To design a controller or controller system, we need a PID controller. In this article, we will learn what the PID controller is.

You can learn PID with Simulink, with MATLAB, with Arduino and with Python. You can create your own setup execute in all above-mentioned software and tune a PID controller by yourself and see results and graphs. This is the best way to learn and understand the PID controller.

Before the PID controller, a continuous controller was used in centrifugal governor to control the speed of rotation.

It was in 1922 when the first-time American engineer Nicolas developed PID theoretically.

Around in the mid-50s due to cheap electronics market, electronic PID controller became popular.

Popular standard on that time of 3-15 psi is taken by 10-50 mA and today's popular standard 4-20 mA.


PID controller is an algorithm that contains a mathematical form of an equation used to control field devices by keeping the process variable at setpoint by adjusting the manipulated variable.

Here, the process variable is a transmitter, a manipulated variable is the control valve and setpoint is given using the onboard controller or by using PLC, DCS, SCADA and HMI.

Let's take an example of a control loop. We have a temperature transmitter used to monitor temperature and which gives you a process variable. We want set point at 100-degree Celcius.

If Temperature goes beyond 100 degrees, let say 105 degrees then an error will be generated.

Error = PV - SP

= 105 - 100

= 5

Here, an error of 5 degrees is generated. As soon as an error is there, the control valve will take an adjustment and allow the temperature to stay maintained at 100-degree celsius. This is how the control loop works.

Above mentioned is the block diagram of the PID controller. Process variable continuously matched with a set point and produces an error. error is then fed to PID control algorithm. Based on the calculation control valve get command of how far or close it has to move.

Based on an application, you can choose what control algorithm you need to use. It can be only P- controller, PI- Controller, PD controller or PID controller.

Proportional (P):

P term or proportional says that how far it has to move in order to keep PV at a set point.

Term P is proportional to the current value of the SP − PV error. For example, if the error is large and positive, the control output will be proportionately large and positive, taking into account the gain factor "K".

Using proportional control alone will result in an error between the setpoint and the actual process value because it requires an error to generate the proportional response.

If there is no error, there is no corrective response.

Integration (I):

I or integration term says that how long integration term has to contribute to killing error.

I for past values of the SP − PV error and integrates them overtime to produce the I term.

For example, if there is a residual SP − PV error after the application of proportional control, the integral term seeks to eliminate the residual error by adding a control effect due to the historic cumulative value of the error.

When the error is eliminated, the integral term will cease to grow. This will result in the proportional effect diminishing as the error decreases, but this is compensated for by the growing integral effect.

Derivative (D):

D or Derivative term take action based on the speed of error.

Term D is the best estimate of the future trend of the SP − PV error, based on its current rate of change.

It is sometimes called "anticipatory control", as it is effectively seeking to reduce the effect of the SP − PV error by exerting a control influence generated by the rate of error change.

The more rapid the change, the greater the controlling or damping effect.

Mathematical form:

There are different forms of PID controller is used but out of them all equations the below one is most common.

Kp e(t) + Ki ∫e (t) dt + Kd de(t)/dt

While tuning you can implement above-mentioned equation to get the desired result.

What is a Digital PID Controller?

A digital PID controller senses the sensor signal, for example from a thermocouple or RTD and connects the measurement to engineering units, such as degree Fahrenheit or Celsius, that are then displayed in a digital format.


The following is the graph which displays the behaviour of the P, PI and PID controller. Mostly you always left with an offset with P-type mode.

Hope, this article gives some insight into the PID controller. If you like this then share among your friends.

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