The block diagram given below represents a discrete-time closed-loop control system. The output of each delay...

 

   

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The block diagram given below represents a discrete-time closed-loop control system. The output of each delay element (indicated by z') is assigned a state variable. r(k) y(k) 2-1 -1.1 X₂(k) -0.3 X₁(k) a) Name the input of each delay element in terms of the state variable assigned to it and relate it with the other signals of the system b) Determine the state equations in the form x(k+1) = A x(k) + B r(k) and the output y(k)= Cx(k) + Dr(k) c) Find the transfer function G(z) = Y(z) / R(z) of this SISO system The block diagram given below represents a discrete-time closed-loop control system. The output of each delay element (indicated by z') is assigned a state variable. r(k) y(k) 2-1 -1.1 X₂(k) -0.3 X₁(k) a) Name the input of each delay element in terms of the state variable assigned to it and relate it with the other signals of the system b) Determine the state equations in the form x(k+1) = A x(k) + B r(k) and the output y(k)= Cx(k) + Dr(k) c) Find the transfer function G(z) = Y(z) / R(z) of this SISO system