Consider the temperature control system of Fig. P7.5-3. This system is described in Problem 1.6-1. For this

Question:

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 20 1 - 8-Ts S 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. R(s) T Controller D(z) Volts Disturbance R(S) -E-Ts S M(s) Volts 1 Chamber 2.5 $+0.5 2 $+0.5 Sensor 0.04 C(s)