system defined by: X2 x = x3 + x₂x3 + x² -5x₁-5.8x2 + x₁x₂] J + [9] y = [1 0 0]x a) Find the equilibrium point(s) of the

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System Defined By X2 X X3 X X3 X 5x 5 8x2 X X J 9 Y 1 0 0 X A Find The Equilibrium Point S Of The 1 (42.1 KiB) Viewed 158 times

system defined by: X2 x = x3 + x₂x3 + x² -5x₁-5.8x2 + x₁x₂] J + [9] y = [1 0 0]x a) Find the equilibrium point(s) of the system, assume ueq=-1. b) Linearize the system around the equilibrium point(s) c) Design a full-order state observer with desired eigenvalues of (-14, -14, -16) d) Simulate the observer designed in part (c) using MATLAB and plot the actual and the estimated states on the same graph assuming x (0) = [3 0 -1]" and (0) = [00 oj e) Design a state feedback u=-K & such that the closed-loop eigenvalues are placed at (-2,-4, -5} f) Simulate using Matlab/SIMULINK the overall closed-loop system of the controller and observer designed in c) and e). g) Design an LQR controller using Matlab such that the following objective function is minimized J = f y² + u² dt Plot the output and the control signal.