“Control Actions of Controllers”

Let’s have an overview about Control Actions. What are control actions and its definition? What is the significance ? What is the requirement of the Control Actions in Process Control?

So , basically what controller does?

It actually compares actual value of the output by taking the reference of input and produces control signal which will reduce the generated deviation to a smaller value.

So , the control signal produced by the controller called as Control Actions.

Basic Control Action

Classification

Proportional Controller.

It is a type of linear feedback control system in which a correction is applied to the controlled variable which is proportional to the difference between the desired value.

The proportional controller helps in reducing the steady-state error, thus makes the system more stable.

The slow response of the over damped system can be made faster with the help of these controllers.

The proportional controller produces an output, which is proportional to error signal.

The proportional controller produces an output, which is proportional to error signal. u(t)∝e(t)⇒u(t)=Kpe(t)

By applying Laplace Transform U(s)=Kpe(s) ⇒U(s)/E(s)=KP

Where,

U(s) is the Laplace transform of the actuating signal u(t)

E(s) is the Laplace transform of the error signal e(t)

KP is the proportionality constant

2.Derivative Controller

The derivative controller produces an output, which is derivative of the error signal.

It should be used in combinations with other modes of controllers because of it has steady-state error. It produces saturation effects and also amplifies the noise signals produced in the system.

u(t)=KD*de(t)/dtu(t)

Apply Laplace transform on both sides.

U(s)=KDsE(s)

U(s)/E(s)=KDs

Therefore, the transfer function of the derivative controller is KDs.

Where, KDis the derivative constant.

The block diagram isthe unity negative feedback closed loop control system along with the derivative controller.

3.Integral Controller.

Integral control action is expressed as follows:

fI(t) is the integral control action and Ki is the integral constant.

Because of the continuous change in the control action (caused by integration) the constant Ki is often referred to as the reset constant.

The integral controller produces an output, which is integral of the error signal.

u(t)=KI∫e(t)dt

Apply Laplace transform on both the sides -

U(s)=KIE(s)s

U(s)E(s)=KIs

Therefore, the transfer function of the integral controller is KIs

Where, KI is the integral constant.

4.Proportional Derivative Controller.

In a proportional derivative controller output is directly proportional to the summation of proportional of error and differentiation of the error signal.

The proportional derivative controller produces an output, which is the combination of the outputs of proportional and derivative controllers.

u(t)=KPe(t)+KDde(t)

Apply Laplace transform on both sides -

U(s)=(KP+KDs)E(s)

U(s)/E(s)=KP+KDs

Therefore, the transfer function of the proportional derivative controller is KP+KDs

5.Proportional Integral Control

u(t)=KPe(t)+KI∫e(t)dt

Apply Laplace transform on both sides -

U(s)=(KP+KI/s)E(s)

U(s)/E(s)=KP+KI/s

Therefore, the transfer function of proportional integral controller is KP+KI/s

6.Proportional Integral Derivative.

The proportional integral derivative controller produces an output, which is the combination of the outputs of proportional, integral and derivative controllers.

u(t)=KPe(t)+KI∫e(t)dt+KD*de(t)/dt

Apply Laplace transform on both sides -

U(s)=(KP+KI/s+KDs)E(s)

U(s)/E(s)=KP+KI/s+KDs

Therefore, the transfer function of the proportional integral derivative controller is KP+KI/s+KDs

The proportional integral derivative controller is used to improve the stability of the control system and to decrease steady state error.