FreeBody Analysis Basics
1. Assign translational(rotational) position variables and reference directions to each translational(rotational) mass. Points
that have no mass but fall between, for instance, springs and dashpots in series are also assigned pos
SYSTEMATIC NODE ANALYSIS
059:008 Electrical Circuits
M. AnderslandSpring 2013
Step I:
A. Select a reference node (RN). Number all other nodes 1,2,. . . ,N.
B. View all sources as current sources (CS).
C. Write the KCL equations for the N nonreference nod
Frequency Domain Compensator Design Examples ECE:3600 Spring 2017
Example 1: A lead compensator Gc (s) = kc (s + zc)/(s + pc), pc  > zc  is to
be designed to ensure that the step response of a unity feedback system with
openloop transfer function G(s
HOW TO SKETCH ROOT LOCI
ECE:3600 CONTROL SYSTEMS
ECE Department, The University of Iowa, Spring 2017
To obtain a sketch of the root locus of a given characteristic polynomial Q(s, K) = 0,
A. Rearrange Q(s, K) such that
Q(s, K) = 1 + KP (s)
where K is the
COMMENTS ON THE NYQUIST CRITERION
ECE:3600 CONTROL SYSTEMS
ECE Department, The University of Iowa, Spring 2017
Consider the following closedloop system.
 +
+
6
R(s)
 G(s)
 Y (s)
H(s)
This system is
(i) openloop stable if all of the poles of the ope
ECE:3600 Control Systems
M. AnderslandSpring 2017
Masons Rule
Masons rule states that the transfer function C(s)/R(s) of a linear timeinvariant system represented
by a signal flow graph or block diagram is
P
C(s)
Tk k
G(s) =
= k
R(s)
where
k=
Tk =
=
k =
Root Locus Compensator Design Examples ECE:3600 Spring 2017
Example 1: A lead compensator Gc (s) = kc (s+zc )/(s+pc ),
pc  > zc  is to be designed to ensure that the step response
of a unity feedback system with openloop transfer function
G(s) = 80/[
Transient Step Response Specifications
ECE:3600 CONTROL SYSTEMS
ECE Department, The University of Iowa, Spring 2017
j
For systems with transfer function
H(s) =
complex pole
. .
.
.
6
n2
s2 + 2n s + n2
p
n 1 2
and complex pole locations
?
6
S
Sn
SS
jd
=
COMPENSATORS
ECE:3600 CONTROL SYSTEMS
ECE Department, The University of Iowa, Spring 2017
There are two basic approaches to compensation . . .

