(a) (b) (c) (d) (e) (f) Consider the water tank system shown below. u A A2...

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(a) (b) (c) (d) (e) (f) Consider the water tank system shown below. u A A2 h h R R Tank-1 Tank-2 Figure 3 Establish the state-space representation for the system in the form x=Ax+ Bu,y=Cx where x is a vector of water levels in the tanks, u is the water inlet rate at tank-1, y is the water level of tank-2. The parameters of the tank system are A =1, A2 = 2, R = 3, R = 4 Show that the system is controllable. Derive the transfer function relating water inlet rate at tank-1 and the water level at tank-2. State the characteristic equation; determine the natural frequency, damping factor, and open-loop poles. It is required to bring, using state feedback, the closed-loop poles to -1, -2. Determine the required gain coefficients. Comment on the system responses, original and feedback, with respect to their rise-times. (a) (b) (c) (d) (e) (f) Consider the water tank system shown below. u A A2 h h R R Tank-1 Tank-2 Figure 3 Establish the state-space representation for the system in the form x=Ax+ Bu,y=Cx where x is a vector of water levels in the tanks, u is the water inlet rate at tank-1, y is the water level of tank-2. The parameters of the tank system are A =1, A2 = 2, R = 3, R = 4 Show that the system is controllable. Derive the transfer function relating water inlet rate at tank-1 and the water level at tank-2. State the characteristic equation; determine the natural frequency, damping factor, and open-loop poles. It is required to bring, using state feedback, the closed-loop poles to -1, -2. Determine the required gain coefficients. Comment on the system responses, original and feedback, with respect to their rise-times.