## Adaptive control technology encompasses a wide range of mathematical and empirical techniques that allow a feedback controller to automatically update not only its next output, but its entire control strategy to accommodate changes in the behavior of the controlled process. Self-tuning controllers capable of adjusting their own proportional (P), integral (I), and derivative (D) parameters wer...

02/01/2004

Adaptive control technology encompasses a wide range of mathematical and empirical techniques that allow a feedback controller to automatically update not only its next output, but its entire control strategy to accommodate changes in the behavior of the controlled process. Self-tuning controllers capable of adjusting their own proportional (P), integral (I), and derivative (D) parameters were among the first adaptive controllers available as commercial products.

Their mission is conceptually simple—observe the behavior of the controlled process and fine tune the P, I, and D parameters until the closed-loop system performs as desired. Unfortunately, PID tuning is often more of an art than a science (see "Loop Tuning Fundamentals," Control Engineering , July 2003).

Self-tuning PID controllers simplify matters by executing the necessary tuning procedures automatically. Most observe the process' reaction to a disturbance and set their tuning parameters accordingly. However, no two controllers go about accomplishing those tasks in the same way.

## Techniques vary

Heuristic self-tuners, for example, attempt to duplicate the decision-making process of an experienced operator. They adjust the tuning parameters according to a series of expert tuning rules such as "IF the controller overreacts to an abrupt disturbance, THEN lower the derivative parameter."

A more common approach to automatic parameter selection involves a mathematical model of the process—an equation that relates the current value of the process output to a history of previous outputs as well as the inputs applied by the controller. If the model is accurate, the controller can predict the future effect of its present efforts and tune itself accordingly.

For example, a process that reacts sluggishly to a step input can be modeled with an equation that predicts the next output as a weighted sum of just two measurements—the most recent input and the most recent output. A self-tuner can choose the weights in that sum to mathematically fit the model to match the input/output relationship that the process has demonstrated in the past.

With the model in hand, the self-tuner can then determine how much proportional, integral, and derivative action the process can tolerate. In the case of a sluggish process, the model will show that the controller is free to apply aggressive control efforts. The self-tuner can then set the P, I, and D parameters to relatively high values.

## Performance issues

 The controller observes the error between the setpoint and the process variable to calculate the next control action. The tuner determines the appropriate tuning parameters for the controller by analyzing the recent history of control actions (process inputs) and the resulting values of the process variable (process outputs).

Exactly how high or low the controller decides to set its tuning parameters depends on the performance objectives specified by the operator. If, for example, the settling time is to be limited to some maximum value, the required tuning parameters can be determined by analyzing the time constant and the deadtime of the process model. On the other hand, if excessive overshoot is the operator's principal concern, the controller can be configured to select tuning parameters that will limit the rate of change of the process variable.

Self-tuning controllers also differ in their data collection techniques. Some apply a series of artificial disturbances to the process to observe how it reacts. Others make do with data collected during normal loop operations. The latter approach limits waste and inconvenience caused by intentionally disturbing the process, but generally produces much less useful information about the process' behavior.

Which of these tuning variations is appropriate for a given application depends on how the closed-loop system is required to perform and whether or not the required performance is physically possible.

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