# Self-Tuning Controllers Auto-Select P, I, D Values

September 1, 1997

Tuning a PID controller is conceptually simple–observe the behavior of the controlled process and fine tune the controller’s proportional (P), integral (I), and derivative (D) parameters until the closed-loop system performs as desired. However, PID tuning is often more of an art than a science. The best choice of tuning parameters depends upon a variety of factors including the dynamic behavior of the controlled process, the controller’s objectives, and the operator’s understanding of the tuning procedures.

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 go about accomplishing those tasks in the same way.

‘Heuristic’ self-tuners, for example, attempt to duplicate the decision-making process of an experienced operator. They adjust their 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.’

Model-based approach
A more common approach to automatic parameter selection, however, involves a mathematical ‘model’ of the process–an equation that relates the present value of the process output to a history of previous outputs and previous 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 gives the current output as a weighted sum of the most recent output and the most recent input. A self-tuner can choose the weights in that sum to fit the model to the observed process behavior. With the model in hand, the self-tuner can go on to 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 will then set the P, I, and D parameters to relatively high values.

Variations on the theme
Exactly how high or low the tuning parameters should be set 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 in order to observe how it behaves. Others make do with data collected during normal loop operations. The latter approach limits the waste and inconvenience caused by intentionally disturbing the process, but generally produces much less useful information about the process’ behavior.

Which of these many variations is appropriate for a given application of self-tuning control is up to the operator. A single universally applicable technique has yet to be developed.