MAE 171A:
Due on April 29, 2015
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
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 1, 2015
Intro
Models for Contro
Homework set 4
MAE 171A
Due: April 29, 2015
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)
(b) G(s)H(s) =
K(s+4)
2s(s+2)
(c) G(s)H(s) =
Solutions to Homework set 7
MAE 171A
Due: June 3, 2015
Consider the following state space dynamic systems.
1.
0 1 0
0
C = 1 0 0 , A = 0 0 1 , B = 0
0 0 1
1
2.
1
0
0
0
0
0
1
0
, B =
0
2
0
0
1
0
MAE 171A: Solutions to
Homework Set 1
Due on April 8, 2015
1
Find the Laplace Transforms
(a) f (t) = e0.4t cos(12t)
The laplace transform of f1 (t) = cos(wt) is given as
L cfw_f1 (t) = F1 (s)
w
L cfw
Homework set 6
MAE 171A
Due: May 27, 2015
1. Sketch the Bode plots for the following transfer functions
(a)
G(s) =
s+1
s( 1 s + 1)
3
G(s) =
1
s+1
4
1
s( 2 s + 1)
(b)
(c)
G(s) =
(d)
G(s) =
1
s( 3.5 s
s
MAE 171 A:
Feedback Control Systems
Chapter 9
Gain and Phase Margins and the Nyquist
Criterion (Continued)
May 15, 2015
Second-Order System: K G =
Positive encirclements are CW.
Nyquist Plot
Bode P
Intro
MAE 171 A:
Feedback Control Systems
An Introduction to Modern Control Theory
Jason L. Speyer
Mechanical and Aerospace Engineering
University of California, Los Angeles
Spring Quarter
Chapter 12
Design 3 problem - Solution
May 25, 2011
1. The attitude system of the rocket consists of a gimballed engine acting through a leaver-arm to
generate a torque about the center of gravity of the rocket.
MAE 171 A:
Feedback Control Systems
Chapter 9
Gain and Phase Margins and the Nyquist
Criterion
May 6, 2015
Gain and Phase Margin
A margin of safety in ensuring stability in the presence of
uncertaint
MAE 171A: Homework set 5
Due on May 6, 2015
For the block diagrams in Figure 1 the eect of
dierent compensators are studied.
First, determine the closed-loop transfer function for a) and b).
a)
C = Gp
MAE 171 A:
Feedback Control Systems
Chapter 9
Frequency Response
May 3, 2015
Background
The system frequency response can be found experimentally by a
frequency sweep, illustrated below
A sint
G(s)
B
Homework set 1
MAE 171A
Due: April 8, 2015
1. Find the Laplace transforms
(a) f (t) = e0.4t cos(12t)
(b) f (t) = sin(4t + )
3
(c) f (t) = t2 eat
(d) f (t) = cos(2t)cos(3t)
(e) f (t) = tu1 (t) (t T )u1
Intro
MAE 171 A:
Feedback Control Systems
Jason L. Speyer
Mechanical and Aerospace Engineering
University of California, Los Angeles
Spring Quarter
Lecture 1
March 30, 2015
Intro
Feedback and Control
Homework set 2
MAE 171A
Due: April 15, 2015
1. Find the value of the output c(t) at t =
(a) Let the input be a unit step, u(t), and the plant transfer function be
s+1
G(s) = (s+.5)(s+3)
(b) Let the i
MAE 171 A:
Feedback Control Systems
Chapter 3
Dynamic System Response
April 12, 2015
System Time Response Characteristics
Time response characteristics fall into three categories:
Transient response s
Design Problem 2
MAE 171A
Due: April 29, 2015
A control system has the job of driving a controlled shaft so that its angle
of rotation duplicates the angle of another command shaft, which is positione
Homework set 3
MAE 171A
Due: April 22, 2015
1. A second order system has a damping ratio of 0.5, a natural frequency
of 100 rad/s and a dc gain of 1. Find the step response of the system to
a unit ste
MAE 171 A:
Feedback Control Systems
Chapter 6
Feedback Control
April 12, 2015
Objectives of Feedback Control Systems
Generally, the objectives of a feedback controller are to
improve system performan
MAE 171A: Solution : Homework set 2
Due on April 15, 2015
1
Find the value of the output c(t) at t=
(a) Let the input be a unit step, and the plant transfer
function be
G(s) =
s+1
(s + .5)(s + 3)
(1)
MAE 171 A:
Feedback Control Systems
Chapter 7
Root Locus
April 19, 2015
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 represen
MAE 171 A:
Feedback Control Systems
Chapter 8
Root Locus Compensator Design
April 29, 2015
Aircraft Pitch-Rate Autopilot
To illustrate root locus compensator design, an aircraft
pitch-rate command sy
MAE 171A: Homework set 3
Due on April 22, 2015
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
(
Design Problem 1
MAE 171A
Due: April 15, 2015
Certain devices require a constant temperature environment for proper operation. Examples are gyroscopes, accelerometers and crystals used as frequency
st