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Tuning a PID (Three-Mode) Controller |
Controller Operation
There are
three common types of Temperature/process controllers:
On/Off CONTROL
An on-off controller is the simplest form of temperature control device.
The output from the device is either on or off, with no middle state. An
on/off controller will switch the output only when the temperature
crosses the setpoint. For heating control, the output is on when the
temperature is below the setpoint, and off above the setpoint.
With
simple On/Off control, since the temperature crosses the setpoint to
change the output state, the process temperature will be cycling
continually, going from below setpoint to above, and back below. In
cases where this cycling occurs rapidly, and to prevent damage to
contactors and valves, an on-off differential, or “hysteresis,” is added
to the controller operations. This differential requires that the
temperature exceed setpoint by a certain amount before the output will
turn off or on again. On-off differential prevents the output from
“chattering” or fast, continual switching if the temperature cycling
above and below setpoint occur very rapidly.
“On-Off” is the most commonly used form of control, and for most
applications it is perfectly adequate. It’s used where a precise control
is not necessary, in systems which cannot handle the energy being turned
on and off frequently, and where the mass of the system is so great that
temperatures change extremely slowly.
Backup alarms are typically controlled with “On-Off” relays. One special
type of on-off control used for alarm is a limit controller. This
controller uses a latching relay, which must be manually reset, and is
used to shut down a process when a certain temperature is reached.
Proportional Control
Proportional control is designed to eliminate the cycling above and
below the setpoints associated with On-Off control. A proportional
controller decreases the average power being supplied to a heater for
example, as the temperature approaches setpoint. This has the effect of
slowing down the heater, so that it will not overshoot the setpoint, but
will approach the setpoint and maintain a stable temperature.
This
proportioning action can be accomplished by different methods. One
method is with an analog control output such as a 4-20 mA output
controlling a valve or motor for example. With this system, with a 4 mA
signal from the controller, the valve would be fully closed, with 12 mA
open halfway, and with 20 mA fully open.
Another method is “time proportioning” i.e. turning the output on and
off for short intervals to vary the ratio of “on” time to “off” time to
control the temperature or process.
With
proportional control, the proportioning action occurs within a
“proportional band” around the setpoint temperature. Outside this band,
the controller functions as an on-off unit, with the output either fully
on (below the band) or fully off (above the band). However, within the
band, the output is turned on and off in the ratio of the measurement
difference from the setpoint. At the setpoint (the midpoint of the
proportional band), the output on:off ratio is 1:1; that is, the on-time
and off-time are equal. If the temperature is further from the setpoint,
the on- and off-times vary in proportion to the temperature difference.
If the temperature is below setpoint, the output will be on longer; if
the temperature is too high, the output will be off longer.
The
proportional band is usually expressed as a percent of full scale, or
degrees. It may also be referred to as gain, which is the reciprocal of
the band. Note, that in time proportioning control, full power is
applied to the heater, but cycled on and off, so the average time is
varied. In most units, the cycle time and/or proportional band are
adjustable, so that the controller may be better matched to a particular
process.
One
of the advantages of proportional control is the simplicity of
operation. However, the proportional controller will generally require
the operator to manually “tune” the process, i.e. to make a small
adjustment (manual reset) to bring the temperature to setpoint on
initial startup, or if the process conditions change significantly.
Systems that are subject to wide temperature cycling need proportional
control. Depending on the precision required, some processes may require
full “PID” control.
PID (Proportional Integral Derivative)
Processes with long time lags and large maximum rate of rise (e.g.,
a heat exchanger), require wide proportional bands to eliminate
oscillation. The wide band can result in large offsets with changes in
the load. To eliminate these offsets, automatic reset (integral) can be
used. Derivative (rate) action can be used on processes with long time
delays, to speed recovery after a process disturbance.
The
most sophisticated form of discrete control available today combines
PROPORTIONAL with INTEGRAL and DERIVATIVE or PID .
