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 $1.2 \mathrm{~s}$. (a) Using the Nyquist criterion, determine the stability of the system for $K_a=K=1$. (b) Determine a suitable value for $K_a$ for a stable system that will yield a phase margin greater than $50^{\circ}$ when $K=1$.