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Before presenting tuning rules, some discussion of the effect of each mode in a PID controller on the transient response of a controlled process will be instructive.
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Consider a typical loop as shown in Fig. 19.1 in which the process is second-order and the measuring element is a transport lag. (The transfer function of the valve is taken as 1.) Load responses for this process for four types of controllers (P, PD, PI, PID) are shown in Fig. 19.2. For each response curve, the process was subjected to a unit-step change in load (U = l/s) and the controller parameters were selected by tuning rules to be presented later. Regardless of the specific tuning rules used, the responses shown in Fig. 19.2 are typical of well-tuned controllers for systems found in industry. The nature of the response for each type controller will now be described. (The reader should also refer to Figs. 10.7 and 17.14 to reinforce this discussion.)
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PROPORTIONAL CONTROL. As shown in Fig. 19.2, proportional control produces an overshoot followed by an oscillatory response, which levels out at a value that does not equal the set point; this ultimate displacement from the set point is the offset. PROPORTIONAL-DERIVATIVE CONTROL. For this case the response exhibits a
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smaller overshoot and a smaller period of oscillation compared to the response for proportional control. The offset that still remains is less than that for proportional control.
PROPORTIONAL-INTEGRAL CONTROL. In this case, the response has about
the same overshoot as proportional control, but the period is larger; however, the response returns to the set point (offset = 0) after a relatively long settling time. The most beneficial influence of the integral action in the controller is the elimination of offset.
ems .
FIGURE 19-1 @pical control system used to study the effect of controller modes on load responses shown in Fig. 19.2.
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FIGURE 19-2 Load response of a typical contml system using various modes of control (process shown in Fig. 19.1).
PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROL. As one might expect,
the use of PID control combines the beneficial features of PD and PI control. The response has lower overshoot and returns to the set point more quickly than the responses for the other types of controllers. From the nature of the responses just described, we can make the following generalizations. Integral action, which is present in PI and PID controllers, eliminates offset. The addition of derivative action speeds up the response by contributing to the controller output a component of the signal that is proportional to the rate of change of the process variable. For simple, low-order (first or second-order) processes that can tolerate some offset, P or PD control is satisfactory. For processes that cannot tolerate offset and are of low order, PI control is required. For processes that are of high-order (those with transport lag or many first-order lags in series), PID control is needed to prevent large overshoot and long settling time. Before the availability of microprocessor-based controllers, it was customary to select a controller based on price. Pneumatic and electronic controllers with proportional action were the least expensive and those with PID action were the most expensive. It was considered uneconomical to purchase a controller with more control actions than needed by the process. Today this price incentive no longer exists in the selection of the type of controller, for the modern microprocessorbased controller comes with all three actions, as well as other functions such as lead-lag and transport lag. A discussion of the features of modem controllers will be given in Chap. 35. There is probably little justification to select a P or PD controller for most processes. The PI controller is often the choice because it eliminates offset and requires only two parameter adjustments. Ruring a PID controller is more difficult because three parameters must be adjusted. The presence of derivative action can also cause the controller output to be very jittery if there is much noise in the signals. We now turn our attention to some of the criteria for good control that are used to judge whether or not a control system is well tuned.
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