For the temperature control system of Problem 7.5-3 and Fig. P7.5-3, let K = 1 .

(a) Determine the stability of the system.

(b) Plot the Bode diagram, and the Nyquist diagram.

(c) If the system is stable, determine the gain and phase margins. If the system is unstable, find the value of K that gives a phase margin of 45° .

(d) From the Nyquist diagram, determine the value of K >0 for which the system is marginally stable.

(e) Find the frequency ω at which the marginally stable system will oscillate.

Problem 7.5-3

Problem 1.6-1

A thermal test chamber is illustrated in Fig. P1.6-1(a). This chamber, which is a large room, is used to test
large devices under various thermal stresses. The chamber is heated with steam, which is controlled by an
electrically activated valve. The temperature of the chamber is measured by a sensor based on a thermistor,
which is a semiconductor resistor whose resistance varies with temperature. Opening the door into the
chamber affects the chamber temperature and thus must be considered as a disturbance.

Transcribed Image Text:

= Consider the temperature control system of Fig. P7.5-3. This system is described in Problem 1.6-1. For this problem, ignore the disturbance input, let T = 0.6 s, and let the digital controller be a variable gain K such that D(z) = K. Hence m(kT) = Ke(kT), where e(t) is the input to the sampler. It was shown in Problem 6.2-4 that 1 S -Ts 2 s + 0.5 = 1.037 z - 0.7408 (a) Write the closed-loop system characteristic equation. (b) Use the Routh-Hurwitz criterion to determine the range of K for stability. (c) Check the results of part (b) using the Jury test. (d) Let T = 0.06 s. Find the range of K for which the system is stable.