The
proportional, integral and derivative terms must be individually
adjusted or “tuned” to a particular system.
It
provides the most accurate and stable control of the three controller
types, and is best used in systems which have a relatively small mass,
those which react quickly to changes in energy added to the process. It
is recommended in systems where the load changes often, and the
controller is expected to compensate automatically due to frequent
changes in setpoint, the amount of energy available, or the mass to be
controlled.
Temperature Control
Tuning a PID (Three-Mode) Controller
Tuning a temperature controller involves setting the proportional,
integral, and derivative values to get the best possible control for a
particular process. If the controller does not include an autotune
algorithm or the autotune algorithm does not provide adequate control
for the particular application, the unit must then be tuned using a
trial and error method.
The following
definitions may be needed:
- Cycle
time — Also known as duty cycle; the total length of time for
the controller to complete one on/off cycle. Example: with a 20
second cycle time, an on time of 10 seconds and an off time of
10 seconds represents a 50 percent power output. The controller
will cycle on and off while within the proportional band.
-
Proportional band — A temperature band expressed in degrees (if
the input is temperature), or counts (if the input is process)
from the set point in which the controllers’ proportioning
action takes place. The wider the proportional band the greater
the area around the setpoint in which the proportional action
takes place. It is sometimes referred to as gain, which is the
reciprocal of proportional band.
-
Integral, also known as reset, is a function which adjusts the
proportional bandwidth with respect to the setpoint, to
compensate for offset (droop) from setpoint, that is, it adjusts
the controlled temperature to setpoint after the system
stabilizes.
-
Derivative, also known as rate, senses the rate of rise or fall
of system temperature and automatically adjusts the proportional
band to minimize overshoot or undershoot.
A
PID (three-mode) controller is capable of exceptional control stability
when properly tuned and used. The operator can achieve the fastest
response time and smallest overshoot by following these instructions
carefully. The information for tuning this three mode controller may be
different from other controller tuning procedures. Normally an AUTO PID
tuning feature will eliminate the necessity to use this manual tuning
procedure for the primary output, however, adjustments to the AUTO PID
values may be made if desired.
After the controller is installed and wired:
1. Apply
power to the controller.
2. Disable
the control outputs. (Push enter twice)
3. Program
the controller for the correct input type (See Quick Start Manual).
4. Enter
desired value for setpoint 1
5. For time
proportional relay output, set the cycle time to 10 seconds or greater.
- Press MENU until OUT1 is displayed.
- Press ENTER to access control output 1 submenu.
- Press MENU until cycle time is displayed.
- Press ENTER to access cycle time setting.
- Use MAX and MIN to set new cycle time value.
- Press ENTER when finished.
6. Set
prop band in degrees to 5% of setpoint 1. (If setpoint 1 = 100,
enter 0005. Prop band = 95 to 110). Note: Micro-Infinity takes
degrees ( if input is temperature) / counts (if input is process) as
Proportional Band value.
- If ID is
disabled: - Press MENU 1 time from run mode to get to setpoint
1; confirm SP1 LED is flashing. - Use MAX and MIN to set new
setpoint value.
- If ID is
enabled: - Press MENU until Set Point is displayed. - Press
ENTER to access setpoint 1 setting. - Use MAX and MIN to set new
setpoint value.
- Press
ENTER to stored setting when finished.
7. Set
reset and rate to 0.
- Press
MENU until OUT1 is displayed.
- Press
ENTER to access control output 1 submenu.
- Press
MENU until autopid is displayed.
- Press
ENTER to access autopid setting.
- Press
MAX to disable autopid; press ENTER when done.
- Press
MENU until Reset Setup is displayed.
- Press
ENTER to access Reset setting.
- Use MAX
and MIN to set Reset to 0; press ENTER to store the new setting.
- Display
advances to Rate Setup.
- Press
ENTER to access Rate setting.
- Use MAX
and MIN to set Rate to 0; press ENTER to store the new setting.
- Press
MIN 2 times to return to run-mode. Should the unit reset, press
ENTER twice to put it into stand-by mode.
