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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 is shown in Figure P9.17. The disturbance is represented by U(s), and the chemical process by G3 and G4. The controller is represented by G1 and the valve by G2. The feedback sensor is H(s) and will be assumed to be equal to 1. We will assume that G2, G3, and G4 are all of the form
where τ3, = τ4 = 4 s and K3 = K4 = 0.1. The valve constants are K2 = 20 and τ2 = 0.5 s. We want to maintain a steady-state error less than 5% of the desired reference position.
(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.
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