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a | Lecture Chemical process control - Chapter 11 Dynamic Behavior of Closed-Loop Control Systems Chapter 11 Chapter 11 Next, we develop a transfer function for each of the five elements in the feedback control loop. For the sake of simplicity, flow rate w1 is assumed to be constant, and the system is initially operating at the nominal steady rate. Process Chapter 11 In section 4.1 the approximate dynamic model of a stirredtank blending system was developed: K1 K2 X ( s) = X1 ( s ) + W2 ( s ) (111) τs + 1 τs + 1 where Vρ w1 1− x τ= , K1 = , and K2 = (112) w w w Chapter 11 The symbol denotes the internal setpoint composition expressed as an equivalent electrical current signal. is related to the actual composition set point by the composition sensortransmitter gain Km: Chapter 11 (117) CurrenttoPressure (I/P) Transducer The transducer transfer function merely consists of a steadystate gain KIP: Pt ( s ) Chapter 11 = K IP (119) P ( s) Control Valve As discussed in Section 9.2, control valves are usually designed so that the flow rate through the valve is a nearly linear function of the signal to the valve actuator. Therefore, a firstorder transfer function is an adequate model W2 ( s ) Kv = (1110) Pt ( s ) τv s + 1 Composition SensorTransmitter (Analyzer) We assume that the dynamic behavior of the composition sensor transmitter can be approximated by a firstorder transfer function, but τm is small so it can be neglected. Xm ( s) = Km Chapter 11 Controller X ( s) Suppose that an electronic proportional plus integral controller is used. P ( s) 1 = Kc 1 + (114) E ( s) τI s P ( s) where and E(s) are the Laplace transforms of the controller p ( t) output and the error signal e(t). Kc is dimensionless. Chapter 11 1. Summer 2. Comparator Chapter 11 3. Block Y(s) .
