# PID loop tuning parameters and control fundamentals

## It is important to understand what proportional-integral-derivative (PID) control is and the parameters for closed-loop, open-loop and cascading loops and the parameters involved.

March 28, 2023
Non-integrating process model. Courtesy: ControlSoft, Inc.

#### Learning Objectives

• Understand the fundamentals of proportional-integral-derivative (PID) tuning and what each element is used for.
• Learn how to set PID tuning parameters.
• Know the difference between closed-loop and open-loop tuning procedures and where they are best-suited.

## PID loop tuning insights

• Proportional-integral-derivative (PID) control is based on feedback with the output of a device or process measured and compared with the set point. This is a constant calculating process.
• PID loop tuning comes in many forms, and it is critical for the engineer to understand which loop tuning is needed for the application as well as the parameters required to help ensure accurate measurements are delivered.

Tuning a control loop is a complex activity driven by relatively simple control laws. The objective is to orchestrate one or more of the parameters to yield a process that is stable within specified boundaries. This guide is a primer on the process of tuning a proportional-integral-derivative (PID) control loop.

### What is PID control?

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

Not every controller uses all three of the mathematical functions in PID. Many processes can be handled to an acceptable level with just the proportional-integral terms. However, fine control, and especially overshoot avoidance, requires the addition of derivative control.

In proportional control, the correction factor is determined by the size of the difference between the set point and the measured value. The problem is that as the difference approaches zero, so too does the correction, with the result that the error never goes to zero.

The integral function addresses this problem by considering the cumulative value of the error. The longer the set point-to-actual value difference persists, the greater the correction factor calculated. However, when there is a delay in the response to the correction, this leads to an overshoot and possibly oscillation about the set point.

Avoiding this outcome is the purpose of the derivative function, which looks at the rate of change being achieved, progressively modifying the correction factor to lessen its effect as the set point is approached.

### Setting PID tuning parameters

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

It may be beneficial to assign the processes to four broad groups:

### Closed-loop tuning procedure

The first step of tuning a closed loop is to understand the process. Identify the loop that needs tuning and determine the speed of the loop. If the loop has a response time from less than one second to about 10 seconds, the loop is fast, and using a PI controller should be sufficient. If the loop has a response time of several seconds up to about 30 seconds,  choose a PI or PID controller. For slow loops with a response time of more than 30 seconds, using a PID controller is recommended.

The second step is to understand the controller. The proportional term could be either a proportional gain or a proportional band. The integral term can be a time constant, a reset rate, or an integral gain (reset rate times proportional gain). The derivative term can be a time constant or a derivative gain (derivative time constant times proportional gain). For this tutorial, proportional gain, integral reset rate, and derivative gain are assumed.

The final step is to watch for a response. Begin by making a small change of set point (less than 5%) or wait for a disturbance in the process. Then watch the process variable and control output response.

### Open-loop tuning procedure

Similar to the closed-loop procedure, begin by knowing the process and controller. For non-integrating loops, use the following process:

• Put the loop in manual control mode, keep the control output constant, and wait for the process to stabilize.
• Make a small step change on the control output (less than 10%) and watch the response.
• Estimate the process model where:
• Model gain is equal to the process variable divided by the control output change.
• Deadtime is equal to the time lapse between the change of the control output and observable changes on the process variable.
• Time constant is equal to the time it takes for the process variable to reach about 63% of the total changes.
• Select the initial PID values such that:
• P equals 2 divided by the model gain.
• I equals deadtime plus the time constant.
• D equals either deadtime divided by 3 or time constant divided by 6.
• These initial PID values should provide a reasonable closed-loop response. Fine-tune the controller by using the closed-loop tuning method.

For cascaded control applications, such as a tank heated by a steam valve, the tuning procedure begins with the inner loop followed by the outer loop. You need to tune one loop at a time due to the interaction of the inner loop dynamics on the outer loop.

### Common PID control applications

PID controllers are typically used in automatic process control applications in the industry to regulate flow, temperature, pressure, level and other process variables. Proportional and integral controllers are essential for most control loops; the derivative mode is often used for motion control. Temperature control often uses all three control modes.

Benjamin Langton is senior offer manager at Interstates, a CFE Media and Technology content partner. Edited by Chris Vavra, web content manager, Control Engineering, CFE Media and Technology, cvavra@cfemedia.com.

Adapted with permission of ControlSoft, Inc. PID Loop Tuning Pocket Guide. Highland Heights, OH: ControlSoft, Inc., 2022. 6-9.