**PROPORTIONAL CONTROL SYSTEM**

**Proportional control action**

In a
proportional control action, there is a continuous linear relation between the
output m (t) and the actual error signal e (t). Evidently the control valve or
the regulating unit can take up any position right from the fully open to fully
closed. Depending upon the shift of the measured variable from the desired
value, an adjustment is made of the amount of energy supplied (i.e., the
manipulated variable) to the process or plant. The change in the valve position
is proportional to the amount of deviation and is not affected by the rate or
duration of the deviation.

The
proportional control follows the law:

M
(t) =k1 e (t) +m

Where m
is manual reset constant whose value determine the normal value of controller
output. The constant kp, called the proportional sensitivity or gain,

Kp
=

__Change in controller__
Change
in the
deviation

In
Laplace transform we can write as;

K

_{p }= m(s) / e(s)
For a
step or sudden change in deviation we have:

E=0
for t<0

E=e
for t>0

Where e
is constant

Substitution
of this value in equation (i)
gives:

M
= kp e+m

Or m-m
= kp e

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