Figure P13.9 gives the simulation diagram of an automatic control system. The plant is t...

Figure P13.9 gives the simulation diagram of an automatic control system. The plant is the system that is controlled and is a discrete model of a continuous-time system. The compensator, a digital filter, is a system added to give the closed-loop system certain specified characteristics. It can be shown that a system of this type is modeled as shown [1].

(a) Write the state equations for the plant only, with the input m[n] and the output y[n].

(b) Give the transfer function H_p(z) for the plant.

(c) Write the difference equation for the plant.

(d) Write the state equations for the compensator only, with the input e[n] and the output m[n].

(e) Give the transfer function H_c(z) for the compensator.

(f) Write the difference equation for the compensator.

(g) Write the state equations for the closed-loop system, with the input u[n] and the output y[n]. Choose as states those of parts (a) and (d).

(h) Give the transfer function H(z) for the closed-loop system.

(i) Use MATLAB to verily the results in part (h).

(j) Write the difference equation for the closed-loop system.