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Homework 3 AERE 331 Spring 2014 Due 2/28(F)
SOLUTION
PROBLEM 1(25pts) Consider a unity feedback closed loop system with open loop transfer function
K
G(s) =
. The Closed loop system poles are the values of s that satisfy
s ( s + 2)
(a)(5pts) Use the Roo

Exam 1 AERE331 Spring 2014 (Take-Home) Due 2/17(M) Name_
[All work- including plots- MUST be positioned directly beneath the given problem part. Include ALL Matlab
code, well-documented, in the Appendix.] Updated 2/13 @ 3:40pm
PROBLEM 1 (25pts) A simplifi

Homework 1 Spring 2014 AERE 331 Due 1/27(M)
SOLUTION
In this homework we pass through a worm hole to p.667 of the text. We will address the dynamics of the
geosynchronous communications satellite IPSTAR, shown in Figure 10.2(a). The angular dynamics of
th

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Homework 2 Spring 2012
DUE 2/5 (W)
SOLUTION
PROBLEM 1. (15 pts) Consider the system described by: y + 0.2 y + 100 y = 10 x
G p ( s ) = 10 /( s 2 + 0.2 s + 100)
(a)(3 pts) Give the system transfer function:
g s = G p (0) = 0.1
(b)(2 pts) Give the system

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LECTURE 19
Servo Motor for Rudder Position control
References: [1] Franklin & Powell pp.53-58 [2] http:/faculty.dwc.edu/sadraey/Rudder%20Design.pdf
The Motor
Kirkoffs Voltage Law: v(t ) = R a i (t ) + eb (t ) V ( s ) = R a I ( s ) + E b ( s )
Motor Torq

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Lectures 16 and 17
Lead/Lag Compensator Frequency Domain Properties and Design Methods
Definition 1. Consider the compensator (i.e. controller) Gc ( s) K s 1 . For 1 2 , it is called a lead compensator.
s
2
For 2 1 , it is called a lag compensator.
N

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Lecture 24 Introduction to Discrete Time Systems and Their Analog Counterparts
Motivation
Continuous-time (i.e. analog) systems are fundamental to understanding feedback control. However, rarely are analog
controllers implemented to control analog plant

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Lecture 26
Emulation of Continuous Control by Discrete Control
In this lecture we focus on emulating a continuous feedback control system by a discrete one, as shown in Figure 8.1. The
term emulation means to emulate = to behave as. Specifically, we des

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Homework 5
AERE331 Spring 2017 Due 4/5(W)
SOLUTION [with corrections announced in class]
C
PROBLEM 1 (20pts) Consider the first order circuit at right.
i (t )
(a)(4pts) Give the voltage (output) / current (input) transfer functions for the resistor vin

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Lectures 16 and 17
Lead/Lag Compensator Frequency Domain Properties and Design Methods
s 1
. For 1 2 , it is called a lead
s 2
Definition 1. Consider the compensator (i.e. controller) Gc ( s ) K
compensator. For 2 1 , it is called a lag compensato

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Lecture 27
Simulation of Turbulence and Phugoid Response to It
Simulation of atmospheric turbulence is essential for conducting realistic flight dynamics simulations. Matlabs
Aerospace Blockset/Environment/Wind includes tools for simulating specified ty

1
Homework 4 AERE331 Spring 2017 Due 3/10 (F) Name_12pm / 3pm
(a)(10pts) For a unity feedback configuration
with Gc ( s ) 1.0 , use the plot to arrive at
0
estimates of the CL GM and PM, and (ii) estimate
Phase( deg)
M r (i10) dB and r (i10) o
Solution:
R

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Homework 5
AERE331 Spring 2017 Due 4/5(W) Name_ 12pm / 3pm
C
PROBLEM 1 (20pts) Consider the first order circuit at right.
i (t )
(a)(4pts) Give the voltage (output) / current (input) transfer functions for the resistor vin (t )
R vout (t )
and capacitor

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Lecture 24 Introduction to Discrete Time Systems and Their Analog Counterparts
Motivation
Continuous-time (i.e. analog) systems are fundamental to understanding feedback control. However, rarely are analog
controllers implemented to control analog plant

1
Homework 1 AERE331 Spring 2017 Due 1/18(W) Name_ 12:10 or 3:10pm
Note: The solution to each part of a given problem (including all figures) must be placed directly beneath that part. If it is
placed elsewhere it will be ignored. Unless stated otherwise,

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Homework 5
AERE331 Spring 2017 Due 4/5(W)
SOLUTION [with corrections announced in class]
C
PROBLEM 1 (20pts) Consider the first order circuit at right.
i (t )
(a)(4pts) Give the voltage (output) / current (input) transfer functions for the resistor vin

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Lecture 17
Comments on and References to Exam 1
[NOTE: All work, answers and plots must be placed directly beneath the given problem part to receive credit. Matlab
code that supports the same should be placed in the Appendix. I will not go to the Append

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LECTURE 18
An Example of Bode-Based Control System Design
The block diagram of an antenna angular position command control system is shown below.
120 deg
motor: Gm ( s )
s ( s 1) volt
G s (s )
c
1000
deg . r (t )
G
(
s
)
antenna:
ant
s 2 50s 1000 de

