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To simulate the PI Controller for unit step input


To simulate the PI 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 Integral Control:Output power equals to the sum of proportion and integration coefficients. The higher the proportion coefficient, the less the output power at the same control error. The higher the integration coefficient, the slower the accumulated integration coefficient. PI control provides zero control error and is insensitive to interference of the measurement channel. The PI control disadvantage is slow reaction to disturbances. To adjust the PI controller, you should first set the integration time equal to zero, and the maximum proportion time. Then by decreasing the coefficient of proportionality, achieve periodic oscillations in the system. Close to the optimum value of the coefficient of proportionality is twice higher than that at which any hesitation, and close to the optimum value of the integration time constant - is 20% less than the oscillation period.

This can be mathematically expressed as


Transfer Function

X(s)/F(s) = KpS + K I/S3+ 10s2 + (20 + K P)S + KI

Let reduce the Kp to 30 and Ki equal to 70


num = 1;

den = [ 1 10 20];

Plant = tf(num,den);


Kp = 30;

Ki = 70;

Contr = tf([Kp Ki],[1 0]);


t = 0:0.01:0.2;




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