PROPORTIONAL CONTROL OR P Controller (Definition of Controller and its working principle basic formula graphical representation, transfer function of ideal proportional controller)

Definition of proportional Controller:

The proportional controller produces an output signal (pressure in the case of a pneumatic controller, current or voltage for an electronic controller) that is proportional to the error E. This action may be expressed as

p = K_c Є + p_s -------------------- (1)

_Here p= output signal from controller, psig or ma

        K_c = gain, or sensitivity

        Є = error = set point – measured variable

        p_s = a constant

The error E, which is the difference between the set point and the signal from the measuring element, may be in any suitable units. However, the units of set point and measured variable must be the same, since the error is the difference between these quantities.

When the system is in steady state error Є is zero (0) and output signal is equal to the constant ‘p_s’.

For proportional controller the deviation variables are

P = p - p_s ------------------------- (2)

As at time t=0 error is zero, steady state value of the error will become zero. Therefore error Є itself becomes deviation variable.

Form equation (1) and (2) gives,

P (t) = K_c Є

 Now using Laplace Transform the transfer function can be written as 

 

The above expression gives the transfer function for ideal proportional controller.