Transcribed Text
For a nanopositioning system, the state space model is given as
x(t) = Ax(t) + Bu(t)
y(t) = Cx(t) + Du(t)
where
-4790.982
260.409
-3933.738
17042.514
4672.442
26578.402
-10.959
-2229.497
-25471.236
16750.235
-3213.078
19748.549
-230.720
22832.225
-3706.695
2607.289
11798.873
4208.786
A
665.066
-5370.194
1453.685
-10826.167
-53263.219
-11997.418
216.400
514.573
317.544
-203.013
-3213.385
-76935.464
19.945
-287.670
1006.765
-658.835
339.566
-3698.415
T
B = -6424.444
3342.568
-781.593
267.667
275.787
- -103.631
C
=
-0.357
-
-1.996
0.250
-0.803
- -5.779
-43.225]
D
=
[0]
Design an MPC (e.g., steady state MPC) for this system, and verify the performance of your
controller using 30Hz triangle signals and 80Hz sinusoidal signals as the reference trajectories
the nanopositioner needs to track. Plot the reference and system output y(t) in the sample
figure, and also plot the tracking error (r(t)-y(t)) in a separate figure as well.
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load mpc1_controller
A = [[-4790.982, 260.409, -3933.738, 17042.514, 4672.442, 26578.402]; ...
[-10.959, -2229.497, -25471.236, 16750.235, -3213.078, 19748.549]; ...
[-230.720, 22832.225...