Lab 11
AERE 421
Problem 1 (All units in meters)
Phase angle plot
Problem 2 (All units in meters)
Modal solution 1st natural Frequency
Modal solution 2nd natural Frequency
Modal solution 3rd natural Frequency
Modal solution 4th natural Frequency
Modal solu
Lab 10
Problem 1 (all units in meters)
Side view
Top view
Hand calculation gives 162425 N the FACT calculated in Ansys (148735) is close (9% error)
Problem 2 (all units in meters)
Sub 1 (Vertical force of -1N)
Sub 2 (Vertical force of -1N)
Sub 1(Horizonta
Lab 6
Problem 1
! All units in Pa and Meters !
Vector Displacement
XY Stress
Stiffener Stress
Problem 2
! All units in Pa and Meters !
Contour plot Displacement vector sum
XY Stresses
YZ stresses
XZ stresses
Stiffener stress XZ
*Note only Stiffener stress
AERE 421
Homework 3
All units in meters, Newtons, and mm^4
A)
New Iyy,Izz=
Iyy=3.63146E-7
Izz=-4.3145E-6
B)
Pzz=1.1923E7N
Pyy=1.0035E5N
Pa=356008N
C) Combined bending and Torsion
Mode 1 Top View
Mode 1 Front View
Mode 2 Top View
Mode 2 Front View
Mode 3 T
Lab 9
Problem 1 (All units in inches)
regular Ansys Linear Solution
Non- linear
Mechanics of materials solution
DMX = 30.015
The difference is that the non linear solution is closer to the value from mechanics of materials. Making
it more accurate than th
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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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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
1
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 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
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Homework 1 AERE331 Spring 2017 Due 1/18(W)
SOLUTION
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, place all Ma
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Exam 3 Spring 2017 AerE331 Due 4/28(F) Name_ 12pm / 3pm
PROBLEM 1(35pts) Consider a plant state x Ax B u with initial condition x 0 , and output y Cx Du .
(a)(5pts) Arrive at the solution of this ODE problem in the Laplace domain [i.e. solve for Y(s ) ]
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Homework 3 AERE331 Spring 2017 Due 2/22 (W) Name/Section_
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 loudnes
1
Exam 3 Spring 2017 AerE331 Due 4/28(F) Name_ 12pm / 3pm
PROBLEM 1(35pts) Consider a plant state x Ax B u with initial condition x 0 , and output y Cx Du .
(a)(5pts) Arrive at the solution of this ODE problem in the Laplace domain [i.e. solve for Y (s )
1
Homework 6 AERE331 Spring 2017 Due 4/19(W) Name_ 12pm/3pm
[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
1
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 3 AERE331 Spring 2017 Due 2/22 (W) Name/Section_
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 loudnes
1
Lecture 20 State Space Representation of Transfer Functions
The state space approach to feedback control systems is central to a graduate level course in feedback control systems. It
is often referred to as modern control. This approach is based on elem
1
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 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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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
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