O N E
Introduction
ANSWERS TO REVIEW QUESTIONS
1. Guided missiles, automatic gain control in radio receivers, satellite tracking antenna 2. Yes  power gain, remote control, parameter conversion; No  Expense, complexity 3. Motor, low pass filter, inertia
ME 380
Chapter 1 HW
January 20, 2012
Chapter 1 HW Assignment & Hints (due Mon., January 23, 2012)
Review Questions.
Please answer the following Review Questions:
1, 2, 4, 8, 9, 14, 15.
These should be pretty easy.just refer to the text.
Problems. Please d
ME 380
Chapter 1 HW
January 23, 2012
Chapter 1 HW Solution
Review Questions.
1. Name three applications for feedback control systems.
1. Elevator
2. Robot vehicle or manipulator arm
3. Spacecraft
2. Name three reasons for using feedback control systems an
ME 380
Chapter 2 HW
February 3, 2012
ME 380 Chapter 2 HW Solution
Review Questions.
1. What mathematical model permits easy interconnection of physical sysems? The transfer function
model.
3. What transformation urns the solution of dierential equations i
ME 380
Chapter 3 HW
February 13, 2012
Chapter 3 HW Solution
Problem 19. Consider a DC motor driving a load through a gear train:
bL
The specications for the Pittman 7214 DC motor (taken from the manufacturers data sheet) are:
Jm = 1.54 106 kgm2 (not show
ME 380
Chapter 4 HW
February 27, 2012
Chapter 4 HW Solution
Review Questions.
1. Name the performance specication for rst order systems. Time constant .
2. What does the performance specication for a rst order system tell us? How fast the system responds.
ME 380
Chapter 5 HW
March 9, 2012
Chapter 5 HW Solution
Review Questions. 1, 6. As usual, I think these are just a matter of text lookup.
1. Name the four components of a block diagram for a linear, timeinvariant system. Lets see, I guess
from the text F
ME 380
Chapter 7 HW
April 1, 2012
Chapter 7 HW Assignment & Hints
Review Questions. 1, 3, 4, 5, 9. As usual, I think these are just a matter of text lookup.
Problem 2. (a) The steadystate error can be read right from the plot.
(b) Now the input is r(t) =
ME 380
Chapter 7 HW
April 4, 2012
Chapter 7 HW Solution
Review Questions.
1. Name two sources of steadystate errors.
1. System conguration (TYPE too low)
2. Type of applied input (ramp, parabolic, etc.
3. Name the test inputs used to evaluate steadystat
ME 380
Chapter 7 HW
April 15, 2012
Chapter 8 HW Assignment & Hints (complete)
Review Questions. 1, 4, 5, 7. As usual, I think these are just a matter of text lookup.
Problems. 1abegh, 2abc, 8, 30 41, 60.
Problem 1. Look at RL sketches a, b, e, g, h and, i
T H I R T E E N
Digital Control Systems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the answer to the antenna control challenge in Chapter 5, the equivalent forward transfer function found by neglecting the dyna
T W E L V E
Design via State Space
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Design of Controller and Observer
a. We first draw the signalflow diagram of the plant using the physical variables of the system as state variables.
Writing the state e
T H R E E
Modeling in the Time Domain
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: StateSpace Representation
. Ea(s) 150 For the power amplifier, V (s) = s+150 . Taking the inverse Laplace transform, ea +150ea = p 150vp. Thus, the state equation
F O U R
Time Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: OpenLoop Response
The forward transfer function for angular velocity is, 0(s) 24 G(s) = V (s) = (s+150)(s+1.32) P a. 0(t) = A + Be150t + Ce1.32t 24 b. G(s) = 2 . Therefore, 2n
F I V E
Reduction of Multiple Subsystems
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Designing a ClosedLoop Response
a. Drawing the block diagram of the system:
Pots
Pre amp
Power amp
Motor, load and gears
ui +
10
K
150 s+150

0.16 s (s+1.32)
S I X
Stability
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Stability Design via Gain
From the antenna control challenge of Chapter 5, 76.39K T(s) = 3 s +151.32s2+198s+76.39K Make a Routh table: s3 s2 s1 s0 1 151.32 29961.3676.39K 151.32 76.39K
S E V E N
SteadyState Errors
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: SteadyState Error Design via Gain
76.39K a. G(s) = s(s+150)(s+1.32) . System is Type 1. Step input: e() = 0; Ramp input: 1 2.59 = 76.39K = K ; Parabolic input: e() = . 15
E I G H T
Root Locus Techniques
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Transient Design via Gain
a. From the Chapter 5 Case Study Challenge: 76.39K G(s) = s(s+150)(s+1.32) 1 Since Ts = 8 seconds, we search along  2 , the real part of poles
N I N E
Design via Root Locus
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: LagLead Compensation
76.39K a. Uncompensated: From the Chapter 8 Case Study Challenge, G(s) = s(s+150)(s+1.32) = 7194.23 1 6.9 s(s+150)(s+1.32) with the dominant poles a
T E N
Frequency Response Techniques
SOLUTION TO CASE STUDY CHALLENGE
Antenna Control: Stability Design and Transient Performance
First find the forward transfer function, G(s). Pot: K1 = Preamp: K Power amp: 100 G1(s) = s(s+100) Motor and load: Kt 1 1 1 J
E L E V E N
Design via Frequency Response
SOLUTIONS TO CASE STUDIES CHALLENGES
Antenna Control: Gain Design
a. The required phase margin for 25% overshoot ( = 0.404), found from Eq. (10.73), is 43.49o. 50.88K From the solution to the Case Study Challenge
ME 380
Chapter 8 HW
April 23, 2012
Chapter 8 HW Solution
Review Questions.
1. What is a root locus? A plot of the possible closedloop pole locations as some parameter varies from 0 to .
4. Do the zeros of a system change with a change in gain? No.
5. Whe