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Unformatted text preview: 1 Chapter 8 Figure 8.1 Schematic diagram for a stirredtank blending system. Feedback Controllers 2 Chapter 8 Basic Control Modes Next we consider the three basic control modes starting with the simplest mode, proportional control . Proportional Control In feedback control, the objective is to reduce the error signal to zero where ( 29 ( 29 ( 29 (81) sp m e t y t y t = and ( 29 ( 29 ( 29 error signal set point measured value of the controlled variable (or equivalent signal from the sensor/transmitter) sp m e t y t y t = = = 3 Chapter 8 Although Eq. 81 indicates that the set point can be timevarying, in many process control problems it is kept constant for long periods of time. For proportional control, the controller output is proportional to the error signal, ( 29 ( 29 (82) c p t p K e t = + where: ( 29 controller output bias (steadystate) value controller gain (usually dimensionless) c p t p K = = = 4 Chapter 8 5 Chapter 8 The key concepts behind proportional control are the following: 1. The controller gain can be adjusted to make the controller output changes as sensitive as desired to deviations between set point and controlled variable; 2. the sign of K c can be chosed to make the controller output increase (or decrease) as the error signal increases. For proportional controllers, bias can be adjusted, a procedure referred to as manual reset . Some controllers have a proportional band setting instead of a controller gain. The proportional band PB (in %) is defined as p 100% (83) c PB K = 6 Chapter 8 In order to derive the transfer function for an ideal proportional controller (without saturation limits), define a deviation variable as ( 29 p t r ( 29 ( 29 (84) p t p t p r = Then Eq. 82 can be written as ( 29 ( 29 (85) c p t K e t r = The transfer function for proportionalonly control: ( 29 ( 29 (86) c P s K E s r = An inherent disadvantage of proportionalonly control is that a steadystate error occurs after a setpoint change or a sustained disturbance. 7 Chapter 8 Integral Control For integral control action, the controller output depends on the integral of the error signal over time, ( 29 ( 29 1 * * (87) τ t I p t p e t dt = + where , an adjustable parameter referred to as the integral time or reset time, has units of time. τ I Integral control action is widely used because it provides an important practical advantage, the elimination of offset. Consequently, integral control action is normally used in conjunction with proportional control as the proportionalintegral (PI) controller: ( 29 ( 29 ( 29 1 * * (88) τ t c I p t p K e t e t dt = + + & 8 Chapter 8 The corresponding transfer function for the PI controller in Eq. 88 is given by ( 29 ( 29 τ 1 1 1 (89) τ τ I c c I I P s s K K E s s s r + = + = Some commercial controllers are calibrated in terms of (repeats per minute) rather than (minutes, or minutes per repeat)....
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 Spring '09
 Dr.MuhammadAlArfaj
 Kc, controller output

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