Emerson E2 Integral Mode, Proportional Constant Kp, Why I Mode is Necessary, Proportional Offset

Throttling Range on page D-1.

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THROTTLING	OUTPUT AT
RANGE	SETPOINT
	(shown here as 50%)

0% 100%

CONTROL INPUT

26512028

Figure D-1- Throttling Range

Example 1: Suppose a Case Control application has a throttling range of 10 degrees. Also, for simplicity’s sake, assume only the Proportional Mode is active and the pro- portional constant Kp is one. The system begins with a 0% output at the bottom of the Throttling Range and with an input value of 24°F. Because the throttling range is 10 degrees, Proportional Mode will gradually add 100% to the output percentage as the input changes to 34° over time.

Suppose, for example, the input increases by one degree every time an update occurs. The following adjust- ment would then likewise occur after every update:

“P” mode adj. = (1.0)(1 degree) / 10 degrees = 0.1 = 10%

After 10 updates, the input value would be 34°F and the output would be 100%. The same would happen if it were five updates at two degrees each or one hundred updates at 0.1 degrees each. In every case, the tempera- ture travels a total of 10 degrees, and because the throt- tling range is also 10 degrees, the output travels from 0% to 100% proportionally.

Higher Throttling Range values will result in a wider 0-100% range, and therefore will result in smaller reaction to changes in input values.

Proportional Constant (Kp)

The Proportional Constant is simply a multiplier that can be used to fine-tune the size of the Proportional Mode adjustment. Raising the value of Kp results in a greater reaction to input value changes, while lowering it results in a smaller reaction.

Changing Kp is essentially the same thing as changing the value of the throttling range. For example, having a TR of 10 and a Kp of 2 is the same as having a TR of 5 and a Kp of 1. Mathematically speaking, the effective propor- tional range is calculated by dividing the Throttling Range by Kp.

If Proportional Mode is functioning incorrectly in your system, it may be more appropriate for you to change the Throttling Range value to a more appropriate value. Kp is designed as a fine-tuning constant (for example, it might be used to speed up reaction slightly by setting it to 1.04, or to slow down reaction by setting it to 0.98).

Integral Mode

The Integral Mode (also called “I” Mode) is the por- tion of PID control that seeks to make the input equal to the setpoint. When an update occurs, the Integral Mode measures the difference between the current input value and the setpoint. The size of this difference determines Integral Mode’s output percentage adjustment.

Why “I” Mode is Necessary

Though Proportional Mode handles the majority of the workload during PID control, there are two major short- comings that make the “I” Mode necessary.

Proportional Offset

Proportional Mode, if left to operate all by itself, is only capable of stopping the error from changing. When the error is not changing, neither is the “P” portion of the output. This means the system may reach stability at any value, regardless of whether it is above or below the set- point (see Figure D-2). Proportional Mode alone has no mechanism that can bring the error to zero after stability has occurred. The “I” Mode is necessary in order to move the input in the direction of the setpoint.

D-2 • E2 RX/BX/CX I&O Manual 026-1610 Rev 13 14-SEP-2011