MAE 171A Homework #1 Solutions
Summer 2014
Solution 1:
(a) Use frequency shift transform
s
s2 + 122
=
s + 0.4
L e0.4t cos(12t) =
(s + 0.4)2 + 122
L(cos(12t) =
=
s2
s + 0.4
+ 0.8s + 144.16
(b) Use trig
171A Project Solutions
Summer 2014
Solution 1:
The functional block diagram is given by
+
e
c
Compensator
v
Amp
i
M
Motor
Wheel Inertia
Satellite Inertia
The dynamic equations are given by
v(t) = Ka (
MAE 171A Homework #3 Solutions
Summer 2014
Solution 1:
(a) First, reduce the block diagram as shown:
G2
+
r
+
y
G1
1+G1
The transfer function for R to Y in the gure above is given by
G1
Y
= G2 +
R
1 +
MAE 171A Homework #1 Solutions
Summer 2014
Solution 1:
In each of these problems, if the poles are stable, we may apply the Final Value Theorem.
(a) The output transfer function is given by
Y (s) = G(
Name: _
UID: _
MAE 171A
Final Exam August 13, 2014
Problem 1) (40%)
Consider the feedback control system of figure with a compensator
K(s) = K(1 + 1/s ) and a plant G(s) = 1/(s-1) .
a) Draw the root l
MAE 171A
Winter 2015
Design Project 2
Due February 20/2015
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
Use MATLAB for any of the following questions.
EmblﬂmlConsider the plant transfer function
G[s] = [bs + k]/ [52[lHMS2 + [M + m]bs + [M + m}k]
to be put in the unity feedback loop [see figure]. This is
MAE 171A
Winter 2015
Design Project 1
Due January 30/2015
Certain devices require a constant temperature environment for proper operation.
Examples are gyroscopes, accelerometers and crystals used as
MAE 171A
Summer 2017
Homework
Problem 1 Consider the following transfer function (H(s) = 1)
G(s) =K(s2 + 4)(s2 + 16)/s(s2 + 9)(s2 + 25)
(a) Show the root locus.
(b) Find the gain K that achieves the l
MAE 171A
Winter 2015
Homework 1
Due January 16, 2015
Problem 1. Find the Laplace transforms
0.4t
(a) f ( t )=e cos ( 12 t)
(b) f (t)=sin ( 4 t+ /3)
2 at
(c) f ( t )=t e
(d) f ( t )=cos ( 2 t )cos ( 3
MAE 171A
Winter 2015
Homework 2
Due January 23/2015
Find the value of the output y(t) at t big
(a)
Let the input be a unit step, u(t), and the plant transfer function be
G(s)=
(b)
Let the input be an
MAE 171A
Winter 2105
Homework 3
Due January 30, 2015
Problem 1 Sketch the output time response of a step input into the following
transfer functions. Use partial fractions to decompose the response.
a
MAE 171A
Winter 2015
Homework 4
Due February 6, 2015
Problem 1 Sketch the step response of the systems
a) G(s) = (s+2)/(s2+3s+36)
b) G(s) = (-s+2)/(s2+3s+36)
Hint: write G(s) = zsG(s) + G(s) where z =
MAE 171A
Winter 2015
Homework 7
Due March 13/2015
Use MATLAB for any of the following questions.
Problem 1) Sketch the Nyquist Plots for the following transfer functions.
Indicate when the Nyquist plo
MAE 171 A:
Feedback Control Systems
Chapter 9
Gain and Phase Margins and the Nyquist
Criterion (Continued)
May 23, 2012
Second-Order System: K G =
K
2s
s2
2 + +1
n
Second-Order System: K G =
Bode Plo
1 Draw the root locus for the following transfer
functions as K goes from U to 00.
(a) Grams} =
The steps of drawing the root locus [BL] are following
(9
Polc:p=ﬂ,—3 [11:2]
36.1“013 = —1 (m :1]
11—11
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)
Use MATLAB fer any {if the fellewing questinns.
Prﬂblem 1] Sketch the Nyquist Plots for the following transfer ﬁtnetiens.
Indicate when the Nyquist plot indicates stability. Comment your results.
1. G
MAE 171A
Winter 2015
Design Project 3
Due March 13/2015
Consider the design of a satellite attitude control system. The satellite is
assumed to be in drag free space. We are interested in controlling
MAE 171A
Winter 2015
Homework 6
Due March 6/2015
Use MATLAB for any of the following questions.
Problem 1 Consider the plant transfer function
G(s) = (bs + k)/ (s2[mMs2 + (M + m)bs + (M + m)k])
to be
MAE 171A
Winter2015
Homework 5
Due February 23/2015
Problem 1 Draw the root locus for the following transfer functions as K goes
from 0 to1.
(a) G(s)H(s) = 3K(s+1)/s(s+3)
(b) G(s)H(s) = K(s+4)/2s(s+2)
MAE 171A: Dynamic Systems Control
Lecture 5: Dynamical System Properties
eect of zeros
Goele Pipeleers
Recall from Lecture 4 . . .
System Poles and Step Response
1
rst-order system: G(s) =
=
s + s +
MAE 171A: Dynamic Systems Control
Lecture 6: Stability
Goele Pipeleers
Overview of the Lectures so Far
L1: review of the Laplace transform and transfer function
L2: deriving a transfer function mode
MAE 171A: Dynamic Systems Control
Lecture 7: Framework of Control Systems
Goele Pipeleers
Overview
So Far: Mainly Systems Theory
L1: review of the Laplace transform and transfer function
L2: derivin
MAE 171A: Dynamic Systems Control
Lecture 8: Steady-state Error and System Type
Goele Pipeleers
Recall from Lecture 7
Feedback Control
control conguration
r
D (s )
controller
u
w
G (s )
system
y
v
r: