•The derivative partof the controller responds to the rate of change of the error.•In the real industrial controller, R is a potentiometerso that the derivative time constant can be varied.•When the derivative time constant is high(high R), the derivative part of the control is more effective. It introduces a large overcorrection when a rapid change in error occurs.•When the derivative time constant is small(low R), the derivative part of the control is less effective. It introduces only a small overcorrection due to rapid change in error.•The reference variable which is commonly used when dealing with derivative control is rate time, which is the amount of time allowed for the measured variable to change through the full controller range, if it is to drive the final correcting device through its full range adjustment, assuming a 100% proportional band.•Proportional plus derivativecontrol is seldom used in industrial temperature control, but is popular in industrial servo control systems.

Proportional Plus Integral Plus Derivative Control•In some processes, proportional plus integral plus derivative controlis needed because they have very difficult control problems which cannot be handledby proportional plus integral control, such as:–Very rapid load changes–Long time lagbetween applying the corrective action and the appearance of the results of that corrective action in the measurement.•The derivative controlis also called rate control.•In proportional plus integral plus derivative control, the corrective action is determined by three things.– The magnitude of the error: This is the proportional part.– The time integral of the error, or the magnitude of the error multiplied by the time that it has persisted: This is the integral part.– The time rate of change of error: A rapidly changing error causes a greater corrective action than a slowly changing error. This is the derivative part.•The derivative partof the controller attempts to “look ahead”and foresee the process is in for a bigger changethan might be expected based on the present measurements.

Proportional Plus Integral Plus Derivative Control•Below is a diagram of a system which uses proportional plus integral plus derivative control.Prop.Band AdjustValve PositionPot0%open50%open100%openIncreasing Valve OpeningErrorPot.PositiveErrorNegativeErrorSet-Point SpringIncreasing TemperatureFuelVariable Position Control ValveProcessTemperatureSensingBulbMotorElectronicAmplifierBellowsIncreasing TemperatureRderCderRintCintIncreasing ResetRateIncreasing RateTime

Proportional Plus Integral Plus Derivative Control•Proportional plus integral plus derivativecontroller is often called PID controller.

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