How to Tune a PID Controller

Many rules have evolved over the years to address the question of how to tune a PID controller. Probably the first, and certainly the best known, are the Zeigler-Nichols (ZN) rules.

First published in 1942, Zeigler and Nichols described two methods of tuning a PID loop. The first method entails measuring the lag or delay in response and then the time taken to reach the new output value. The second depends on establishing the period of a steady-state oscillation. In both methods these values are then entered into a table to derive values for gain, reset time and rate.

ZN is not without issues. In some applications it produces a response considered too aggressive in terms of overshoot and oscillation. Another drawback is that it can be time-consuming in processes that reacts slowly. For these reasons some control practitioners prefer other rules such as Tyreus-Luyben or Rivera, Morari and Skogestad.

Manual tuning of PID controller is done by setting the reset time to its maximum value and the rate to zero and increasing the gain until the loop oscillates at a constant amplitude. (When the response to an error correction occurs quickly a larger gain can be used. If response is slow a relatively small gain is desirable).

Then set the gain to half of that value and adjust the reset time so it corrects for any offset within an acceptable period. Finally, increase the rate until overshoot is minimized.

Most PID controllers sold today incorporate auto-tuning functions. Operating details vary between manufacturers, but all follow rules where the controller “learns” how the process responds to a disturbance or change in set point and calculates appropriate PID settings.

Newer and more sophisticated PID controllers, such as OMEGA's Platinum series of temperature and process controllers, incorporate fuzzy logic with their auto-tune capabilities. This provides a way of dealing with imprecision and nonlinearity in complex control situations, such as are often encountered in manufacturing and process industries and helps with tuning optimization.

In the case of a temperature controller like OMEGA’s CNi8 series, when "Auto Tune" is selected the controller activates an output. By observing both the delay and rate with which the change is made it calculates optimal P, I and D settings. Manual tuning PID temperature controller allows for fine-tuning if needed. (Note that this controller requires the set point to be at least 10°C above the current process value for auto tuning to be performed).

PID controller gain tuning can be difficult. The proportional method is the easiest to understand. In this instance, the output of the proportional factor is the product of gain and measured error ε. Thus, larger proportional gain or error makes for greater output from the proportional factor. Setting the proportional gain too high causes a controller to repeatedly overshoot the setpoint, leading to oscillation. While setting the proportional gain too low make the loop output negligible. One way to offset this steady-state error is using the Zeigler-Nichols method of setting the I and D gains to zero and then increasing P gain until the loop output starts to oscillate.