Proportional-Integral (Pi) Control - Honeywell AUTOMATIC CONTROL SI Edition 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:
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 reset,
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
ENGINEERING MANUAL OF AUTOMATIC CONTROL
TEMPERATURE
CONTROLLER
RETURN
SENSOR
DISCHARGE
AIR
FAN
SUPPLY
C2720
Change in setpoint
x 100
x 100
x 100
In an application requiring negative compensation, a change
in outdoor air temperature at the compensation sensor from –
18 to 16 C resets the hot water supply temperature (primary
sensor) setpoint from 94 to 38 C. Assuming a throttling range
of 7 Kelvins, the required authority is calculated as follows:
Authority =
Change in compensation input
94 – 38 + 7
=
16 – (–18)
Authority = 185%
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 5 to 115 C (span of
110 Kelvins), an outdoor air temperature (compensation) sensor
range of -30 to 30 C (span of 60 Kelvins), and a throttling
range of 5 Kelvins, the calculation for negative reset would be
as follows:
60
Authority =
110
Authority = 98%
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
CONTROL FUNDAMENTALS
Change in setpoint + TR
x 100
Change in setpoint TR
x
Change in compensation input
94 – 38 + 5
x x 100
16 – (–18)
x 100
x 100