Honeywell AUTOMATIC CONTROL Engineering Manual page 34

CONTROL FUNDAMENTALS
The reset action of the integral component shifts the
proportional band as necessary around the setpoint as the load
on the system changes. The graph in Figure 36 shows the shift
of the proportional band of a PI controller controlling a
normally open heating valve. The shifting of the proportional
band keeps the control point at setpoint by making further
corrections in the control signal. Because offset is eliminated,
the proportional band is usually set fairly wide to ensure system
stability under all operating conditions.
HEATING
VALVE
POSITION
CLOSED
50% OPEN
0%
50%
LOAD
LOAD
100% OPEN
90 95
= CONTROL POINT
THROTTLING RANGE = 10 DEGREES F
Fig. 36. Proportional Band Shift Due to Offset.
Reset of the control point is not instantaneous. Whenever
the load changes, the controlled variable changes, producing
an offset. The proportional control makes an immediate
correction, which usually still leaves an offset. The integral
function of the controller then makes control corrections over
time to bring the control point back to setpoint (Fig. 37). In
addition to a proportional band adjustment, the PI controller
also has a reset time adjustment that determines the rate at
which the proportional band shifts when the controlled variable
deviates any given amount from the setpoint.
SETPOINT
CONTROL POINT (LOAD CHANGES)
DEVIATION
FROM
SETPOINT
VALVE
POSITION
PROPORTIONAL CORRECTION
T1
Fig. 37. Proportional-Integral Control Response to
Load Changes.
ENGINEERING MANUAL OF AUTOMATIC CONTROL
PROPORTIONAL BAND
FOR SEPARATE LOAD
CONDITIONS
100%
LOAD
105 110
100
SETPOINT (°F)
C2097-1
OPEN
INTEGRAL ACTION
CLOSED
T2 T3 T4
C2098
TIME
Reset error correction time is proportional to the deviation
of the controlled variable. For example, a four-percent deviation
from the setpoint causes a continuous shift of the proportional
band at twice the rate of shift for a two-percent deviation. Reset
is also proportional to the duration of the deviation. Reset
accumulates as long as there is offset, but ceases as soon as
the controlled variable returns to the setpoint.
With the PI controller, therefore, the position of the final
control element depends not only upon the location of the
controlled variable within the proportional band (proportional
band adjustment) but also upon the duration and magnitude of
the deviation of the controlled variable from the setpoint (reset
time adjustment). Under steady state conditions, the control
point and setpoint are the same for any load conditions, as
shown in Figure 37.
PI control adds a component to the proportional control
algorithm and is described mathematically by:
V = KE +
Where:
V = output signal
K = proportionality constant (gain)
E = deviation (control point - setpoint)
T = reset time
1
K/T = reset gain
1
dt = differential of time (increment in time)
M = value of the output when the deviation
is zero
Integral windup, or an excessive overshoot condition, can
occur in PI control. Integral windup is caused by the integral
function making a continued correction while waiting for
feedback on the effects of its correction. While integral action
keeps the control point at setpoint during steady state
conditions, large overshoots are possible at start-up or during
system upsets (e.g., setpoint changes or large load changes).
On many systems, short reset times also cause overshoot.
Integral windup may occur with one of the following:
— When the system is off.
— When the heating or cooling medium fails or is not
available.
— When one control loop overrides or limits another.
Integral windup can be avoided and its effects diminished.
At start-up, some systems disable integral action until measured
variables are within their respective proportional bands.
Systems often provide integral limits to reduce windup due to
load changes. The integral limits define the extent to which
integral action can adjust a device (the percent of full travel).
The limit is typically set at 50 percent.
24
K
∫ Edt + M
T
1
Integral