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How Do PID Controllers Work: Application & Theory

This article answers the question what is a PID controller, how do PID controllers work and what is the theory behind PID.

What is a PID controller?

A PID (Proportional Integral Derivative) controller is a common instrument used in industrial control applications. A PID controller can be used for regulation of speed, temperature, flow, pressure and other process variables. Field mounted PID controllers can be placed close to the sensor or the control regulation device and be monitored centrally using a SCADA system.

Example: Temperature Control using a Digital PID controller

A typical PID temperature controller application could be to continuously vary a regulator which can alter a process temperature. This may be a pulsed switching device for electrical heaters or by opening and closing a gas valve. A heat only PID temperature controller uses a reverse output action, i.e. more power is applied when the temperature is below the setpoint and less power when above. PID control for injection and extrusion applications often employ additional cooling control outputs and usually require multiple controllers.

A PID controller (sometimes called a three term controller) reads the sensor signal, normally from a thermocouple or RTD, and converts the measurement to engineering units e.g. Degrees C. It then subtracts the measurement from a desired setpoint to determine an error.

The error is acted upon by the three (P, I & D) terms simultaneously:

PID Controller Theory

The following section examines PID controller theory and provides further explanation of the question `how do PID controllers work'.

Proportional (Gain)

The error is multiplied by a negative (for reverse action) proportional constant P, and added to the current output. P represents the band over which a controller's output is proportional to the error of the system. E.g. for a heater, a controller with a proportional band of 10 deg C and a setpoint of 100 deg C would have an output of 100% up to 90 deg C, 50% at 95 Deg C and 10% at 99 deg C. If the temperature overshoots the setpoint value, the heating power would be cut back further. Proportional only control can provide a stable process temperature but there will always be an error between the required setpoint and the actual process temperature.

Integral (Reset)

The error is integrated (averaged) over a period of time, and then multiplied by a constant I, and added to the current control output. I represents the steady state error of the system and will remove setpoint / measured value errors. For many applications Proportional + Integral control will be satisfactory with good stability and at the desired setpoint.

Derivative (Rate)

The rate of change of the error is calculated with respect to time, multiplied by another constant D, and added to the output. The derivative term is used to determine a controller's response to a change or disturbance of the process temperature (e.g. opening an oven door). The larger the derivative term, the more rapidly the controller will respond to changes in the process value.

Tuning of PID Controller Terms

The P, I and D terms need to be "tuned" to suit the dynamics of the process being controlled. Any of the terms described above can cause the process to be unstable, or very slow to control, if not correctly set. These days temperature control using digital PID controllers have automatic auto-tune functions. During the auto-tune period the PID controller controls the power to the process and measures the rate of change, overshoot and response time of the plant. This is often based on the Zeigler-Nichols method of calculating controller term values. Once the auto-tune period is completed the P, I &D values are stored and used by the PID controller.

Data Track manufactures the Tracker 300 range of DIN rail mounted PID controllers. The Tracker 300 range is fully configurable by PC software and features universal input, single loop integrity, autotune PID, heat / cool control actions and condition monitoring features. Visit our product pages for further information. You can find more information on PID control at the following sites:

Wikipedia's Explanation Of A PID Controller
PID Controller Tuning
How Do PID Controllers Work?
PID Control Theory 101
PID Algorithms and Tuning Methods
PID Tutorial
Control Views Q&A