Control proportional-plus-integral

Derivative action is used occasionally with proportional control alone, but more frequently it is used with proportional plus integral control. 

The transfer function for derivative control is sTd, and the frequency response characteristics are a phase angle of +90° and an amplitude ratio of a)Td. Control stability results from the leading phase angle. 

Proportional plus integral control (also called proportional plus reset) has the transfer function 

The frequency response characteristics are sketched in Fig. 6 at low frequencies. Note that the integral action provides infinite gain at zero frequency. 

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Proportional plus integral control manipulates the solvent flow rate based on the exit solute concentration in the raffinate. Thus G is a function of GO, KC,... 

A proportional plus integral controller is used to control the level in the reflux accumulator of a distillation column by regulating the top product flowrate. At time t = 0, the desired value of the flow controller which is controlling the reflux is increased by 3 x 10-4 m3/s. If the integral action time of the level controller is half the value which would give a critically damped response and the proportional band is 50 per cent, obtain an expression for the resulting change in level. 

In this example of a five stage extraction column with backmixing, proportional plus integral control of the exit raffinate concentration is to be achieved by regulating solvent flowrate. 

A proportional plus integral controller is used to control the level in the reflux accumulator of a distillation column by regulating the top product flowrate. At time t = 0 the desired value of the flow... 

Figure 5. Dynamics for changes in both set points—proportional plus integral control. Key -----, Sand------, MW. Gc = 2(1 + 0.01/s)l f = (2000, 0.5) .

With the exception of derivative action any of these control modes may be used alone in certain applications. Integral and derivative actions are most usually combined with proportional control to give proportional plus integral control (proportional control with automatic reset) proportional plus derivative control or three-mode control, which is proportional plus integral plus derivative. 

Although proportional plus integral controllers follow quite closely the idealized behavior of Eq. (27), most commercially available three-mode... 

The basic operation of the proportional plus integral controller... 

Figure 24.6. The proportional-plus-integral controller. Integral action is accomplished by the series capacitor C in the feedback loop. The presence of offset causes this capacitor to charge at a rate that depends on RtC, where R, is the reset resistor. This forces the output to change in such a manner as to drive the offset to zero at a rate determined by the adjustment of the reset resistor. Courtesy of the Foxboro Company.

Proportional-plus-integral control is the most generally useful control mode and therefore the one usually applied to automated process-control. Its major limitation is in processes with large dead-time and capacitance if reset time is faster than process dead-time, the controller-response changes are faster than the process, and cycling results. In these cases, derivative control is beneficial. 

Several control design strategies may be appropriate for the control of air and oxygen flow delivery valves. A simple controller is the proportional plus integral controller that can be readily implemented in a microprocessor. For example, the controller for the air valve has the following form ... 

The therapist entry for pressure-controlled ventilation is shown in Figure 18.8 (lower left-hand side). In contrast to the volume-controlled ventilation, where Qj(t) was computed directly from operators entry (Equations 18.1 through 18.3), the total desired flow is generated by the closed-loop airway pressure controller shown in Figure 18.8. This controller uses the therapist-selected inspiratory pressure, respiration rate, and the 1 E ratio to compute the desired inspiratory pressure trajectory. The trajectory serves as the controller reference input. The controller then computes the flow necessary to make the actual airway pressure track the reference input. Assuming a proportional-plus-integral controller, the governing equations are... 

For a microprocessor-based ventilator, the control algorithm for regulating the airway pressure can also be a proportional plus integral controller (Behbehani, 1984 Behbehani and Watanabe, 1986). In this case, the governing equations are identical to Equations 18.9 through 18.11. 

The process temperature is measured in the uncondensed gas as it leaves the chlorine knockout pot or separator. This procedure is more accurate than measurement of the temperature of the liquefied chlorine, which may be subcooled. The tenqierature sensor in Fig. 11.29 is an RTD in a flanged Monel thermowell. The reverse-acting proportional-plus-integral controller adjusts the set point of the refrigeration chiller pressure controller. 

The suction pressure in any case is measured by a d/p cell, as shown in Fig. 11.42, and the proportional-plus-integral controller sends its output to a fail-open globe valve sized to handle the total compressor capacity at 90% of its travel. Compressors are usually a bit oversized, and this provides the additional capacity needed for the steady recycle flow. 

Figure 11.54 shows that the feed header is controlled at a selected pressure so that adjustment of the feed rate to any one electrolyzer does not affect the other flows. The pressure is measured with a Monel or nickel diaphragm seal connected to a pressure transmitter with a capillary system. The fail-open throttling valve is an all PTFE-lined butterfly, controlled by a reverse-acting, proportional-plus-integral controller. Control of the caustic flow to individual electrolyzers is by way of hand valves and local rotameters. This is similar to the arrangement described for brine feed and shown in Fig. 11.11. Again, bipolar systems are amenable to more complete automation.

This should be compared with equation (8.3). It can be shown that for any positive value of Ki, the final response is not offset from the required level. This eliminates the need to have high values of K and a proportional plus integral controller is clearly superior, at least from this standpoint, to one with only proportional control. 

Suppose that an electronic proportional plus integral controller is used. From Chapter 8, the controller transfer function is... 

Figure 4.12 Proportional plus integral controller response to square wave input...

A proportional plus integral controller will give a response period that is longer than a P-only controller but much shorter than an 1-only controller. Typically, the response period of the process variable PV under PI control is approximately 50 per cent longer than for the P-only (1.5th, Figure 4.11). Since this response is much faster than I-only, and only somewhat longer than P-only control, the majority (>90 per cent) of controllers found in plants are PI controllers. The equation for a PI controller is... 

For a step input it is the time required for the output of a proportional-plus-integral controller to change an amount equal to the proportional response alone. 

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