A process (including valve and transmitter) has the approximate transfer function. G(s) = 2e–0.2s/(s + 1) with time constant and time delay in minutes. Determine Pt controller settings and the corresponding gain margins by two methods:
(a) Direct synthesis (τc = 0.3 mm).
(b) Phase margin 40° (assume τc = 0.5 mm).
(c) Simulate these two control systems for a unit step change in set point. Which controller provides the better performance?