The primary objective of many control systems

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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.

Reference no: EM131127809

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