The Derivative Term is not only the last letter in PID (i.e. Proportional-Integral-Derivative) it’s also the most maligned of the three. With its big kick, the Proportional Term provides an immediate correction for changes in control and it is clearly the star of the PID controller. So too, the Integral Term is credited with its tenacious correction of Offset and for steadily pushing a loop back to Set Point. And then there’s Door #3: The lowly Derivative Term. Derivative works to counteract the rate of change of the process variable.
Practitioners are generally correct in their assessment of Derivative and they avoid its use in industrial applications for good reason. Specifically, Derivative can be a hindrance more often than it can help. That may have less to do with how it functions and more to do with the applications on which it’s applied. We’re no longer in the age of pneumatic controllers, and the digital era presents some unique challenges for applications of Derivative. Consider the following:
- Derivative was introduced react to the rate of change of Error. In its effort to eliminate Offset the Integral Term does an admirable job, but often it results in oscillations due to overshoot and it frequently requires excessive settling time. Indeed, the Derivative Term has its greatest influence when a Process Variable is rapidly changing in connection to the oscillatory nature of the Integral response.
- We live in a digital age and process data is subject to quite a bit of noise. One thing about the Derivative Term is that it responds poorly when applied in noisy conditions. Random error in a process signal results in seemingly constant, sharp changes in the Process Variable’s (PV) direction. With each reversal the corresponding slope calculation approaches Infinity and that produces a derivative result that can be excessively volatile.
- Derivative is designed to react to the rate of change of the process variable. In its most common application, temperature control, derivative is used to fight the inertia that the temperature controller builds up. For example, as you increase the heat to a furnace, the temperature will naturally start to rise. If you quickly stop adding heat, the temperature will continue to rise for a short time before settling out. Without Derivative, the proportional and integrating terms will generally apply too much correction, and not pull back quick enough, which causes overshoot. The Derivative term pulls back a little quicker, since derivative is concerned with limiting rate of change, not with getting to set-point.
Don’t mistake the thrust of this post. There is a wide array of industrial applications where the use of Derivative is not only good – it’s ideal. Those are typically processes that limited noise and that have a large Time Constant. Think of temperature control processes that involve significant mass or pH control. In those applications Derivative can be used to counteract the inertia of the process without introducing either volatility or harming the associated process instrumentation.
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