Emerson E2 User Manual

PID Control is a specialized method of closed-loop 

control that strives to maintain equality between an input 
value and a user-defined setpoint by operating a device or 
a number of devices at somewhere between 0% and 100% 
of full capacity. 

PID Control works by making adjustments to the out-

put at a constant rate called the update rate (usually 2-6 
seconds). For every update that occurs, PID Control takes 
a reading from the input sensor or transducer, measures the 
distance between the input and the setpoint (also called the 
error), makes a series of calculations, and adjusts the out-
put percentage in such a way as to move the input towards 
the setpoint in the most efficient manner.

The “calculations” that determine the new value of the 

output after each update are made by three different modes 
of control: Proportional (“P”) Mode, Integral (“I”) Mode, 
and Derivative (“D”) Mode. Each mode of control makes 
its own adjustment to the output percentage, and the three 
adjustments are added to the previous output percentage to 
determine the new output percentage. In mathematical 
terms, every update will affect the output percentage as 
follows:

NEW OUT% = OLD OUT% + (“P” mode adjustment) + (“I” mode 

adjustment) + (“D” mode adjustment)

Each of the three modes (P, I, and D) serves a different 

and important purpose, as described below:

P 

        Proportional Mode

Tries to stop the error from changing. Measures difference 
between current and previous error, and adjusts output per-
centage to prevent any further movement.

I  

         Integral Mode

Tries to bring the error to zero (input = setpoint). 

D   

Derivative Mode

Tries to slow or stop a rapidly changing error so P and I 
Modes may effectively work to eliminate it.

The Proportional Mode in PID determines the system’s 

immediate reaction to a change in the error. Proportional 
Mode simply analyzes the difference between the current 
error and the previous error. Based on the size of this dif-
ference, Proportional Mode will make a change to the out-
put in an attempt to stabilize the input value and keep it 
from changing any further.

Mathematically, the following equation determines the 

“P” Mode adjustment for a single update:

“P” mode adjustment = K

p

 (E – E

-1

)/TR

K

p

 = proportional constant

E = current error

E

-1

 = error during last update

TR = throttling range

In simplest terms, the Throttling Range is the number 

of input value units between a 0% output and a 100% out-
put. For example, in a Case Control application, the Throt-
tling Range would be the number of degrees between the 
input temperature that would result in a 0% output and the 
temperature that would cause a 100% output. Therefore, 
the Throttling Range essentially determines the percentage 
of the output adjustment that will be added to the previous 
percentage when a change in input occurs.

PID Control places this Throttling Range around the 

setpoint. As a result, Proportional Mode works to keep the 
temperature near the setpoint and within the throttling 
range. In most cases, the Throttling Range straddles the 
setpoint evenly on both sides, as shown in Figure D-1. 
However, in some applications such as Condenser Con-
trol, the Throttling Range may be placed elsewhere see