Control Actions (P Controller , PI Controller , PID Controller)

The Control Actions

An automatic controller compares the actual value of the system output with the reference input (desired value), determines the deviation, and produces a control signal that will reduce the deviation to zero or a small value. The manner in which the automatic controller produces the control signal is called the control action.

The controllers may be classified according to their control actions as 

1) Proportional controllers
2) Proportional-plus- integral controllers
3) Proportional-plus-integral-plus-derivative controllers

A two position controller has two fixed positions usually on or off. A proportional control system is a feedback control system in which the output forcing function is directly proportional to error. A integral control system is a feedback control system in which the output forcing function is directly proportional to the first time integral of error. A proportional-plus-integral control system is a feedback control system in which the output forcing function is a linear combination of the error and its first time integral. 

A proportional-plus-derivative control system is a feedback control system in which the output forcing function is a linear combination of the error and its first time derivative. A proportional-plus-derivative-plus-integral control system is a feedback control system in which the output forcing function is a linear combination of the error, its first time derivative and its first time integral.

 

Proportional Control Action

The proportional controller is essentially an amplifier with an adjustable gain. For a controller with proportional control action the relationship between output of the controller u(t) and the actuating error signal e(t) is

Proportional-plus-Integral Control Action

The integral time adjusts the integral control action, while change in proportional gain affects both the proportional and integral action. The inverse of the integral time is called reset rate. The reset rate is the number of times per minute that a proportional part of the control action is duplicated. Fig.5 shows the block diagram of the proportional- plus-integral controller. For an actuating error of unit step input, the controller output is shown in Fig.6.

 

 

Proportional-plus-Integral-plus-Derivative Control Action

It is a combination of proportional control action, integral control action and derivative control action. The equation of the controller is

 

 

Where, Kp is the proportional gain, Ti is the integral time, and Td is the derivative time. The block diagram of PID controller is shown in Fig.9. For an actuating error of unit ramp input, the controller output is shown in Fig.10.