 # Proportional controller In Control System

The proportional controller gives control signal in one to one correspondence with an error over some range. Each value of error about desired value will have corresponding controller output like controller output values are interpolated with respect to error values.

Mathematically this can be represented as Where,

• P = Controller’s output

• ep (t)= Desired Value of controlled variable – Measured Value

• Kp = Proportional gain

• P0 = Controller output with no error

It indicates that, if the error is zero, the output is constant and equal to P0 and if there is an error, for every 1 % error, a correction of Kp % is added to or subtracted from P0, depending on the sign of error.

### Application of proportional controller

Thermostat used in room temperature control expands or compress it’s bimetallic spring as per temperature variation in the room and gives corresponding control signal to heater coil.

Another example is heat exchanger system,

• If there is sudden large flow of cold fluid enters into heat exchanger, since TT (temperature transmitter) detects this sudden change then,

• TC (Temperature controller) compares measured value of temperature with desired temperature value,

• a corresponding error is also large and if we multiply it with proper gain (proportional gain) and subtract from P0,

• Then control signal gradually opens steam flow through the control valve and maintains the temperature inside the heat exchanger. 1. Processes with slower dynamics are controlled effectively.

2. Helps to stabilize higher order processes which have transient instability.