Emerson E2 operation manual Appendix D PID Control, Proportional P Mode, Throttling Range

Appendix D: PID Control

Introduction to PID Control			output after each update are made by three different modes
			of control: Proportional (“P”) Mode, Integral (“I”) Mode,
PID Control is a specialized method of closed-loop			and Derivative (“D”) Mode. Each mode of control makes
control that strives to maintain equality between an input			its own adjustment to the output percentage, and the three
value and a user-defined setpoint by operating a device or			adjustments are added to the previous output percentage to
a number of devices at somewhere between 0% and 100%			determine the new output percentage. In mathematical
of full capacity.			terms, every update will affect the output percentage as
PID Control works by making adjustments to the out-			follows:
put at a constant rate called the update rate (usually 2-6			NEW OUT% = OLD OUT% + (“P” mode adjustment) + (“I” mode
seconds). For every update that occurs, PID Control takes
a reading from the input sensor or transducer, measures the			adjustment) + (“D” mode adjustment)
distance between the input and the setpoint (also called the			Each of the three modes (P, I, and D) serves a different
error), makes a series of calculations, and adjusts the out-
put percentage in such a way as to move the input towards			and important purpose, as described below:
the setpoint in the most efficient manner.
The “calculations” that determine the new value of the
P		Tries to stop the error from changing. Measures difference
	Proportional Mode	between current and previous error, and adjusts output per-
		centage to prevent any further movement.
I		Tries to bring the error to zero (input = setpoint).
	Integral Mode
D		Tries to slow or stop a rapidly changing error so P and I
	Derivative Mode	Modes may effectively work to eliminate it.

Proportional (“P”) Mode

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 = Kp (E – E-1)/TR

Kp = proportional constant

E = current error

E-1= error during last update

TR = throttling range

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

Throttling Range

In simplest terms, the Throttling Range is the number

Introduction to PID Control Appendix D: PID Control • D-1