EE 453
Homework 4
(s+1)
1. Find a realization of the transfer function g(s) = s4 +7s3 +19s
Is your realization
2 +23s+10 .
minimal? If not, find a minimal realization of this transfer function.
2. Find a minimal realization of the given transfer function

EE 453
HMWK 5
1. Use the fact that the matrix exponential eAt is actually the state transition matrix (between 0 and
t) of A to show that eA(t+s) = eAt eAs and also that eAt eAs = eAs eAt .
2. Find the state transition matrix (t, t0 ) of A(t) where:
3 3 1

1
EE 453
HMWK 1
1. Use the field axioms to show that, in any field, the additive identity
and the multiplicative identity are unique.
2. Show that in any vector space, the zero is unique (by zero, we mean
the identity element with respect to the vector ad

26 October 2015
EE 453
Fall 2015
Homework Set 3
1. Find the eigenvalues of the following matrices1 Also, for each eigenvalue,
find as many linearly independent eigenvectors as possible.
0 1 0 0
0 0 1 0
(a) A =
0 0 0 1
1 0 0 0
1
0
1
3
0
(b) A = 1
4 1

EE 453
Homework Set No. 2
1. Let V and W be finite dimensional vector spaces over a common field F and let
A : V W be a linear operator. Show that A is defined completely on V iff it is
defined on some basis for V.
2. Let V and W be finite dimensional vec

EE 450
H OMEWORK #1
O CTOBER 15, 2015
Q1: An incremental encoder is used with a tracking wheel that has a diameter of d cm. The encoder
has NR holes in the outside track and also in the middle track. For each of the following conditions
sets, determine th

EE 450
H OMEWORK #2
O CTOBER 29, 2015
Q1: Obtain the rise time, tr , peak time, t p , maximum overshoot, M p , and settling time, t s , of the unitstep response of a closed-loop system
36
C (s)
=
R(s) s 2 + 2s + 36
Q2: The output of the system given in Fi

EE 450
H OMEWORK #1
O CTOBER 5, 2016
D UE : O CTOBER 13, 2016
Q1: An incremental encoder is used with a tracking wheel that has a diameter of d cm. The encoder
has NR holes in the outside track and also in the middle track. For each of the following condi

Measuring Components
Transducers
A transducer receives information in the form of a physical quantity and transmits
this information in the form of another physical quantity. (ASA definition)
Position and Displacement Measurement
Two basic types: linear a

Elements of Control System Components
Reference Input +
Controller
Actuator
Measurement
Plant
Output
Component Types
In most control systems we encounter five different types of components.
Component type
Quantity
Potential
Electrical
Charge (C)
Voltage (

Servomotors
: position (Greek)
Servo, servosystem: Closed-loop systems to control position,
velocity or acceleration of mechanical loads.
Two-phase AC motors
DC motors
Armature-controlled
Field-controlled
Rotating Amplifiers
Ward-Leonard System
Amp