ECE 451
LECTURE 1
Preface
This lecture reviews several topics from ECE 350, i.e. state variables, controllability and observability, as
well as state variable feedback. It is assumed that students att
ECE 451
LECTURE 3
Preface
This lecture introduces the method of dynamic programming which can be used to solve optimal control
problems. This method was developed by R. Bellman during the early 1960s
ECE 451
LECTURE 5
Preface
This lecture continues our discussion of the method of dynamic programming. We start by solving an
optimal control problem, which was given as an exercise at the end of Lectu
ECE 451
LECTURE 7
Preface
This lecture continues our discussion of the method of dynamic programming and its application to
continuoustime systems resulting in the classic HamiltonJacobiBellman (HJ
The following figure shows a translational mechanical system. Derive a set of differential equations that
describes all variables in this system. Draw the block diagram assuming that:
1. Force F is th
Control is concerned with dynamics in a wider sense:
 seeking understanding of the dynamic behaviour of systems (mechanical, electrical, chemical,
biological, economic, )
 with a view to operate the
Topic 5 (Mathematical Modelling of Various Systems)
Electrical System:
1) Resistance, R
2) Inductance, L
V (t ) = Ri (t )
V (t ) = L
i (t ) = GV (t ), where
i (t ) =
1
G=
R
3) Capacitance
1 t
i (t )dt
Topic 3 (Mathematical Modelling of SpringMassDamper System)
The dynamic performance of physical systems is obtained by utilizing the physical laws of
mechanical, electrical, fluid and thermodynamic
Topic 2 (Mathematical Modelling of System Dynamics Part I)
 set of equations that represents the dynamics of a physical system accurately or, at least it is able
to describe the response or behaviour
ECE 451
LECTURE 6
Preface
This lecture continues our discussion of the method of dynamic programming and our example of its
application to the solution of the discrete regulator problem. We consider a
ECE 451
LECTURE 4
Preface
This lecture continues our discussion of the method of dynamic programming. We start by solving an
optimal control problem, which was introduced at the end of Lecture 3. Next
ECE 451
Homework 1
Due Wednesday, September 7, 2011
1. Use the Smith chart to find the following quantities for the transmission line circuit below:
(a)
The SWR on the line
(b)
The reflection coeffici
Homework 2  Solutions
Problem 1 (Steer Exercise 4.1)
(a) o c / f 3 108 / (18 109 ) 16.67 mm
(b) g g / r (16.67mm) / 64 2.08 mm
(c) l g / 4 (2.08 mm) / 4 0.52 mm
Problem 2 (Steer Exercise 4.5)
R=100 /
ECE 451
Homework 3
Solutions
Problem 1
(a) For Pi Network
V1
I1
Z11
Z 21
Y11
V2
I1
I2 0
I 2 0
Y21
2Z A Z B
V1
ZA ZA ZB
ZA
I1Z11
Z A ZB
I1
I1
V1 V 0
2
V1
I1
ZZ
I1 A B
Z A ZB
Z A Z A ZB
ECE 451
Homework 3
Due Wednesday October 5, 2011
1. Derive the Z and Y matrices for the following twoport networks:
(a)
(b)
2. A fourport network has the scattering matrix shown below
(a)
Is this ne
Homework 4  Solutions
Problem 1 (Steer 61)
(a) No, S12 S21
(b)
Maximum available power condition:
12
V / 50 1 mW V 0.316V E 2V 0.632V
2
(c)
Since S12 = 0, in = S11 = 0.25
2
PR IN PIN (0.25) 2 1 mW 6
ECE 451
Homework 5
Due Wednesday November 2, 2011
Scope/DVM
detector
b3
Zs
Directional Coupler
+
Vs

a3
a1
b1
ZL
Zo
b2
a2
Figure 1
1. Consider the measurement set up shown in Figure 1. Choose Zo as t
ECE 451
Homework 6
Solutions
Problem 1
The voltage and current on a lossless transmission line are
V ( z ) V e z V e z
I ( z ) Yo V e z V e z
Let port 1 be located at z=l with voltage and current
V1
ECE 451
Homework 6
Due Wednesday, November 16, 2011
1. Find the admittance matrix Y of a lossy transmission line. Express your answers
in terms of the propagation constant , the length of the line l a
NAME _
MIDTERM EXAM SOLUTIONS
ECE 451
October 17, 2011
12:00 12:50 p.m.
Instructions: Write your name and section where indicated. Show all work. Indicate the units of
your answers.
Useful constants :
ECE 451 Control Engineering
Fall Semester 2015: C3 LC, Tue & Thu, 5:00 6:15 pm
Professor:
Dennis D. Vaccaro, Ph.D.
Office: 804 SEO
Office Hours: by appointment
Business Phone: 2246254808
Cell Phone:
ECE 451
LECTURE 2
Preface
This lecture introduces the optimal control problem. The concepts of an admissible control, an admissible
trajectory, and the general form of the performance measure are pres
ECE 350: Principles of Automatic Control
UIC: FALL 2010
LECTURE 1
Summary
In this first lecture, we introduce the subject of control engineering and the role that the control engineer
serves in overal
Topic 6 (Block Diagram Analysis)
A block diagram of a system is a pictorial representation of the function performed by each
component and of the flow of signals within a system. In brief, a block dia