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In the previous Tech Tip,
Proper Control Loop Tuning
Saves $, we defined 'proper' control loop tuning
and discussed how it can save your company thousands of dollars annually. But
how do you implement 'proper' loop tuning?
We will not be discussing 'zeros in the right half plane',
so you can relax and consider a straightforward, common sense approach to
'proper' loop tuning. 'Proper' tuning has nothing to do with minimum absolute
error or fastest response time. It is based on three rules of process control:
Rule No. 1 - A process controller can not eliminate
variability, it only moves the variability from the controlled variable to some
other process variable.
Rule No. 2 - A process controller can increase
variability in both the controlled variable and related process variables, if
the closed loop gain exceeds 1 at any frequency.
Rule No. 3 - A process controller can convert
process measurement noise to variability in both the controlled variable and
related process variables.
Let's look at an example to demonstrate rule no. 1. A
temperature controller controls the outlet temp of an indirect heater by varying
the steam flow to the heater. As the outlet temp begins to drop, the controller
responds by opening the steam valve to increase the steam flow. The increase in
steam flow causes the steam header pressure to begin to decrease. The steam
header pressure decrease causes a decreased steam flow in every steam line
leaving the header until the steam header pressure controller reacts to maintain
the header pressure. This cascades back to an increase in feedwater flow and
fuel flows at the boilers. As you can see, by minimizing the variability in
outlet temperature, we have increased variability in steam flow, header
pressure, feedwater flow and fuel flow plus all other loops affected by changes
in these process variables.
Rule No. 2 is best illustrated by the ear-piercing squeal
you sometimes hear in the feedback loop between an audio speaker and a live
microphone. In this example, the microphone acts as an air pressure transmitter,
sending the signal to the audio amplifier. The amplifier acts like a controller
with proportional gain only. The amplified signal is sent to the speakers which
are the final element affecting the air pressure in the room. If the amplifier gain is too high, you will hear just a ringing
sound after any loud noise and the ringing will fade away if the closed loop
gain is less than 1. If the amplifier gain is increased to a point that the
closed loop gain is greater than 1, the ringing will grow louder at the dominant
resonant frequency of the closed loop. Most audio systems use an
'equalizer' to decrease the closed loop gain at the resonant frequency.
Most of the processes in your facility act the same way. If
you have a process upset (equivalent to a loud noise) and the controller gain is
too high, there will be a ringing affect that introduces needless variability
into the process at the dominant resonant frequency. If the closed loop gain is
greater than 1 at the resonant frequency, the loop will oscillate at that
frequency until the controller is placed in manual. In order to correct the
problem, you have to lower the gain at the resonant frequency. This can be done
by reducing the integral time constant or lowering the controller gain. When set
correctly, the integral time constant acts as a low pass filter causing the
overall loop gain to decrease rapidly at frequencies at and above the dominant
resonant frequency.
Fortunately, the controller gain and integral time
constants can be easily calculated from simple open loop bump tests with minimal
impact on operating equipment. Unfortunately, most traditional methods and most
auto-tuning programs on the market result in aggressive gains that are still to
high for optimal control of overall production costs.
The method for calculating the tuning constants are based
on the characteristic response of the loop. The following sections describe the
methods for each type.
First Order Loops
1st order loops are characterized by a crisp initial response to an output
step change followed by an exponential decay to the new PV value.
The bump test is performed by following these steps:
- Place the controller in manual
- Note the output value (OP) before the bump.
- Note the process variable value (PV) before the bump.
- Change the OP value by 5% to 10% depending on process noise.
- Measure the time delay (Td) from the time the output is changed until the
PV begins to respond.
- Measure the process settling time (Tset) from the beginning of the PV
response until it reaches 98% of it's final value.
- Note the process variable final value (PV) after the bump.
- Return the controller to it's previous mode.
Settling time can vary with process changes. Always use the longest estimated
settling time to avoid oscillations. If in doubt, it is better to use less
integral action by increasing the minutes/repeat or decresing the
repeats/minute.
The time delay Td must be less than the settling time Tset. If Td exceeds
Tset, consider using a Smith Predictor instead of a standard PID controller. If
Td is less than Tset, then calculate the following:
Effective settling time: Ts = 4 * ((Tset / 4) + (Td / (5 - Td / Tset / 4)))
Process Gain: Kp = DPV /DOP
Process time constant: Tcon = Ts / 4
Controller Integral or Reset time in Seconds/Repeat: Tr = Tcon
Controller Gain: Kc = Tr / Kp / Lambda
Where:
-
|
Lambda = 1 * Tcon |
for Aggressive tuning (fast response with ringing at
resonant frequency) |
|
Lambda = 2 * Tcon |
for Normal tuning (best response without ringing) |
|
Lambda = 3 * Tcon |
for Safe tuning (a compromise between normal and slow) |
|
Lambda = 4 * Tcon |
for Slow tuning (slow response for non critical loops) |
Next, convert the integral time constant to units that
match your controller using one of the following formulas:
Repeats/Minute: TrRPM = 60 / Tr
Minutes/Repeat: TrMPR = Tr / 60
Repeats/Second: TrRPS = 1 / Tr
Finally, if your controller expresses gain as Proportional
Band:
PB = 100 / Kc
Second Order Loops
2nd order loops are characterized by a s shaped response to an output step
change.
