Linear Control Systems and Design I Prof. Alessandro Rizzo
Homework
Exercise 1
Consider the following linear dynamical system:
x1 = 3x1 + 2x2 + 2u
x2 = x1 x2 + u
y = 2x1 + x2
(1)
Dene a new state vector, z, related to x by
z1 = x1 + x2
z2 = x1 x2
(2)
1.
Linear Control Systems and Design I Prof. Alessandro Rizzo
Homework
Consider the following linear dynamical system:
x1 = x2
x2 = 3x1 2x2 + u
y = x1
1. Write the matrices A, B, C, D that describe the state space form;
2. Compute the transfer function and
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r
S ys T E
L
rZ [
P F S cfw_
D

M
0
3

f L
T RA r ( j $
7
v mi
,v
=
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z
z
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+
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z :s +
s
.
r
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r
c
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>
s
s
+ s 1

s
Simulink Scheme
Step response
0.4
35
0.3
25
0.2
15
0.1
05
0
0
Time offset: 0
5
10
15
20
25
Zero input response starting fr
Linear Systems Theory
Introduction Receptive fields and
mechanisms
Fourier Analysis Signals as sums of sine
waves
Linear, shiftinvariant systems
Definition
Applied to impulses, sums of impulses
Applied to sine waves, sums of sine waves
Application
Some Key Fundamentals of Classical Control
1. Feedback control is a pervasive, powerful, enabling technology that, at first sight, looks
simple and straightforward, but is amazingly subtle and intricate in both theory and
practice.
2. In a dynamical syste
MEGY 6703: Linear Control Theory and Design I
Fall 2015: Midterm
This exam contains 4 problems. Each problem carries 25 points. Show all work. Illegible work will not be
graded.
Problem 1: Consider a simplified model of an armature controlled DC motor sh
ME 6703: Linear Control Theory and Design I
Fall 2013: Midterm
This midterm contains 4 problems. Each problem carries 25 points. Do all problems. Show all work.
Illegible work and/or loose sheets will not be graded. You must show procedures, not only fina
MEGY 3513: Linear Control Theory and Design Prof. Alessandro Rizzo
Final Exam
Note:
The exam is closed notes, closed books. No photocopies are allowed.
Your work should be legible (i.e., be neat). To receive full credit, show all details of your work.
Linear Control Theory & Design
Final Fall2014 solutions
Problem 1:
(a)
( ) = 3() + ()
= ()
Closed loop system pole is = 1.5
Using the feedback controller, the state equation can be written as
( ) = 3() ()
( ) = (3 )()
Closedloop characteristic equat
Root Locus Analysis & Design
Root Locus Analysis & Design
K. Craig
1
Control System Design Overview
Classical Control Design (rootlocus and frequency
response analysis and design, i.e., transform methods) is
applicable to linear, timeinvariant, single