Problem 2 The position of a hard drive head is described by the state space model...

 

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Problem 2 The position of a hard drive head is described by the state space model dx dt = y= (-2.5 0) x + (8) u (01) x a. Determine a state feedback u=-Lx+l,r which places the poles of the closed loop system in s = -4 ± 4i and results in static gain 1 from reference to output. b. Determine a Kalman filter dâ = At+Bu+K(y- Câ) dt for the system. Briefly motivate necessary design choices. Problem 2 The position of a hard drive head is described by the state space model dx dt = y= (-2.5 0) x + (8) u (01) x a. Determine a state feedback u=-Lx+l,r which places the poles of the closed loop system in s = -4 ± 4i and results in static gain 1 from reference to output. b. Determine a Kalman filter dâ = At+Bu+K(y- Câ) dt for the system. Briefly motivate necessary design choices.