Two- and three-mode controllers

Although the primary functions of proportional, derivative, and reset have already been introduced, many of their features remain to be defined. The discussion will be restricted to the commonly available controllers, i.e.,. proportional-plus-derivative, proportional-plus-reset, and proportional plus reset-plus-derivative. (Reset controllers are rarely used in process work and are not available as standard items from most manufacturers. Derivative by itself is not recognized as a controlling mode.) 

It has been pointed out that perfect derivative action is not available in conventional controllers. Derivative gain is limited to about 10, and the maximum available phase lead is in the vicinity of 45 . In effect, derivative is therefore accompanied by a lag, whose time constant is Ho the value of the derivative time. 

In most controllers, derivative acts on the output. Physically, it is a lag introduced in the feedback path around the controller amplifier. Therefore, if he output of the controller is constant, no derivative action will take place no matter what the controlled variable may be doing. This situation occurs whenever the controller s output has reached one of Its limits. The output of a pneumatic controller, for example, can go as low as zero or as high as 20 psi (the supply pressure), although the range of the control valve-hence the proportional band-is 3 to 15 psi. 

No derivative action will take place, then, until the controlled variable approaches the proportional band as in Fig. 4.2. In the discussion on two-capacity processes, this property placed a limitation on the width of the proportional band required for critical damping. 

In most controllers, derivative action does not distinguish between measurement and set point. The purpose of derivative is to speed the response of the closed loop, but the set point lies outside the loop. The controlled variable cannot change instantaneously, because of the lags inherent in the process. But it is normal to introduce set-point changes instantaneously, which derivative action amplifies into gross output 

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TABLE 4.2 Determination of Optimum Settings for Two- and Three-mode Controllers... 

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