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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...
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