(Solution) - A process including valve and transmitter has the approximate -(2025 Original AI-Free Solution)

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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 (?c = 0.3 mm).
(b) Phase margin 40° (assume ?c = 0.5 mm).
(c) Simulate these two control systems for a unit step change in set point. Which controller provides the better performance?