The primary objective of many control systems is to

Question

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.