Overcoming the deadtime dilemma

Vance J. VanDoren, consulting editor

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Arguably the trickiest problem to overcome with a feedback controller is process deadtime--the delay between the application of a control effort and its first effect on the process variable. During that interval, the process does not respond to the controller's activity at all, and any attempt to manipulate the process variable before the deadtime has elapsed inevitably fails.

Deadtime occurs in many different control applications, generally as a result of material being transported from the site of the actuator to another location where the sensor measures the process variable. Not until the material has reached the sensor can any changes caused by the actuator be detected. If the controller expects a result any sooner, it will determine that its last control effort had no effect and will continue to apply ever larger corrections until the process variable begins to change in the desired direction. By that time, however, it will be too late. The controller will have already overcompensated for the error that it was trying to correct, perhaps to the point of causing an even larger error in the opposite direction.
The Smith predictor
In 1957, Otto Smith, a Professor at the University of California-Berkeley, determined that this overcompensation problem could be eliminated if the controller could see an immediate response to its efforts. Without actually eliminating deadtime, Smith created a model-based control strategy that allows the controller to predict the future effect of its present efforts and react immediately to those predictions.
Mr. Smith's strategy is shown in the figure below. It consists of an ordinary feedback loop plus an inner loop that introduces two extra terms directly into the feedback path. The first term is an estimate of what the process variable would look like in the absence of any disturbances. It is generated by running the controller output through a process model that intentionally ignores the effects of load disturbances. If the model is otherwise accurate in representing the behavior of the process, its output will be a disturbance-free version of the actual process variable.

The mathematical model used to generate the disturbance-free process variable consists of two elements hooked up in series. The first element represents all of the process behavior not attributable to deadtime. The second element represents nothing but the deadtime. The deadtime-free element is generally implemented as an ordinary differential or difference equation that includes estimates of all the process gains and time constants. The second element of the model is simply a time delay. The signal that goes in to it comes out delayed, but otherwise unchanged.
The second term that Smith's strategy introduces into the feedback path is an estimate of what the process variable would look like without disturbances and deadtime. It is generated by running the controller output through the first element of the process model (the gains and time constants), but not through the time delay element. It thus predicts what the disturbance-free process variable will be once deadtimehas elapsed.
Subtracting the disturbance-free process variable from the actual process variable yields an estimate of the disturbances. By adding this difference to the predicted process variable, Smith's strategy creates a feedback variable that includes the disturbances, but not the deadtime. The deadtime is essentially moved outside of the loop. There is still a delay between the application of the controller's efforts and its first effects on the process variable, but the controller need not wait for the deadtime to elapse before determining what the next control effort should be.

Consulting Editor Vance J. VanDoren, Ph.D., P.E., is president of VanDoren Industries, West Layafette, Ind.