# The Importance of Tuning a PID Controller

Heat treatment processes demonstrate the need for proportional-integral-derivative (PID) control. To guarantee consistent product quality, the temperature within a furnace or oven should be maintained within narrow limits.

Any disturbance, such as when a product is withdrawn or added or a ramp operation is applied, must be handled appropriately. Although simple in concept, the mathematics underpinning PID control are intricate and accomplishing optimal performance involves choosing process-specific values for various interacting parameters.

The process of finding these values is called “tuning”. When tuned optimally, a PID temperature controller reduces deviation from the set point, and reacts to disturbances or set point changes rapidly but with minimum overshoot.

This article discusses ways to tune a PID controller. Even though several controllers provide auto tune capabilities, an understanding of PID tuning techniques will help to achieve optimal performance.

The sections of the article addresses:

• Basics of PID control
• PID tuning methods
• Manual tuning
• Tuning heuristics
• Auto tune
• Common applications of PID controllers
OMEGA Temperature Control Solutions

## What is PID Control?

PID control is based on feedback. The output of a device or process, such as a heater, is measured and compared with the set point or target. If a difference is detected, a correction is calculated and applied. The output is once again measured and any required correction is recalculated.

Temperature and process controllers

All controllers do not use all three of these mathematical operations. Several processes can be performed to an acceptable level with only the proportional-integral terms. However, fine control, and particularly overshoot avoidance, requires the addition of derivative control.

In proportional control, the correction factor is determined by the size of the difference between measured value and set point. The issue with this regard is that as the difference approaches zero, so does the correction, which results in the error never touching zero.

The integral operation addresses this by taking into account the cumulative value of the error. The longer the set point-to-actual value difference persists, the greater the size of correction factor calculated.

However, when there is a delay in response to the correction, this results in an overshoot and perhaps oscillation about the set point. Avoiding this is the purpose behind the derivative function. This focuses on the rate of change being accomplished, progressively altering the correction factor to reduce its effect as the set point is approached.

## How to Set PID Controllers?

Every process has unique characteristics, even when the equipment is essentially identical. Airflow around ovens will differ, ambient temperatures will change fluid viscosity and density, and barometric pressure will alter from hour to hour. The PID settings (mainly the gain applied to the correction factor together with the time used in the derivative and integral calculations, (termed “rate” and “reset”) must be chosen to match these local differences.

In broad terms, there are three methods to determine the optimal combination of these settings: manual tuning, tuning heuristics, and automated techniques.

## How to Tune a PID Controller Manually?

With sufficient information about the process being controlled, it may be possible to measure optimal values of gain, reset, and rate for the PID controller. Often, the process is highly complex, but with some knowledge, particularly about the speed with which it reacts to error corrections, it is possible to realize a rudimentary level of tuning.

Manual tuning is performed by setting the reset time to its highest value and the rate to zero and increasing the gain until the loop oscillates at a steady amplitude. (When the response to an error correction happens fast a larger gain can be used. If the response is slow a moderately small gain is desirable).

Then the gain of the PID controller is set to half of that value and the reset time is adjusted, so it corrects for any offset within an acceptable period. Finally, the rate of the PID loop is increased until overshoot is reduced.

## Tuning Heuristics

Many rules have evolved over the years to answer the question of how to tune a PID loop. Probably the first, and the most widely-known, are the Zeigler-Nichols (ZN) rules.

Initially published in 1942, Zeigler and Nichols illustrated two techniques of tuning a PID controller. A step change is applied to the system and then the resulting response is observed. The first method involves measuring the delay or lag in response and then the time taken to achieve the new output value.

The second technique relies on determining the period of a steady-state oscillation. In both techniques these values are then entered into a table to obtain the values for reset time, gain, and rate for the control system.

ZN is not without problems. In certain applications, it produces a response that is considered too aggressive in terms of oscillation and overshoot. Another disadvantage is that it can be time-consuming in processes that respond only gradually. For these reasons certain control practitioners choose other rules such as Rivera, Morari and Skogestad or Tyreus-Luyben.

## Auto Tune

Most process controllers sold currently add in auto-tuning functions. Operating details vary between manufacturers but all follow rules similar to those explained above. The PID controller essentially “learns” how the process responds to a change or a disturbance in set point, and measures precise PID settings.

In the case of a temperature controller, like OMEGA’s CNi8 series, when “Auto Tune” is chosen the controller triggers an output. By monitoring both the rate and delay with which the change is made, it calculates optimal P, I and D settings, which can then be fine-tuned manually if required. (Note that this controller needs the set point to be a minimum of 10 °C above the existing process value for auto tuning to be performed).

Newer and more advanced PID controllers, such as OMEGA’s Platinum series of temperature and process controllers, integrate fuzzy logic with their auto tune capabilities. This provides a way of handling imprecision and nonlinearity in complex control situations, such as are frequently encountered in process and manufacturing industries, and aids with tuning optimization.

## Common Applications of PID Control

Furnaces and ovens used in industrial heat treatment are needed to realize stable results regardless of how the humidity and mass of material being heated may differ. This makes such equipment suitable for PID control. Pumps used for moving fluids are a similar application, where difference in media properties could alter system outputs unless an effective feedback loop is employed.

Motion control systems also employ a type of PID control. However, as the response is orders of magnitude quicker than the systems illustrated above these require a different form of controller to that mentioned here.

PID control simulator

## Why a PID Controller Is Advantageous?

As correction factors are measured by comparing the output value to the set point, and using gains that reduce oscillation and overshoot while impacting the change as rapidly as possible, PID controllers are used to manage several processes.

A PID tuning technique involves determining proper gain values for the process being controlled. While this can be achieved manually or by using control heuristics, most of the latest controllers offer auto tune capabilities. However, it remains crucial for control professionals to be aware of what happens once the button in pressed.

This information has been sourced, reviewed and adapted from materials provided by OMEGA Engineering Ltd.

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