Emerson E2 operation manual Derivative Mode, I Mode Calculation, Saturation

TEMPERATURE		TEMPERATURE
S E T	P O I N T	S E T	P O I N T
	TIME		TIME
“P” MODE ONLY		“P” + “I” MODES

Figure D-2- Comparison of “P” Mode vs. “P” + “I” Mode

Saturation

Once the input value has wandered outside Propor- tional Mode’s throttling range, the output percentage will be at 0% (if below the Throttling Range) or at 100% (if above the Throttling Range). At this point, PID is consid- ered to be in saturation, meaning it is operating at full (or zero) capacity and is not able to react any further to changes that occur beyond the throttling range.

Proportional Mode cannot distinguish between a satu- rated and an unsaturated system; it simply makes propor- tional adjustments to the output percentage. Therefore, once an input value in a saturated system changes direc- tion, Proportional Mode reacts to correct the movement, regardless of how much error exists. As the temperature changes direction and again moves in the direction of the

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setpoint, Proportional Mode will reduce the 100% output percentage in an attempt to stop the movement and stabi- lize the temperature.

To put it another way, when a system is saturated, the input changes the placement of the Throttling Range. As shown in Figure D-2, as the input rises above the Throt- tling Range, the top end of the Throttling Range rises with it. When the input finally changes direction, the Throttling Range remains at its new position.

The “I” Mode covers for Proportional Mode’s inability to account for saturation. When the input value is outside the throttling range, “I” Mode will continue to adjust the output percentage to bring the input value towards the set- point

		CHANGES DIRECTION, THROTTLE RANGE REMAINS				AS INPUT IN SATURATED SYSTEM
	SATURATION					CHANGES DIRECTION, THROTTLE RANGE REMAINS
					SATURATION
							“I” CORRECTS ERROR AND BRINGS
THROTTLING RANGE	100%			THROTTLING RANGE	100%		THROTTLING RANGE BACK TO NORMAL
		S E T	P O I N T			S E T	P O I N T
	0%	THROTTLING RANGE			0%	THROTTLING RANGE
		FOLLOWS INPUT DURING				FOLLOWS INPUT DURING
		SATURATION				SATURATION

“P” MODE ONLY TIME “P” + “I” MODES TIME

Figure D-3- Saturation in “P” vs. “P” + “I” Modes

The “I” Mode Calculation

To determine the “I” Mode adjustment for each update, the following calculation occurs:

When changing the value of Ki, it should be noted that small adjustments yield large results. For this reason, it is suggested that Ki should remain close to 1.0 and certainly no less than 0.5 and no greater than 2.0.

“I” mode adjustment = Ki * (current error)

Ki in this equation is called the integral constant. It is simply a multiplier that increases or decreases the speed at which the “I” Mode will increase or decrease the percent- age.

Derivative Mode

The Proportional and Integral Modes provide a good method of controlling a closed-loop system. However, in special circumstances where the input value is changing rapidly, there may be a lag time between when the error is noted and the length of time it takes the system to compen-

Introduction to PID Control Appendix D: PID Control • D-3