P9.13 A controller is used to regulate the temperature of a mold for plastic part fabrication, as shown in Figure P9.13. The value of the delay time is estimated as 1.2 s.

(a) Using the Nyquist criterion, determine the sta

bility of the system for K K a = = 1.

(b) Determine a suitable value for Ka for a stable system that will yield a phase margin P M. . ≥ 50° when K = 1. 

FIGURE P9.13 Temperature controller. R(s) Desired temperature Controller K (K + ) Heating dynamics Y(s) Temperature