In this problem we consider the effects of the disturbance input in Fig. P8.4-3.

(a) Suppose that the disturbance input is a unit step, which models the door to the chamber remaining open. Find the steady-state error in the temperature $c(t)$ for the uncompensated system in Problem 8.4-3.

(b) Repeat part (a) for the phase-lag compensated system in Problem 8.4-3(e).
(c) Repeat part (a) for the PI-compensated system in Problem 8.10-5.

Problem 8.4-3

Shown in Fig. P8.4-3 is the block diagram of the temperature control system described in Problem 1.6-1.
For this problem, ignore the disturbance input. In Fig. P8.4-3 the sensor gain of H = 0.04 has been shifted
into the forward path to yield a unity feedback system. The stability characteristics are unchanged, since
the loop transfer function has not changed. Note that c(t) is the chamber temperature in degrees Celsius. It
is shown in Problem 6.2-4 that with T = 0.6, the function G(z)H is given by

Transcribed Image Text:

R(s) +. E(s) T H D(z) Disturbance Rd(s) 1-8-75 S FIGURE P8.4-3 Modified temperature control system. 2 s+0.5 Gp(s) 2 s+0.5 C(s) H 0.04 C(s)