NOTE: On units with dual three-mode outputs, the primary and
secondary proportional parameter is independently set and may be tuned
separately. The procedure used in this section is for a HEATING primary
output. A similar procedure may be used for a primary COOLING output or
a secondary COOLING output.
A. TUNING OUTPUTS FOR HEATING CONTROL
- Enable
the OUTPUT (Press Enter) and start the process.
- The
process should be run at a setpoint that will allow the
temperature to stabilize with heat input required.
- With
RATE and RESET turned OFF, the temperature will stabilize with a
steady state deviation, or droop, between the setpoint and the
actual temperature. Carefully note whether or not there are
regular cycles or oscillations in this temperature by observing
the measurement on the display. (An oscillation may be as long
as 30 minutes). 3. The tuning procedure is easier to follow if
you use a recorder to monitor the process temperature.
- If there
are no regular oscillations in the temperature, divide the PB by
2 (see Figure 1). Allow the process to stabilize and check for
temperature oscillations. If there are still no oscillations,
divide the PB by 2 again. Repeat until cycles or oscillations
are obtained. Proceed to Step 5.
- If
oscillations are observed immediately, multiply the PB by 2.
Observe the resulting temperature for several minutes. If the
oscillations continue, increase the PB by factors of 2 until the
oscillations stop.
- The PB
is now very near its critical setting. Carefully increase or
decrease the PB setting until cycles or oscillations just appear
in the temperature recording.
- If no
oscillations occur in the process temperature even at the
minimum PB setting skip Steps 6 through 15 below and proceed to
paragraph B.
- Read the
steady-state deviation, or droop, between setpoint and actual
temperature with the “critical” PB setting you have achieved.
(Because the temperature is cycling a bit, use the average
temperature.)
- Measure
the oscillation time, in minutes, between neighboring peaks or
valleys (see Figure 2). This is most easily accomplished with a
chart recorder, but a measurement can be read at one minute
intervals to obtain the timing.
-
Now,
increase the PB setting until the temperature deviation, or
droop, increases 65%. The desired final temperature deviation
can be calculated by multiplying the initial temperature
deviation achieved with the CRITICAL PB setting by 1.65 (see
Figure 3). Try several trial-and-error settings of the PB
control until the desired final temperature deviation is
achieved.
-
You have now
completed all the necessary measurements to obtain optimum
performance from the Controller. Only two more adjustments are
required — RATE and RESET.
-
Using the
oscillation time measured in Step 7, calculate the value for
RESET in repeats per minutes as follows:
RESET = (5/8 ) x To
Where To = Oscillation Time in Seconds. Enter the value for RESET in
OUT 1 (follow the same procedure as outlined in preparation section,
step 7 to set RESET).
-
Again using
the oscillation time measured in Step 7, calculate the value for
RATE in minutes as follows:
RATE = To 10
Where T = Oscillation Time in Seconds. Enter this value for RATE in
OUT 1 (follow the same procedure as outline in preparation section,
step 7 to set RATE).
-
If overshoot
occurred, it can be reduced by increasing the proportional band
and the RESET time. When changes are made in the RESET value, a
corresponding change should also be made in the RATE adjustment
so that the RATE value is equal to:
RATE = (4/25) x RESET
-
Several
setpoint changes and consequent Prop Band, RESET and RATE time
adjustments may be required to obtain the proper balance between
“RESPONSE TIME” to a system upset and “SETTLING TIME”. In
general, fast response is accompanied by larger overshoot and
consequently shorter time for the process to “SETTLE OUT”.
Conversely, if the response is slower, the process tends to
slide into the final value with little or no overshoot. The
requirements of the system dictate which action is desired.
-
When
satisfactory tuning has been achieved, the cycle time should be
increased to save contactor life (applies to units with time
proportioning outputs only. Increase the cycle time as much as
possible without causing oscillations in the measurement due to
load cycling.
-
Proceed to
Section C.
