MAE 171A
Spring 2013
Homework 3
Due May 1/13
Problem 1 Sketch the output time response of a step input into the following
transfer functions. Use partial fractions to decompose the response.
a) G(s) = 10/(
3.2 Find the Laplace transform of the following time functions:
Solution: (b) f (t ) = 3 + 7t + t 2 + (t )
cfw_ f (t ) = cfw_3 + cfw_7t + cfw_t 2 + cfw_ (t )
3 7 2!
= + 2 + 3 +1
ss
s
3
2
s + 3s + 7 s + 2
=
s3
3.3 Find the Laplace transform of the followi
Practice Problems for Final Exam
This set of problems covers the class materials after the midterm exam. A focus of the nal exam will be more
on this part of the materials. However, you are encouraged to go over the practice problems for the midterm
exam
MAE 171A  Winter, 2013
P ROBLEM S ET 4
Due: Thursday, 2/7, 1:50pm (In class)
Reading:
Pages 170186 in FPE6.
[ Pages 166186 in FPE5.]
Problems:
Consider the unity feedback control system shown below:

For Problems 13, assume that the plant and control
3.32 In aircraft control systems, an ideal pitch response (qo ) versus a pitch command (qc ) is
described by the transfer function
Q0 ( s )
2 ( s + 1/ )
=2n
2
Qc ( s ) s + 2n s + n
The actual aircraft response is more complicated than this ideal transfer
MA 171A HW#4 Solution
1. (a) Let w = v = 0 to nd the transfer function with r. From the block diagram,
Y = GU = GD(R Y ) = GDR GDY.
Solving for H := Y /R, we have
H (s) =
(b). Let G =
GD
k (s 1)
=2
1 + GD
s + (k )s k
a(s)
b(s) ,
D=
c(s)
d(s) .
The system
Practice Problems for Midterm Exam
1. Sketch the output y (t) of P (s) = 2/(1 + 3s) in response to the step input u(t) = 3.
Solution: The static gain () is P (0) = 2 and the time constant is = 3. The transfer function is stable
and of rst order, so its st
MAE 171A
Spring 2013
Design Project 1
Due May 3/13
Certain devices require a constant temperature environment for proper operation.
Examples are gyroscopes, accelerometers and crystals used as frequency standards.
Intro
MAE 171 A:
Feedback Control Systems
Jason L. Speyer
Mechanical and Aerospace Engineering
University of California, Los Angeles
Spring Quarter
Lecture 1
April 2, 2012
Intro
Feedback and Control Systems: Introduction
I
A system is a collection of comp
Homework set 7
MAE 171A
Due: May 28, 2014
Sketch the Nyquist Plots for the following transfer functions. Determine
the gain and phase margins of these systems where the Nyquist plot indicates
stability.
1.
G(s) =
2.
G(s) =
K
,
(s + 1)(s + 2)
K
,
(s + 1)(s
MAE 171A  Root Locus
Spring 2012
r
R(s)
r
C(s)
Y (s)
G(s)
r
r
H(s)
The closedloop (CL) transfer function of the system represented by the block diagram above is
Y (s)
C(s)G(s)
C(s)G(s)
=
=
R(s)
1 + C(s)G(s)H(s)
1 + K L(s)
where K is a constant gain. (We
MAE 171 A:
Feedback Control Systems
Chapter 7
Root Locus
April 15, 2014
Root Locus
Consider the the feedback loop
Y (s)
K(s)G(s)
= GCL (s) =
R(s)
1 + K(s)G(s)H(s)
Let the denominator (which represents the closedloop poles) be
1 + K(s)G(s)H(s) = 0 K(s)G
MAE 171A:
Due on April 28, 2014
1
Draw the root locus for the following transfer
functions as K goes from 0 to .
(a) G(s)H(s) =
3K(s+1)
s(s+3)
The steps of drawing the root locus (RL) are following
1
P ole : p = 0, 3
(n = 2)
zero : z = 1
(m = 1)
nm=1
2 re
MAE 171 A:
Feedback Control Systems
Chapter 9
Gain and Phase Margins and the Nyquist
Criterion (Continued)
May 17, 2014
=
SecondOrder System: K G
Positive encirclements are CW.
Nyquist Plot
Bode Plot
40
K
2s
s2
2 + +1
n
=0
< 0.5
slope = 40db/dec
Im(
MAE 171 A:
Feedback Control Systems
Chapter 3
Dynamic System Response
April 6, 2014
System Time Response Characteristics
Time response characteristics fall into three categories:
I
Transient response soon after a command.
I
Steadystate response long afte
MAE 171 A:
Feedback Control Systems
Chapter 9
Frequency Response
April 30, 2014
Background
The system frequency response can be found experimentally by a
frequency sweep, illustrated below
A sint
G(s)
B sin(t+)
1
0
B
A
90
or by measuring the system impu
MAE 171 A:
Feedback Control Systems
Chapter 8
Root Locus Compensator Design
April 27, 2014
Aircraft PitchRate Autopilot
To illustrate root locus compensator design, an aircraft
pitchrate command system is to be developed for a Lear Jet in
steady level
MAE 171 A:
Feedback Control Systems
Chapter 9
Gain and Phase Margins and the Nyquist
Criterion
May 5, 2014
Gain and Phase Margin
A margin of safety in ensuring stability in the presence of
uncertainty in the system model is measured by the change in gain
MAE 171 A:
Feedback Control Systems
Chapter 6
Feedback Control
April 8, 2014
Objectives of Feedback Control Systems
Generally, the objectives of a feedback controller are to
improve system performance in the sense of
I
Speed as measured by the risetime.
Intro
MAE 171 A:
Feedback Control Systems
Jason L. Speyer
Mechanical and Aerospace Engineering
University of California, Los Angeles
Spring Quarter
Lectures 2 & 3
April 4, 2012
Intro
Models for Control
Definition: Linear System
A function f (x) is a linea
Design Problem 4
MAE 171A
Due: June 4, 2014
We consider the design of a satellite attitude control system. The satellite is
assumed to be in drag free space. We are interested in controlling rotation about
its axis of rotational symmetry. We do this by me
Sample Problems for Final Exam
This set of problems covers the class materials after the midterm exam. A focus of the final exam will be more
on this part of the materials. However, you are encouraged to go over the sample problems for the midterm
exam as