Proportional-Integral (Pi) Control - Honeywell AUTOMATIC CONTROL Engineering Manual

OUTDOOR AIR
TEMPERATURE
SENSOR
Fig. 35. Discharge Air Control Loop with Reset.
Compensation can either increase or decrease the setpoint
as the compensation input increases. Increasing the setpoint
by adding compensation on an increase in the compensation
variable is often referred to as positive or summer
compensation. Increasing the setpoint by adding compensation
on a decrease in the compensation variable is often referred to
as negative or winter compensation. Compensation is most
commonly used for temperature control, but can also be used
with a humidity or other control system.
Some controllers provide compensation start point capability.
Compensation start point is the value of the compensation
sensor at which it starts resetting the controller primary sensor
setpoint.
COMPENSATION AUTHORITY
Compensation authority is the ratio of the effect of the
compensation sensor relative to the effect of the primary sensor.
Authority is stated in percent.
The basic equation for compensation authority is:
Change in setpoint
Authority =
Change in compensation input
For proportional controllers, the throttling range (TR) is
included in the equation. Two equations are required when the
throttling range is included. For direct-acting or positive
compensation, in which the setpoint increases as the
compensation input increases, the equation is:
Change in setpoint – TR
Authority =
Change in compensation input
Direct-acting compensation is commonly used to prevent
condensation on windows by resetting the relative humidity
setpoint downward as the outdoor temperature decreases.
For reverse-acting or negative compensation, in which the
setpoint decreases as the compensation input increases, the
equation is:
Change in setpoint + TR
Authority =
Change in compensation input
TEMPERATURE
CONTROLLER
RETURN
SENSOR
DISCHARGE
AIR
FAN
SUPPLY
C2720
x 100
x 100
x 100
In an application requiring negative reset, a change in outdoor
air temperature at the reset sensor from 0 to 60F resets the hot
water supply temperature (primary sensor) setpoint from 200
to 100F. Assuming a throttling range of 15 degrees F, the
required authority is calculated as follows:
Change in setpoint + TR
Authority =
Change in compensation input
200 – 100 + 15
=
Authority = 192%
The previous example assumes that the spans of the two
sensors are equal. If sensors with unequal spans are used, a
correction factor is added to the formula:
Authority =
Compensation sensor span
Primary sensor span
Correction Factor
Assuming the same conditions as in the previous example,
a supply water temperature sensor range of 40 to 240F (span
of 200 degrees F), an outdoor air temperature (compensation)
sensor range of -20 to 80F (span of 100 degrees F), and a
throttling range of 10 degrees F, the calculation for negative
reset would be as follows:
100
Authority =
200
Authority = 92%
The effects of throttling range may be disregarded with PI reset
controls.

PROPORTIONAL-INTEGRAL (PI) CONTROL

In the proportional-integral (PI) control mode, reset of the
control point is automatic. PI control, also called "proportional-
plus-reset" control, virtually eliminates offset and makes the
proportional band nearly invisible. As soon as the controlled
variable deviates above or below the setpoint and offset
develops, the proportional band gradually and automatically
shifts, and the variable is brought back to the setpoint. The
major difference between proportional and PI control is that
proportional control is limited to a single final control element
position for each value of the controlled variable. PI control
changes the final control element position to accommodate
load changes while keeping the control point at or very near
the setpoint.
23 ENGINEERING MANUAL OF AUTOMATIC CONTROL
CONTROL FUNDAMENTALS
x 100
60 – 0
Change in setpoint ± TR
x
Change in compensation input
200 – 100 + 10
x x 100
6 0 – 0
x 100
x 100