Cascade Compensation

Feedback Compensation
F
F
+ h+
6
+h
+
6
C

G

H


G
C
H
Typical compensators (the C
Parity Interlacing Principle
ECE:3600 CONTROL SYSTEMS
ECE Department, The University of Iowa, Spring 2017
Many compensators are, by construction, stable; that is all of the compensators transfer functions poles lie in the OLHP. Examples include: lead comp
EE 475 Fall 2009 Quiz #8
Name:
1. In order to have transient die out, all closedloop poles of the system must be _
2. Use , , n , and d to fill in the spaces below.
Settling time is inversely proportional to _
_
Rise time is inversely proportional to _
_
EE 475 Fall 2009 Quiz #9
Name:
1. For prototype second order systems, give the approximate formula for the following
specs in terms of zeta and wn:
a. Tp = _
b. Tr = _
c. Ts = _
d. Mp = _
2. Give the formula for the real part and imaginary part of the clo
EE 475 Fall 2009 Quiz #3
Name:
1.
If h(t) is the impulse response of a system, the system is BIBO stable iff
.
2.
Assume no pole/zero cancelation. A system is A.S. if its poles
.
3.
a*s2 +b*s+c is A.S. if
4.
a*s3 +b*s2+cs+d is A.S. if
5.
6.
7.
8.
.
.
EE 475 Fall 2009 Quiz #1
Name: solution
1.
Lcfw_(t) =
1
; (unit impulse)
2.
Lcfw_u(t) =
1/s
; (unit step)
3.
L1cfw_
4.
The poles of
5.
The finite zeros of
6.
Whenever there is feedback loop, one needs to worry about
.
1
= e^(at) or e^(at)*u(t)
s a
s 1
a
EE 475 Fall 2009 Quiz #6
Name:
1.
The unit step response of a system is given below. On the graph mark the
definition and numerical value of the following specifications: yss, ess, tp, ymax, ts
for +2%, td, tr, and Mp.
EE 475 Fall 2009 HW #5
Due: 10/02/2009
1.
Write the mystep.m file as described in class that will compute all step response
specifications, display them graphically in the step response plot, and also return a
vector containing all the numbers for future
EE 475 Fall 2009 Quiz #3
Name:
1.
If h(t) is the impulse response of a system, the system is BIBO stable iff
h(t ) dt
is finite
0
.
2.
Assume no pole/zero cancelation. A system is A.S. if its poles
all have
negative real parts .
3.
a*s2 +b*s+c is A.S. if
EE 475 Fall 2009 Quiz #9
Name:
Solution
1. For prototype second order systems, give the approximate formula for the following
specs in terms of zeta and wn:
a. Tp = _ pi/(wnsqrt(1zeta^2)
b. Tr = _ 1.8/wn or 2/wn
c. Ts = _ 3 or 4 or 5/(zeta*wn), or ln(tol
EE 475 Fall 2009 Quiz #4
Name:
1.
Assume no pole/zero cancelation. A system is A.S. if its poles
.
2.
a*s2 +b*s+c is A.S. if
3.
a*s3 +b*s2+cs+d is A.S. if
.
.
4.
5.
6.
7.
For the block digram below
a) List the forward path gains:
.
b) List the loop gains:
EE 475 Fall 2009 Quiz #4
Name:
1.
Assume no pole/zero cancelation. A system is A.S. if its poles
.
2.
a*s2 +b*s+c is A.S. if
3.
a*s3 +b*s2+cs+d is A.S. if
.
.
4.
5.
6.
7.
For the block digram below
a) List the forward path gains:
.
b) List the loop gains:
EE 475 Fall 2009 HW #5
Due: 10/02/2009
1.
Write the mystep.m file as described in class that will compute all step response
specifications, display them graphically in the step response plot, and also return a
vector containing all the numbers for future
EE 475 Fall 2009 Quiz #6
Name:
1.
Solution
The unit step response of a system is given below. On the graph mark the
definition and numerical value of the following specifications: yss, ess, tp, ymax, ts
for +2%, td, tr, and Mp.
EE 475 Fall 2009 HW #1
Due: 8/31/2009
1.
Read sections 1.2 and 1.3, answer chapter 1 review T/F questions, check your
answer at the given web site, and then report how you did.
2.
Answer chapter 2 review questions 1, 7, 8, 9, 10, and 11, check your answer
szi
spi
N
D
N
szi
N
szi
D
D
spi
D
N
D
N
N
N
D
D
N
D
spi
k = 0 => D + k N = D => Poles of T = roots of D => rootlocus starts at pi
D + k N = k N => Poles of T = roots of N => rootlocus ends at zi
s root of D + k N iff s* root of D + k N
pi
zi
N
IMPACT OF SPEECH ACT
1
Chapter I
The Problem and Its Background
In language usage, we are not only restricted to produce correct utterances or
phrases rather than to use language in appropriate way and this is what pragmatics
means. Speech acts have emerg
Do: 96, 98, 99(c,d,g), 928
Consider the standard unity gain feedback set up. The frequency response of the forward path gain is
given by the follow Bode plots. For each case:
a) Determine the system type and find closedloop steady state tracking erro
EE 475 Fall 2009 Quiz #11
Name:
1. The desired region for the closedloop dominant pole corresponding to ts <= XX
second is the half plane to the
=
of a
line located at real (s)
.
2. The desired region for the closedloop dominant pole corresponding to tr
EE 475 Fall 2009 Quiz #1
Name:
1.
Lcfw_(t) =
; (unit impulse)
2.
Lcfw_u(t) =
; (unit step)
3.
Lcfw_r(t) =
; (unit ramp)
4.
L1cfw_
5.
If
1
=
s a
;
s 1
A
B
, then A =
s ( s 1)
s s 1
;
B=
;
6.
7.
The Euler identity says ejx =
8.
The poles of
s 1
are:
s (
EE 475 Fall 2009 HW #6
Due: 10/12/2009
1.
Write a Matlab script file containing the following parts: 1) defining the plant; this
is where you can edit the plant TF numerator and denominator. 2) defining desired
specifications; this is where you can edit t
EE 475 Fall 2009 Quiz #8
Name:
1. In order to have transient die out, all closedloop poles of the system must be _
stable, or in the open left half plane
2. Use , , n , and d to fill in the spaces below.
Settling time is inversely proportional to _ _
Ris