Q4. Homework 6

Q.4. Consider the linear system as given below: 0 -3 i =-+1 u y = [-2 1]x (a) Determine if the system is observable? (b) Revisit Q.4. of HW6 to recall the control system pole placement specification. Design a full state estimator having poles 2 times faster than the closed-loop poles of state-feedback control. Write down the closed-loop state-space equation combining the controlled plant and the full-state estimator. Show that the eigenvalue of the combined system is the same as the poles of the controlled system plus the poles of the estimator. Q.4. Consider the linear system as given below: 0 * = 4x+014 = u y=[-2 1]x (a) Determine if the system is controllable? (b) Design a state feedback controller to place the closed loop poles at [-1,-3] by direct computation. (c) Repeat (b) using companion form. (d) Repeat (b) using Ackerman formula (see lecture notes for the same). Q.4. Consider the linear system as given below: 0 -3 i =-+1 u y = [-2 1]x (a) Determine if the system is observable? (b) Revisit Q.4. of HW6 to recall the control system pole placement specification. Design a full state estimator having poles 2 times faster than the closed-loop poles of state-feedback control. Write down the closed-loop state-space equation combining the controlled plant and the full-state estimator. Show that the eigenvalue of the combined system is the same as the poles of the controlled system plus the poles of the estimator. Q.4. Consider the linear system as given below: 0 * = 4x+014 = u y=[-2 1]x (a) Determine if the system is controllable? (b) Design a state feedback controller to place the closed loop poles at [-1,-3] by direct computation. (c) Repeat (b) using companion form. (d) Repeat (b) using Ackerman formula (see lecture notes for the same)