MA 2054
Polytechnic University
Exam 1
February 27, 2008
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Directions: You have 90 minutes to answer the following questions. You must show
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MAE4050 Assignment 2
Due day: Oct. 6, 2009
1. Give the control canonical form realization and observer canonical-form realization
for the transfer function
G(s) =
4s3 + 25s2 + 45s + 34
2s3 + 12s2 + 20
MAE4050 Assignment 4, Due day: Oct. 20, 2009
1. For
F
0 1
0
0
= 0 1 1 , G = 0
0 0 5
1
Using both Bass-Gura formula and Ackermans formula to find feedback gain K R13 so that
(F GK) = cfw_10.62, 4 + j2
MAE4050 Assignment 1
Due Day: September 24, 2009
1. A system is described by
"
x 1 (t)
x 2 (t)
#
"
=
0
1
6 5
#"
x1 (t)
x2 (t)
#
"
+
0
1
#
u
with u(t) = 0 and x1 (0) = x2 (0) = 10. Determine x1 (t) and
ACE3010 Assignment 5, Due Date Nov. 5, 2009
1. The following system describes an undamped harmonic oscillator
x 1 = x2 , x 2 = 02 x1 (t) + u(t), y(t) = x1 (t)
(1)
where 0 = .
(a) Design a state-feedba
Multivariable optimization with
inequality constraints
Minimize f (X)
subject to
gj (X) 0,
j=1, 2,m
The inequality constraints can be transformed to equality constraints
by adding nonnegative slack va
Multivariable optimization with equality constraints
Problem statement:
Minimize f = f (X) subject to gj(X)=0, j=1,2,.,m where
x1
x
X 2
xn
Here m is less than or equal to n, otherwise the pr
2. Classical optimization techniques
Single variable optimization
Useful in finding the optimum solutions of continuous and differentiable
functions
These methods are analytical and make use of the
Gaussian Quadratures
Newton-Cotes Formulae
use evenly-spaced functional values
Did not use the flexibility we have to select the quadrature points
In fact a quadrature point has several degrees of
Polytechnic Institute of NYU
MA 2054
Sample Final
May , 2012
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Directions: You have 120 minutes to answer the following questions. You must show
all your
MA 2054
Polytechnic University
Exam2
April 2 , 2008
Print Name:
Signature:
ID #:
Instructor/Section:
Directions: You have 90 minutes to answer the following questions. You must show
all your work as n