Process Instrumentation and Control step by step plz A conti

Process Instrumentation and Control step by step plz

A continuous time system is sampled at a sampling frequency of 10 Hz (T = 0.1 s). The resulting discrete time system in state space representation is: X_k+1 = [.9 0.2 0 0.5]x_k + [0 0.1]u_k y_k = [1 1]x_k A. What is the original continuous time system? I.e what are the a, b, C, D matrices of the original continuous time system? B. Take the Z transform of the state space equation and find the system transfer function T(z) = Y(z)/U(z) (assume all zero initial conditions). C. For a unit step input find the output y_k, use MATLAB inverse z transform command: iztrans. D. Repeat the above by the method of long division k = 0, 1, 2, 3,4, use MATLAB command: deconv. E. Going back to the state space equations: Draw the system block diagram for Y(z) = T(z)U(z) found in part B above, using gain and delay blocks (i.e. 1/z) plus summing junctions as necessary. Label the state variables on the block diagram.

Solution

A) A = 9 B=0.2 C=0 D= 0.5

it is originnal continous form

B) Z transform = 1/1- 2z^-1

C) Yk = C (SI-A)^-1 B