EE 475
Automatic Control
Systems
Fall 2011
MWF 11:00-11:50 am
1252 Howe Hall
Class Webpage
http:/class.ece.iastate.edu/djchen/ee475/2012
Please check the page for
Any announcements
Class notes
HW assignments
Lab assignments
Project requirements
Cl
EE 475 Quiz #14
Name:
1. Suppose systemIs gc is 10 times systemIIs while both have 45 deg PM. Use A)
about the same as, B) about 10 times, C) about 1/10, or D) unknown, to compare the
following:
a. systemIs closed-loop BW is
systemIIs BW.
b. systemIs reso
EE 475 HW #9
Note some of the specs may be difficult or impossible to achieve with the prescribed controller.
Do your best, justify your design decisions and choice of tradeoff, and if possible suggest or add
compensation actions e.g., low pass filters, t
EE475 HW10
Problem 1
1) Design a PD controller for the pendulum on the cart system. Use the linear
approximation model obtained in HW2 (Prob B-3-5).
Use the following parameters:
Length of Pendulum = 1.2827 meters
Moment of Inertia = 2.4532 kg m^2
Pendulu
EE475 HW4
Due Sept 30, 2016.
Readings: Chapter 5-1 5-5 of the Book.
Problem 1
a) The last slide in lecture 8 shows the initial response to a step input whose steady
steady-state value is -4.47deg. Please use the Matlab data file provided.
Measure Mp and t
EE475 HW6
Problem 1
For the block diagram below, find the transfer function from R to Y.
Problem 2
Consider the system given in the following block diagram.
u
+
+
_
+
y
Determine the range of k and p for closed loop stability. Select k and p to place the
EE475
HW8
Due Nov 4.
Read Chap7 and the lecture notes 10
Problem 1
Given the Plant P with the following trnasfer function
P(s)=10/(s^4 + 0.4 s^3 + 50.05 s^2 + 10 s + 0.5)
1) Find poles and zeros
2) Sketch the Bode plot and check it with Matlab.
For the ne
EE 475 Quiz #15
Name:
1. Fill in the blanks:
For a general nxn matrix A
e A0 = _
e Ae 2 A = _
(e )
L ( e At ) = _
At 1
= _
d At
e = _
dt
&
x = Ax + Bu
For
, the TF from u to y is
y = Cx + Du
given by H ( s) = _
&
If x = Ax with x(0) = x0 , then the solu
EE475
1.
plant transfer function
G( s)
HW09
200
.
s 4s 4
2
From plant: PM=16.3, Wgc=14 rad/s
To fix ess to step, let Kp=1
(a).
From specification: Mp=10%
We have PMd=70-Mp+12=60
So Phi=PMd-PM=55.7
Let Wgcd=14 rad/s
Compute Td=tan(phi)/Wgcd= 0.1049
That i
EE475
200 .
s 4s 4
From plant: PM=16.3, Wgc=14 rad/s
Use lead to increase PM
Let Wgcd=14rad/s
phimax=(70-10)-16.3+13=56.7
alpha=(1+sin(phimax)/(1-sin(phimax)=
10.5267
z=Wgcd/alpha^.25= 7.7724
p=Wgcd*alpha^.75= 81.8176
To maintain Dc gain
C_Lead = p/z*(s+z
EE 475 Fall 2008 Final Exam
Name
Instructions:
1. This is a closed-book and closed-notes exam for individual work. You may have
two sheets of formulae of size no larger than US letter. A calculator is allowed.
Any device with wireless functions must be tu
EE 475 Fall 2008 Midterm Exam #1
Instructions:
Name
1. This is a closed-book and closed-notes exam for individual work. You may have
one sheet of formulae of size no larger than US letter. A scientific calculator is
allowed.
2. Time for the exam is 50 min
EE 475 EXAM #2, NAME:_
EE 475 Fall 2008 Midterm Exam #2
Instructions:
1. This is a closed-book and closed-notes exam for individual work. You may have one
sheet of formulae of size no larger than US letter. A scientific calculator is allowed.
2. Time for
EE 475 Quiz #13
Name:
Regarding the loop shaping technique for Bode plot based controller design, answer the
following questions:
1. How many distinct frequency range do we consider:
3
2. At mid-frequency, what design specifications do we use to determine
EE475
HW5
1. A systems unit step response is given below.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
Determine the steady state value:
Determine the steady state error:
Determine the +-1% settling time:
Determine the delay time:
Determine the rise time:
Determine the
Modeling
Use math to describe the operation of the
plant, including sensors and actuators
Capture how variables relate to each other
Pay close attention to how input affects
output
Use appropriate level of abstraction vs
details
Many types of physica
Dynamic Response
Steady State Response: the part of response when t
Transient response: the part of response right after the
input is being applied.
Both are part of the total response
total resp = z.i. resp + z.s.resp.
z.i. resp = Output due to i.c.
Example: car suspension
Car suspension: simplified
Ignore tire deformation.
Suppose y1(t) is measured
from equilibrium position
when gravity has set in.
So gravity is canceled by
spring force at eq. pos.
There are two forces on m:
f spring k elongation
f
Signal Flow Graph
nodes : variables
branches : gains
e.g. y = a x
Compare:
a
x
y
x
e.g. y = 3x + 5z 0.1y
3
x
+
-0.1
x
3
y
5
y
a
z
z
5
+
y
0.1
SFG is equivalent to, but may be simpler than, block dia
The value of a node is equal to the sum of all
signals
Dynamic Response
Unit step signal:
1
u (t ) u s (t )
s
Step response: y(s)=H(s)/s, y(t)=L-1cfw_H(s)/s
Time domain response specifications
Defined based on unit step response
Defined for closed-loop system
U s
H s
Y s
b s bm s m L b1s b0
H s
n
a s
s
State Space circuit model
&
x1
&
x2
M
a12 K x1
b1
a21 a22 K x2 2 u state equation
b
M M O
M
M
x1
y c1 c2 K x2 d u output equation
M
General form:
a11
&
x Ax Bu
y Cx Du
State Variables: x1 vC1 , x2 vC2 , x3 iL
Input Variable: u r (t
EE475 HW1
Due Sept 2, 2016.
Readings: Chapter 1 and Chapter 2 of the Book.
Do the following problems in the book
B-2-2
B-2-3
B-2-6
B-2-7
B-2-8
B-2-10 Do it by hand, show your work, and then verify with Matlab
EE 475 HW #11
Read Chap 9, Chap10-3
1. Do B-9-1 but give 3 forms: (a) and (b) and also a diagonal form.
2. Do B-9-6 by hand.
3. Do B-9-10, 11, 12
4. Do B-9-13, 14, 15, 16, 17. Use Matlab.
5. Do B-10-3 and B-10-4.
6. Do B-10-9 Use Matlab.
EE475
HW7
Read Chap7.1 to Chap7.6
Due OCT 28 2016
Do the following problems form the book.
For the problems that requires drawing the Nypust plot, you should sketch it by hand first,
(helping yourself with Bode plots sketch) and then use Matlab to verify.
EE475 HW2
Due Sept 14, 2016.
Readings: Chapter 3 of the Book.
Do the following problems in the book
B-3-3
B-3-5
B-3-6 Also derive a state-space representation
B-3-7 Also obtain a state-space representation
B-3-11 Also derive a state-space representation