# PID Controller

In this post, we will discuss the PID Controller and the working of the PID Controller.

PID Controller is the most important part of the industrial automation and process control system.

#### PID Controller

A PID Controller (A proportional–integral–derivative controller) is a common control loop feedback controller. The PID Controller is widely and most commonly used in industrial control systems.

We all know that in the feedback controller, a feedback is compared with the reference or set value. An Error signal is generated as a difference between the feedback value and the set value.

A PID controller calculates an “error” value as the difference between a measured process variable (feedback value) and the desired setpoint (set value). The PID controller attempts to minimize the error by adjusting its controller output signal or process control variables.

The PID controller calculation (algorithm) involves three separate constants or parameters, and is so the PID Controller sometimes called three-term control:

The proportional, The integral and The derivative values, denoted by P, I, and D respectively.

These values can be expressed in terms of time:

P depends on the present error,

I depends on the accumulation of past errors,

and D is a prediction of future errors, based on the current rate of change.

The weighted sum of these three actions is used to adjust the process via a control element. This control element may be a control valve or a signal given to variable frequency drive (VFD) to control the rpm or the speed of a motor.

###### Process variable (PV)

The process variable is the current value of the process parameter. The process variable is the parameter that needs to be controlled. For Example- Temperature, Pressure, Level, Flow. The process variable is measured by a sensor or transmitter. The Process variable is provided as feedback to the PID Controller.

###### Setpoint:

The setpoint is the set value at which we want to control the process parameter. For example, if want to control the temperature of any tank or body at 300 degrees Celsius, so the setpoint (SP) will be 300 degrees Celsius. Suppose the value of process parameter is 310 degrees Celsius. So 310 degrees Celsius will be the Process variable (PV).

###### Error:

We all know that in the feedback control system the error is the difference between the feedback signal and the set value.

Error= (Set value)-(feedback signal)

Here, Set value= setpoint (SP)

Feedback signal= Process variable (PV)

Error= setpoint(SP)- Process Variable(PV)

Control Variable: The Control Variable is the output of the controller and is used to minimize the error signal generated. This control variable is given to control valve so that the error can be minimized. The error can be minimized by opening or closing of the control valve.

The control variable is also called the measured variable.

PID Controller can be used as

P only Controller

PI Controller

PID Controller

###### P only Controller:

P only controller use the only Proportional term for controlling. It is discussed earlier that P depends on the present error. The proportional component depends on the present error means only on the difference between the set point and the process variable.

proportional gain (Kp) is the ratio of output response to the error signal.

By increasing the proportional gain, an error will minimize, but With the Proportional Controller Offset (Deviation from Set Point) is present. Increasing the Controller Gain will make the control loop go unstable. So Integral Action is included in Controller to eliminate this Offset.

PI Controller:

I depends on the accumulation of past errors. P depends on the present error. The result is that even a small error term will cause the integral component to increase slowly. The integral response will continuously increase over time unless the error is zero. so the effect is that the Steady-State error should be zero. The steady-state error is the final difference between the process variable and setpoint.

Integral action eliminates the offset.

D depends on the prediction of future errors, based on the current rate of change. Increasing the derivative parameter will cause the control system to react more strongly to changes in the error term but the Derivative Response is highly sensitive to noise in the process variable signal. So most practical control systems use very small derivative time (Td ).

Derivative time (Td) is used for temperature control.

It is clear from the above image that

Controller Output:

Y= E(t)(Kp+1/Ti(integral of E(t)dt)+ Td(Differentiation of E(t)/dt))

here E(t) is error signal.

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