ECE680 FUNWORK 1
HYUNGJU PARK PUID: 00229 - 89226
1. Problem
Figure 1. The -r robot manipulator and its lumped mass representation
1.1. The -r robot manipulator dynamical system. In this homework, we are to
choose one dynamical system and model the system
ECE 680
Fall 2015
Test #2
Solutions
1. Let J (x[k]) be the minimum cost of transfer a state x[k] to some nal state x[2]. Then,
J (x[2]) = 0,
and
J (x[1]) = min 2x[1]2 + u[1]2 + J (x[2]) = min 2x[1]2 + u[1]2 .
u[1]
u(1)
There are no constraints on u[1]. Th
ECE 680
Fall 2015
Test #1
Solutions
1. (15 pts) Find the equilibrium pairs (xe , ue ) corresponding to ue = 2 for the following
nonlinear model,
x
2 x1 x2 1
1 =
+
u,
x2
4 + x2
x2
1
y = x2 + x2 .
1
Setting x1 = x2 = 0 and substituting u = 2, we obtain t
ECE 680
Fall 2011
Test #2
Solutions
1. Use Dynamic Programming to nd u(0) and u(1) that minimize
1
J = (x(2) 1)2 + 2
u2 (k)
k=0
subject to
x(k + 1) = bu(k),
where b = 0.
3
Let J (x(k) be the minimum cost of transfer a state x(k) to some nal state x(2).
Th
ECE 680
Fall 2011
Test #1
Solutions
1. (10 pts) Consider the following model of a nonlinear dynamical system,
x
2 x1 x2 u
1 =
.
x2
4 + x2 + x2 u
1
(4 pts) Find the equilibrium states corresponding to ue = 0.
(6 pts) Find the corresponding linearized m
ECE 680
Fall 2011
Test #2
November 17
Name:
SID #:
Problem Weight Score
1
15
2
15
3
15
4
15
5
10
6
15
7
15
Total
100
Closed books, closed notes, no crib-sheets, no calculators.
Last lecture or tape to be viewed before the exam is lecture #23 of November
ECE 680
Fall 2011
Test #1
October 6
Name:
SID #:
Problem Weight Score
1
15
2
10
3
15
4
10
5
10
6
15
7
10
8
15
Total
100
Closed books, closed notes, no crib-sheets.
No calculators.
Last lecture or tape to be viewed before the exam is lecture #12 of Sept
ECE 680
Fall 2011
Final Exam
Solutions
1. (20 pts) For the matrix
2 + j3
0
0
A= 0
2 j3 0 ,
0
0
5
(i) (10 pts) nd a transformation that transforms A into a modal form, and
(ii) (10 pts) transform A into its modal form.
(i) The matrix A is already in a diag
Optimal Control of a
Double Inverted Pendulum on a Cart
Alexander Bogdanov
Department of Computer Science & Electrical Engineering,
OGI School of Science & Engineering, OHSU
Technical Report CSE-04-006
December 2004
In this report a number of algorithms
so ChapterZ MATLAB® Environment
Figure 2.15
The results of on M—file
execution print into the
command window. The
variables created ore
reflected in the workspace
and the M-tile is listed in
the current folder window.
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the M—file are
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6 .6 Animation
6.6 Animation
We all know the visual impact of animation. If you have a lot of data representing
a function or a system at seve
ECE 680
Fall 2015
FunWork #1
Due on September 16
Consider the double inverted pendulum on a cart (DIPC) shown in Figure 1. Derive a
state-space model of this system. The state variables are dened as, x1 = x, x2 = 1 ,
x3 = 2 , x4 = x, x5 = 1 , and x6 = 2
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ECE 680
Fall 2003
Funwork Set #3
Due on October 23, 2003
(1) Consider the ground vehicle model described by equation (1.54) in Subsection 1.7.2 of
the text. Let the input signal be u = f the front wheel steer angle, and r = 0. Select
an appropriate input
1
Duality: dual linear programs
()
March 15, 2007
1 / 37
1
Duality: dual linear programs
2
Upper/Lower bounds for linear programming problems: Example
()
March 15, 2007
1 / 37
1
Duality: dual linear programs
2
Upper/Lower bounds for linear programming pro
Patrick McCormick
ECE680 Funwork 5
Fall 2011
Select two or three operating points and construct linear models using the
method of Section 8.5.2. Then, construct a TSK model. Use the local models
or the TSK model as a basis for your MPC design.
The operati
1
How to find a start solution for the simplex method
()
March 15, 2007
1 / 14
1
How to find a start solution for the simplex method
2
What to do if it is not easy to find a start solution: 2-phase method
()
March 15, 2007
1 / 14
1
How to find a start sol
Proceedings of the 4th International Symposium on Communications,
Control and Signal Processing, ISCCSP 2010, Limassol, Cyprus, 3-5 March 2010
Optimal Control Systems with Prescribed Eigenvalues
Vladimir Kucera, Fellow, IEEE and lifi Cigler
Abstract- The