Problem: A system is described by: , +3 y- y2 = u1 2 + 2 (, + z- z) + 4 (Y2 - y) = 12+5 u1 z + 6 z - 2, + Y3 = uz Using Mathematica Software find (a) (10p) Obtain the state space equations and the corresponding matrices A, B, C, and D. (b) (10p) Design a state feedback controller which will give closed-loop poles at I = (-3, -4,-4.-5.-51 (c) (10p) Simulate the output of the state feedback closed-loop system to unit step inputs and zero initial state, (d) (10p) Design an output feedback controller which will give as many closed-loop poles from the set I. (e) (10p) Simulate the output of the output feedback closed-loop system to unit step inputs and zero initial state Notes: Show all your relevant work. Solution Problem: A system is described by: , +3 y- y2 = u1 2 + 2 (, + z- z) + 4 (Y2 - y) = 12+5 u1 z + 6 z - 2, + Y3 = uz Using Mathematica Software find (a) (10p) Obtain the state space equations and the corresponding matrices A, B, C, and D. (b) (10p) Design a state feedback controller which will give closed-loop poles at I = (-3, -4,-4.-5.-51 (c) (10p) Simulate the output of the state feedback closed-loop system to unit step inputs and zero initial state, (d) (10p) Design an output feedback controller which will give as many closed-loop poles from the set I. (e) (10p) Simulate the output of the output feedback closed-loop system to unit step inputs and zero initial state Notes: Show all your relevant work. Solution