To simulate the PD Controller for unit step input

Aim

To simulate the PD Controller for unit step input.

System Configuration:

1. Ram: 4 GB
2. Processor: Intel Core i3
3. Operating system: Window 7
4. Software: MATLAB

Circuit Diagram:

Plant:A system to be controlled.

Controller:Provides excitation for the plant; Designed to control the overall system behavior.

Proportional Derivative Control: As the name indicates, it is a combination of proportional and derivative control actions. It is widely used in industrial applications. Its control action is mathematically expressed as

This control action sometimes fails to eliminate the offset of proportional controllers. It is also called rate control action. In P-D controller, the output varies with respect to rate of change of actuating error signal.

Transfer Function

????(????)/????(????) = ????_DS + K _P/S²+ (10 + ????_D)S + (20+ K_P)

Let reduce the Kp to 300 and Kd equal to 10

Program:

num = 1;

den = [ 1 10 20];

Plant = tf(num,den);

Step(plant);

Kp = 300;

Kd = 10;

Contr = tf([Kd Kp],1);

Sys_cl=feedback(contr*plant,1)

t = 0:0.01:0.2;

step(sys_cl,t)

Observations:

Result:Simulation of P-D Controller done successfully by using MATLAB