Image Processing Reference
In-Depth Information
Mean square error between estimated and
measured TRCs (w/testing data)
1.2
1
0.8
Equal-space set
Optimal set
0.6
0.4
0.2
0
2
3
4 5
Number of gray level strips
6
7
8
FIGURE 9.54
Mean-square error from the two gray-level selection methods for 2, 4, and 8
patches.
PROBLEMS
9.1
Let the state-space equations for the level 1 electrostatic system be
x
(
k
) þ
v
(
k
)
10
01
0
:
9798
0
x
(
k
þ
1
) ¼
0
:
4574
14
:
9315
x
(
k
)
10
01
y
(
k
) ¼
Use the control law shown in Equation 9.26 with the feedback gain matrix given
.
0
:
8165
0
as K
¼
0
:
025
0
:
0469
100]
T
a. Show the evolution of
the states for x
d
¼
[
550
and x(0)
¼
87]
T
with respect to 10 pitch numbers.
b. Show that the steady-state error is held to zero, even when one of the elements
of the Jacobian matrix, say b
22
, is lowered by 20%.
c. Calculate the steady-state values of the actuator vector, v(k), for (a)
and (b).
[
588
9.2
Determine the controllability and observability matrices and then ranks for
Problem 9.1. What are the eigenvalues of the open-loop system with and
without the integrator in the loop? Is the system open loop stable in both
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