The primary objective of many control systems is to maintain the output variable at the desired or reference condition when the system is subjected to a disturbance [22]. A typical chemical reactor control scheme. The disturbance is represented by U(s), and the chemical process by G3 and G4. The controller is represented by G{ and the valve by G2. The feedback sensor is H(s) and will be assumed to be equal to l .We will assume that G2, G3, and GA are all of the form

where T3, = T4 = 4 s and #3 = K4 = 0.1. The valve constants are K2 = 20 and T2 = 0.5 s. We want to maintain a steady-state error less than 5% of the desired reference position.
(a) When G(s) = K1. find the necessary gain to satisfy the error-constant requirement. For this condition, determine the expected overshoot to a step change in the reference signal r(f).

(c) Estimate the settling time (with a 2% criterion) of the step response of the system for the controller of parts (a) and (b).
(d) The system is expected to be subjected to a step disturbance U(s) - A/s. For simplicity, assume that the desired reference is r(t) = 0 when the system has settled. Determine the response of the system of part (b) to the disturbance.

Ki G(s)