 30 2014
Reading Assignment:
FPE (6th ed.), Sections 4.14.3 (The material not discussed in cl
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
Homework 8 Solutions
Spring 2014
Problem 1
Consider the transfer function
H(s) =
1
,
s+a
where a > 0. Prove that the Nyquist plot of H is
ECE 486, Spring 2016
PROBLEM SET 3  SOLUTION
Due Thursday, Feb 11
Reading: FPE, Sections 3.33.6.
Problems: (unless otherwise noted, you can use a calculator/computer to arrive at numerical answers)
1. Using techniques for block diagram reduction discuss
ECE 486
Assignment # 4
Issued: February 20
Due: February 27, 2014
Reading Assignment:
FPE, Sections 4.14.3, 5.1.
Problems:
1. Consider the following feedback system, where K is a constant gain and
G(s) =
R
+
s3
+
1
:
+ 2s + 1
2s2
K
G
Y
Using the RouthHurw
ECE 486
First Midterm Exam
This is a closedbook closednotes test, with only one sheet of notes (doublesided) allowed, and
no calculators. For scratch work you may use backs of pages and the additional sheets provided.
You have three problems to solve i
ECE 486
Solution to Second Midterm Exam
This is a closedbook closednotes test, with only two sheet of notes (doublesided) allowed, and
no calculators. For scratch work you may use backs of pages and the additional sheets provided.
You have ve problems
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
HOMEWORK 6 SOLUTION
Spring 2012
Problem 5.21
(a) Using Rouths stability criterion, determine all values of K for which the system is stab
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
Homework 3 Solutions
Spring 2014
Problem 1
Consider the following transfer function H(s) =
s2
9
.
+ 4s + 9
(a) Specs: tr 0.7 and ts 1.6
n
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
Homework 4 Solutions
Spring 2014
Problem 1
Consider the following feedback system, where K is a constant gain and
G(s) =
R
+
1
:
s3 + 2s2
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
HOMEWORK #7 SOLUTION
Spring 2012
Problem 6.3
Sketch the asymptotes of the Bode plot magnitude and phase for each of the following openloo
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
HOMEWORK 4  SOLUTION
Spring 2012
Problem 3.42
Suppose that unity feedback is to be applied around the listed openloop systems. Use Rout
Problem Set # 5
ECE 486: Control Systems
Instructor:M.A. Belabbas, [email protected], CSL 166
Homework TA :Yuan Yao, [email protected]
Due date: Thu Oct 16 2014
Reading Assignment:
FPE (6th ed.), Sections 5.1 to 5.3
Problems:
1. Consider the plan
ECE 486
MIDTERM #1 INFO AND PRACTICE EXAM
Fall 2011
Please read the following information carefully and start preparing for the exam.
Time and place. The first midterm exam will be held on Thursday, Oct 6, in class (9:3010:45am).
There is no conflict exam
Problem Set # 3
ECE 486: Control Systems
Instructor:M.A. Belabbas, [email protected], CSL 166
Homework TA :Yuan Yao, [email protected]
Due date: Tue Sep 23 2014
Reading Assignment:
FPE (6th ed.), Sections 3.3 and 3.6
Problems:
1. Consider the fol
ECE 486
First Midterm Exam: Solutions
This is a closedbook closednotes test, no calculators allowed. Some useful facts are summarized
in the back of the exam. For scratch work you may use backs of pages and the additional sheets
provided. You have four
ECE 486
Control Systems
Spring 2014
Exam I Information
The rst midterm exam will be held in class
153 Mechanical Engineering Bldg Thu, March 20, 9:30 10:50 a.m.
The exam is closedbook, closednotes, no calculators allowed (and you will not need one). The
ECE 486
Second Midterm Exam
This is a closedbook closednotes test, with only two sheet of notes (doublesided) allowed, and
no calculators. For scratch work you may use backs of pages and the additional sheets provided.
You have ve problems to solve in
Chapter 1
Introduction
1.1 What Is Mathematical Control Theory?
Mathematical control theory is the area of applicationoriented mathematics that deals with the basic principles underlying the analysis and design of control systems. To control an object me
ECE 486
Sample Midterm 1
Useful approximations for 2ndorder system,
H(s) =
Rise time, peak time, settling time,
r
tr
2
n
2
s2 + 2n s + n
1.8
n
tp =
+

n
1
Gc
2
t5%
s
Gp
3
n
y
Problem 1
(10 points)
Consider the system given by the block diagram below:
UNIVERSITY OF ILLINOIS AT URBANACHAMPAIGN
Department of Electrical and Computer Engineering
ECE 486: Control Systems
Sample Midterm 1 Solutions
Problem 1
Y
=
U
1+
G
P1 P2
K1 K2 P1 P2
1 + K2 P2 + K1 K2 P1 P2
Problem 2
Secondorder system with peak time tp
University of Illinois at UrbanaChampaign
Department of Electrical and Computer Engineering
ECE486
Homework 6 solutions
Fall 2014
Problem1
a)Design a lead compensator so that the specication (i) and (ii) are met.
Base on the given specs, we need > 0.41 f
I, _, permit the University of Illinois to
charge my student account $180.00 if I do not return the ECE 120 lab
kit in good shape by November 6, 2014.
Signature: _
Printed Name: _
NetID: _
Date: _
I, _, permit the University of Illinois to
charge my stude