Lecture 25
Introduction to Some Matlab c2d Code in Relation to Sampled Systems
There are many ways to convert a continuous time function, cfw_h(t ) ; t [0, ) into a discrete time function
cfw_h(kT ) ; k cfw_0,1, . Recall that the table of Laplace/z-trans

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AERE331 Exam 2 Spring 2017 (Take-Home) Due 3/27(M) Name_ 12pm / 3pm
PROBLEM 1 (30pts) The drone package delivery system at right lowers a package of mass
m. The length, of the cable will increase as the package is lowered. The package dynamics
can be mo

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Lecture 15
Problems from Ch.6 and Derivations
Bode Diagram
Since the open loop phase never comes close to -180o the closed
loop system will be stable for all K.
-5
-10
-15
-20
60
Phase (deg)
Example 1. [Book 6.16(a)] For a closed loop system with open
K

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Homework 6 AERE331 Spring 2017 Due 4/19(W) SOLUTION
[Note: I have included partial Matlab code in the Appendix. It may guide you to more organized coding.]
PROBLEM 1 (30pts) While the Dirac delta function (also termed the unit impulse), (t ) , is an 1 /

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Homework 4 AERE331 Spring 2017 Due 3/10 (F)
SOLUTION
PROBLEM 1(40pts) The experimentally
obtained position/torque FRF for a robot arm is
shown at right. Call it Gr (i ) .
(a)(10pts) For a unity feedback configuration
with Gc ( s) 1.0 , use the plot to a

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Lecture 27
Simulation of Turbulence and Phugoid Response to It
Simulation of atmospheric turbulence is essential for conducting realistic flight dynamics simulations. Matlabs Aerospace
Blockset/Environment/Wind includes tools for simulating specified ty

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Lecture 23 & 24
Element
Resistor:
Picture
Inductor:
RLC Circuits and Op Amps
Symbol
R
Voltage/Current Relation
v(t ) = R i (t ) V ( s ) = R I ( s )
v(t ) = L d i (t ) / dt V ( s ) = ( Ls ) I ( s )
L
t
Capacitor:
v(t ) = (1 / C ) i ( )d
C
V ( s ) = (1 /

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Homework 4 AERE331 Spring 2017 Due 3/10 (F) Name_12pm / 3pm
PROBLEM 1(40pts) The experimentally
obtained position/torque FRF for a robot arm is
shown at right. Call it Gr (i ) .
(a)(10pts) For a unity feedback configuration
with Gc ( s) 1.0 , use the pl

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Lecture 9 The Root Locus Concept
Consider a feedback control system with open loop G ( s ) K
the values of s that solve the equation: 1 K
s2
s z1
K
. The closed loop poles are
s ( s 5)
( s p1 )( s p2 )
s z1
0 . This equation is exactly the equation:
( s

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Lecture 6
More on Estimation of J in The Quadcopter Animation
Tg (t )
[ http:/www.gperco.com/2014/05/quadcopter-stability-and-neural-networks.html ]
G p ( s)
Tc (t )
Recall that the closed loop system transfer function model for the quadcopter is:
WP (

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Exam 1 Spring 2017 AERE 331 Take-Home Due 2/13(M) Name_ 12pm / 3pm
[NOTE: All work, answers and plots must be placed directly beneath the given problem part to receive credit. Matlab
code that supports the same should be placed in the Appendix. I will n

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Homework 3 AERE331 Spring 2017 Due 2/22 (W)
SOLUTION
PROBLEM 1 (25pts) The human ear is a dynamical system. The input is a sound wave with a given intensity and the
output is what the person hears. Figure 1 below gives what are called equal loudness con

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Lecture 22 Some State Space Examples in Relation to Flight Dynamics
Example 1. Consider a general aviation aircraft constrained to pure yaw motion (e.g. in a wind tunnel), described by:
0.76 4.55 4.6 r . Recall that in this setting the yaw rate is: (t

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Lecture 15
Problems form Ch.6 and Derivations
BodeDiagram
Example 1. [Book 6.16(a)] For a closed loop system with open
K ( s 2)
loop G ( s )
, draw the Bode plot of this open loop for
s 20
K = 1, and then use the plot to determine the range of K for wh

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Homework 6 AERE331 Spring 2017 Due 4/19(W)
SOLUTION
[Note: I have included partial Matlab code in the Appendix. It may guide you to more organized coding.]
PROBLEM 1 (30pts) While the Dirac delta function (also termed the unit impulse), (t ) , is an
1/

Lecture 14
The System Frequency Response Function
To begin, consider a dynamical system with transfer function
g
Y ( s)
G ( s ) s . The system frequency response function (FRF)
X (s)
s 1
gs
is simply G (i )
. In polar form, we have
1 i ( )
G (i ) M ( )e

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Homework 5
AERE331 Spring 2017 Due 4/5(W) Name_ 12pm / 3pm
C
PROBLEM 1 (20pts) Consider the first order circuit at right.
i (t )
(a)(4pts) Give the voltage (output) / current (input) transfer functions for the resistor vin (t )
R vout (t )
and capacitor