B. TUNING PROCEDURE WHEN NO OSCILLATIONS ARE OBSERVED
- Measure
the steady-state deviation, or droop, between setpoint and
actual temperature with minimum PB setting.
- Increase
the PB setting until the temperature deviation (droop) increases
65%.
- Set the
RESET in OUT1 to a low value (50 secs). Set the RATE to zero (0
secs). At this point, the measurement should stabilize at the
setpoint temperature due to reset action.
- Since we
were not able to determine a critical oscillation time, the
optimum settings of the reset and rate adjustments must be
determined by trial and error. After the temperature has
stabilized at setpoint, increase the setpoint temperature
setting by 10 degrees. Observe the overshoot associated with the
rise in actual temperature. Then return the setpoint setting to
its original value and again observe the overshoot associated
with the actual temperature change.
-
Excessive overshoot implies that the Prop Band and/or RESET are
set too low, and/or RATE value is set too high. Overdamped
response (no overshoot) implies that the Prop Band and/or RESET
is set too high, and/or RATE value is set too low. Refer to
Figure 4. Where improved performance is required, change one
tuning parameter at a time and observe its effect on performance
when the setpoint is changed. Make incremental changes in the
parameters until the performance is optimized. Figure 4 Setting
RESET and/or RATE PV
-
When
satisfactory tuning has been achieved, the cycle time should be
increased to save contactor life (applies to units with time
proportioning outputs only.). Increase the cycle time as much as
possible without causing oscillations in the measurement due to
load cycling.
C. TUNING THE PRIMARY OUTPUT FOR COOLING CONTROL
The
same procedure is used as defined for heating. The process should be run
at a setpoint that requires cooling control before the temperature will
stabilize.
D. SIMPLIFIED TUNING PROCEDURE FOR PID CONTROLLERS
The
following procedure is a graphical technique of analyzing a process
response curve to a step input. It is much easier with a strip chart
recorder reading the process variable (PV).
- Starting
from a cold start (PV at ambient), apply full power to the
process without the controller in the loop, i.e., open loop.
Record this starting time.
- After
some delay (for heat to reach the sensor), the PV will start to
rise. After more of a delay, the PV will reach a maximum rate of
change (slope). Record the time that this maximum slope occurs,
and the PV at which it occurs. Record the maximum slope in
degrees per minute. Turn off system power.
- Draw a
line from the point of maximum slope back to the ambient
temperature axis to obtain the lumped system time delay Td (see
Figure 5) . The time delay may also be obtained by the equation:
Td = time to max. slope – (PV at max. slope – Ambient)/max.
slope
- Apply
the following equations to yield the PID parameters: Pr. Band =
Td x max. slope Reset = Td/0.4 secs. Rate = 0.4 x Td minutes
- Restart
the system and bring the process to setpoint with the controller
in the loop and observe response. If the response has too much
overshoot, or is oscillating, then the PID parameters can be
changed (slightly, one at a time, and observing process
response) in the following directions: 5. Refer to figure 4,
vary the proportional band, the Reset value, and the Rate value
to achieve best performance.
Example: The chart recording in Figure 5 was obtained by applying
full power to an oven. The chart scales are 10°F/cm, and 5 min/cm. The
controller range is -200 - 900°F, or a span of 1100°F. Maximum slope =
18°F/5 minutes = 3.6°F/minutes. Time delay = Td = approximately 7
minutes.
Proportional Band = 7 minutes x 3.6°F / minutes = 25.2°F.
Note: Prop Band in Micro-Infinity is set in degrees/ counts. Reset =
7/.04 minutes = 17.5 min. or 1050 secs. Note: Reset in Micro-Infinity is
specified in seconds Rate = 0.4 x 7 minutes = 2.8 min. or 168 secs.
Set
Prop Band to: 025.0; Set Reset to: 1050 Set Rate to: 168 Follow step 6
and 7 of the preparation section to set new values for Prop Band, Reset,
and Rate.
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