Output of the proportional controller is proportional to error of the input at that time. Error is the difference between Setpoint and Process Value.

OP α Ep

Ep = (SP - PV)

Where,

OP = Controller Output

Ep = Error Value

So,

OP = Kp * Ep

OP = Kp * (SP – PV)

Where,

Kp = Proportional Constant / Gain

SP = Setpoint

PV = Process Value

**Note:** Take error by subtracting PV from SP. Vice versa may lead confusion during controller types.

There are two types of proportional controller. They are,

1. Reverse Acting

2. Direct Acting

**1. Reverse Acting Proportional Controller**

In reverse acting proportional controller the output will decreases as increase in process value.

OP = Kp * (SP – PV)

OP = (Kp) * (SP – PV)

OP↓ α –PV ↑

Make **Kp as Positive** for reverse acting proportional controller

**2. Direct Acting Proportional Controller**

In direct acting proportional controller the output will increases as increase in process value.

OP = Kp * (SP – PV)

OP = (-Kp) * (PV - SP)

OP↑ α PV ↑

Make **Kp as Negative** for direct acting proportional controller

**Example:**

Here, we are controlling water level in a tank irrespective of input and out flow rates. Form this example we can easily understand direct acting and reverse acting of proportional controllers.

**Controller 1** is used to control the inlet flow of water by taking level transmitter signal as a process value. If the water level in the tank increases then PV will increase. Now we need to decrease OP value proportionally to close the valve to maintain water level in the tank. This is done by choosing direct acting proportional controller.

OP↓ α –PV ↑ where, Kp is positive

Similarly, **Controller 2** is used to control the outlet flow of water by taking level transmitter signal as a process value. If the water level in the tank increases then PV will increase. Now we need to increase OP value proportionally to open the valve to maintain water level in the tank. This is done by choosing reverse acting controller.

OP↑ α PV ↑ where, Kp is Negative

**Effect of Kp in Proportional controller**

Kp is most critical parameter in proportional controller. Kp value not only decides the proportional type but also smoothness of the operation. Kp is also called as gain of the controller. It will amplify the error value.

If Kp = 1 then controller opt is the error.

OP = SP – PV

If Kp > 1 then controller output will reduce the proportional band of the controller.

**Proportional band** is an operating range of the controller which is defined as inverse of gain. The value is expressed in terms of percentage.

PB = (1 / Kp)*100 where PB = Proportional Band

If Kp = 1 then PB = 100%. So, operating range is 100 percent

If Kp = 2 then PB = 50%. So, operating range becomes 50 percent

**Offset** is the minimal input which results in large change in output.

Proportional controller is **cost effective** controller. But having it own drawbacks like Proportional band and offset. This is overcome with the help of additional controllers like derivative controller and integral controller. **Proportional Integral Derivative controller** is most popular controller commonly called as **PID** controller.