Consider the thermal stress chamber depicted in Fig. P4.3-9. Let T = 0.6 s . Ignore the disturbance input d(t) for this problem.

(a) Find the system transfer function C(z) E(z) .

(b) Draw a discrete simulation diagram, using the results of part (a), and give the state equations for this diagram.

(c) Draw a continuous-time simulation diagram for the plant, and give the state equations for this diagram.

(d) Use the state-variable model of part (c) to find a discrete state model for the system. The states of the discrete systems are the same as those of the continuous-time system.

(e) Draw a simulation diagram for the discrete state model in part (d).

(f) Use Mason’s gain formula to find the transfer function in part (e), which must be the same as that found in part (a).

Fig. P4.3-9

Transcribed Image Text:

E(s) e(t) T 1-e-T's S D(s) d(t) Voltage M(s) m(t) Chamber 2.5 s+0.5 2.5 s+0.5 Sensor 0.04 Temperature (C) c(t)