To simulate the P Controller for unit step input

Aim

To simulate the P 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 control, in engineering and process control, 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 (setpoint, SP) and the measured value (process variable, PV). In the proportional control algorithm, the controller output is proportional to the error signal, which is the difference between the setpoint and the process variable. In other words, the output of a proportional controller is the multiplication product of the error signal and the proportional gain.

This can be mathematically expressed as

Pout ∝ e(t)

where

P0: Controller output with zero error.

Pout: Output of the proportional controller

Pout= KPe(t) + P0

Kp: Proportional gain

e(t): Instantaneous process error at time t.

Transfer Function

X(s)/F(s) = Kp/s ²+ 10s + (20 + Kp)

Let proportional gain Kp = 300

The goal of the problem is to show Kp contribute to obtain

Fast rise time

Minimum overshoot

No steady state error

Program:

num = 1;

den = [ 1 10 20];

Plant = tf(num,den);

Step(plant);

Kp = 300;

Contr = kp;

Sys_cl=feedback(contr*plant,1)

t = 0:0.01:0.2;

step(sys_cl,t)

Observations:

Result:Simulation of P Controller done successfully by using MATLAB