subject: modern control

Consider the state linear system described by the state space equations with the following matrices: 0 1 0 0 A= 0 0 0 -2 1 0 0 0 0 1 -1 0 0 0 0 0 0 -1 1 0 0 -2 1 1 0 0 1 1 1 -2 B [1 0 0 0 0 C = 0 1 0 0 0 Lo 0 1 0 0 0] 0 0] D-10 1 -2 1 1 a) (20p) Design an output feedback system that would provide a closed-loop system with bounded outputs (to stabilize the system); form the closed-loop state equations. b) (20p) Simulate the response of the output feedback closed-loop system for zero desired input, starting at rest, with the initial position of the masses at -1 m, 1 m, 0 m respectively. Plot all states and the outputs of the system for the first 30 seconds. Comment on the performance of the system compared to open-loop response. Consider the state linear system described by the state space equations with the following matrices: 0 1 0 0 A= 0 0 0 -2 1 0 0 0 0 1 -1 0 0 0 0 0 0 -1 1 0 0 -2 1 1 0 0 1 1 1 -2 B [1 0 0 0 0 C = 0 1 0 0 0 Lo 0 1 0 0 0] 0 0] D-10 1 -2 1 1 a) (20p) Design an output feedback system that would provide a closed-loop system with bounded outputs (to stabilize the system); form the closed-loop state equations. b) (20p) Simulate the response of the output feedback closed-loop system for zero desired input, starting at rest, with the initial position of the masses at -1 m, 1 m, 0 m respectively. Plot all states and the outputs of the system for the first 30 seconds. Comment on the performance of the system compared to open-loop response