**How Do PID Controllers Work: Application & Theory**

**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.