The bump test is performed by following these steps:
- Place the controller in manual
- Note the output value (OP) before the bump.
- Note the process variable value (PV) before the bump.
- Change the OP value by 5% to 10% depending on process noise.
- Measure the effective time delay (Td) from the time the output is changed
to the intersection of two lines.the first line is simply an extension of the
PV value before the bump. The second line is drawn tangentially to the PV
curve at the point of inflection. The point of inflection is the point where
the curvature of the PV plot changes direction.
- Measure the effective process settling time (Tset) from the end of Td
until the PV reaches 98% of it's final value.
- Note the process variable final value (PV) after the bump.
- Return the controller to it's previous mode.
Settling time can vary with process changes. Always use the longest estimated
settling time to avoid oscillations. If in doubt, it is better to use less
integral action by increasing the minutes/repeat or decresing the
repeats/minute.
The time delay Td must be less than the settling time Tset. If Td exceeds
Tset, consider using a Smith Predictor instead of a standard PID controller. If
Td is less than Tset, then calculate the following:
Effective settling time: Ts = 4 * ((Tset / 4) + (Td / (5 - Td / Tset / 4)))
Process Gain: Kp = DPV /DOP
Process time constant: Tcon = Ts / 4
Controller Integral or Reset time in Seconds/Repeat: Tr = Tcon
Controller Gain: Kc = Tr / Kp / Lambda
Where:
-
|
Lambda = 1 * Tcon |
for Aggressive tuning (fast response with ringing at
resonant frequency) |
|
Lambda = 2 * Tcon |
for Normal tuning (best response without ringing) |
|
Lambda = 3 * Tcon |
for Safe tuningfor Safe tuning (a compromise between normal
and slow) |
|
Lambda = 4 * Tcon |
for Slow tuning (slow response for non critical loops) |
Next, convert the integral time constant to units that
match your controller using one of the following formulas:
Repeats/Minute: TrRPM = 60 / Tr
Minutes/Repeat: TrMPR = Tr / 60
Repeats/Second: TrRPS = 1 / Tr
Finally, if your controller expresses gain as Proportional
Band:
PB = 100 / Kc
Integrating Loops
Integrating loops are characterized by a changing slope of the PV in response
to an output step change. The slope changes can be any combination of positive,
negative or 0 slopes.
_/ \/ /\ \_
Bump test should be conducted under stable process conditions. Uncontrolled
flows into and out of the vessel should be relatively constant for the duration
of the test. The bump test is performed by following these steps:
- Place the controller in manual. If the PV is not changing, make a small
change in the controller output to cause the PV to gradually decrease (or
increase).
- At time t0, note the output value (OP) and process variable value (PV).
- Wait until the PV has changed about 5% and note the output value (OP) and
process variable value (PV) at t1.
- Quickly change the OP value by 5% to 10% depending on process noise.
- The plot of the PV will change slope at t1. Wait long enough to get a good
measurement of the new slope and note the output value (OP) and process
variable value (PV) at t2.
- Return the controller to it's previous mode.
The only other factor required to tune an integrating loop is the Recovery
time, Trec. Recovery time is the maximum desired time to return to setpoint
after a worst case disturbance. For level controls, Trec should generally be
calculated to provide the maximum safe surge capacity. For other integrating
loops such as batch temperature, the minimum value for Trec should be calculated as 6 times the
process time constant. From these measurements, calculate the following:
Process Gain: Kp = Abs(((PV2 - PV1) / T2 - (PV1 - PV0) /
T1) /
(OP1 - OP0)
)
Controller Integral or Reset time in Seconds/Repeat:
Tr = Trec / 3
Controller Gain:
Kc = 4 / (Tr * Kp)
Next, convert the integral time constant to units that
match your controller using one of the following formulas:
Repeats/Minute: TrRPM = 60 / Tr
Minutes/Repeat: TrMPR = Tr / 60
Repeats/Second: TrRPS = 1 / Tr
Finally, if your controller expresses gain as Proportional
Band:
PB = 100 / Kc
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The next tech tip in this series will cover the details of
calculating recovery time for level controls. If
you need help in the mean time,
click here to request more information about SEACON's Control Audit and
Loop Tuning Services. |
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