Question

Consider a two-tank system, where x, is the level of the first tank, and x2 is the level of the second tank. This dynamic system is described by the -xj-x2. The output to be Q4. following model: dt controlled is the level of the second tank. (a)Write down the state-space model in matrix form. Verify the 20% (b)Design a state feedback controller so that the closed-loop poles are 25% controllability of the system located at -3 and -4 (c) The block diagram of the closed-loop control system is depicted in Fig.Q4, where r is the reference input signal (i)Following the state feedback controller design in (b), what are the numerical values of P and Q in Fig. Q4? write down the transfer function from the reference input to the output. (ii) 30% (d) Compute the steady-state value of the error signal, e= r-y, for unit step input r. Discuss the tracking performance of this state feedback control svstem 25% 12 s +1 S+1 Fig. Q4. State feedback control diagram for the two-tank system in Question 4

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