Transcript Chapter 7

Chapter 9
PID Tuning Methods
Overall Course Objectives
• Develop the skills necessary to function as an
industrial process control engineer.
– Skills
•
•
•
•
Tuning loops
Control loop design
Control loop troubleshooting
Command of the terminology
– Fundamental understanding
• Process dynamics
• Feedback control
Controller Tuning
• Involves selection of the proper values of
Kc, tI, and tD.
• Affects control performance.
• Affects controller reliability
• Therefore, controller tuning is, in many
cases, a compromise between performance
and reliability.
Tuning Criteria
• Specific criteria
– Decay ratio
– Minimize settling time
• General criteria
– Minimize variability
– Remain stable for the worst disturbance upset
(i.e., reliability)
– Avoid excessive variation in the manipulated
variable
Decay Ratio for Non-Symmetric
Oscillations
B
C
Decay Ratio = C/B
Time
Performance Assessment
• Performance statistics (IAE, ISE, etc.)
which can be used in simulation studies.
• Standard deviation from setpoint which is a
measure of the variability in the controlled
variable.
• SPC charts which plot product composition
analysis along with its upper and lower
limits.
Example of an SPC Chart
Product Composition
Upper Limit
Lower Limit
0
1
2
3
4
Time (days)
5
6
7
Classical Tuning Methods
• Examples: Cohen and Coon method, ZieglerNichols tuning, Cianione and Marlin tuning, and
many others.
• Usually based on having a model of the process
(e.g., a FOPDT model) and in most cases in the
time that it takes to develop the model, the
controller could have been tuned several times
over using other techniques.
• Also, they are based on a preset tuning criterion
(e.g., QAD)
Controller Tuning by Pole
Placement
• Based on model of the process
• Select the closed-loop dynamic response
and calculate the corresponding tuning
parameters.
• Application of pole placement shows that
the closed-loop damping factor and time
constant are not independent.
• Therefore, the decay ratio is a reasonable
tuning criterion.
Controller Design by Pole
Placement
• A generalized controller (i.e., not PID) can
be derived by using pole placement.
• Generalized controllers are not generally
used in industry because
– Process models are not usually available
– PID control is a standard function built into
DCSs.
IMC-Based Tuning
• A process model is required (Table 9.4
contain the PID settings for several types of
models based on IMC tuning).
• Although a process model is required, IMC
tuning allows for adjusting the
aggressiveness of the controller online using
a single tuning parameter, tf.
Controller Reliability
• The ability of a controller to remain in
stable operation with acceptable
performance in the face of the worst
disturbances that the controller is expected
to handle.
Controller Reliability
d3
d2
d3 > d2 > d1
y
d1
Time
• Analysis of the closed
loop transfer function
for a disturbance
shows that the type of
dynamic response
(i.e., decay ratio) is
unaffected by the
magnitude to the
disturbance.
Controller Reliability
• We know from industrial experience that
certain large magnitude disturbance can
cause control loops to become unstable.
• The explanation of this apparent
contradiction is that disturbances can cause
significant changes in Kp, tp, and qp which a
linear analysis does not consider.
Controller Reliability Example:
CSTR with DCA0 Upsets
T' (K)
4
D CA0 =-0.5
2
0
D CA0 =0.5
-2
0
40
80
120
Time (seconds)
160
Controller Reliability
• Is determined by the combination of the
following factors
– Process nonlinearity
– Disturbance type
– Disturbance magnitude and duration
• If process nonlinearity is high but disturbance
magnitude is low, reliability is good.
• If disturbance magnitude is high but process
nonlinearity is low, reliability is good.
Tuning Criterion Selection
LC
L
Pl u g Fl ow Re actor
D
Tuning Criterion Selection
Produ ct
Fe e d
LC
Produ ct
Produ ct
Produ ct
Tuning Criterion Selection Procedure
• First, based on overall process objectives,
evaluate controller performance for the loop
in question.
• If the control loop should be detuned based
on the overall process objectives, the tuning
criterion is set.
• If the control loop should be tuned
aggressively based on the overall process
objectives, the tuning criterion is selected
based on a compromise between
performance and reliability.
Selecting the Tuning Criterion
based on a Compromise between
Performance and Reliability
• Select the tuning criterion (typically from
critically damped to 1/6 decay ratio) based
on the process characteristics:
– Process nonlinearity
– Disturbance types and magnitudes
Effect of Tuning Criterion on
Control Performance
2.3
Critically Damped
Level
2.2
DR=1/10
2.1
2
DR=1/6
1.9
0
50
100
150
Time (seconds)
200
• The more aggressive
the control criterion,
the better the control
performance, but the
more likely the
controller can go
unstable.
Filtering the Sensor Reading
• For most sensor readings, a filter time
constant of 3 to 5 s is more than adequate
and does not slow down the closed-loop
dynamics.
• For a noisy sensor, sensor filtering usually
slows the closed-loop dynamics. To
evaluate compare the filter time constant
with the time constants for the acutator,
process and sensor.
Recommended Tuning Approach
• Select the tuning criterion for the control
loop.
• Apply filtering to the sensor reading
• Determine if the control system is fast or
slow responding.
– For fast responding, field tune (trail-and-error)
– For slow responding, apply ATV-based tuning
Field Tuning Approach
• Turn off integral and derivative action.
• Make initial estimate of Kc based on process
knowledge.
• Using setpoint changes, increase Kc until tuning
criterion is met
ys
c
a
b
Time
Field Tuning Approach
Decrease Kc by 10%.
Make initial estimate of tI (i.e., tI=5tp).
Reduce tI until offset is eliminated
Check that proper amount of Kc and tI are used.
c
b
ys
•
•
•
•
a
Time
An Example of Inadequate
Integral Action
Time
• Oscillations not centered about setpoint and slow
offset removal indicate inadequate integral action.
Demonstration: Visual Basic
Simulator
Field Tuning Example
ATV Identification and Online
Tuning
• Perform ATV test and determine ultimate
gain and ultimate period.
• Select tuning method (i.e., ZN or TL
settings).
• Adjust tuning factor, FT, to meet tuning
criterion online using setpoint changes or
observing process performance:
• Kc=KcZN/FT
tI=tIZN×FT
ATV Test
ys
Pu
a
y0
c
c0
h
Time
• Select h so that process
is not unduly upset but
an accurate a results.
• Controller output is
switched when ys
crosses y0
• It usually take 3-4 cycles
before standing is
established and a and Pu
can be measured.
Applying the ATV Results
4h
Ku 
 a
K
ZN
c
 0.45 K u
K cTL  0.31Ku
t
• Calculate Ku from
ATV results.
 Pu / 1.2
• ZN settings
t ITL  Pu / 0.45
• TL settings
ZN
I
Comparison of ZN and TL
Settings
• ZN settings are too aggressive in many
cases while TL settings tend to be too
conservative.
• TL settings use much less integral action
compared to the proportional action than
ZN settings. As a result, in certain cases
when using TL settings, additional integral
action is required to remove offset in a
timely fashion.
Advantages of ATV Identification
Mole Percent
2.3
2.2
Open Loop Test
2.1
ATV Test
2
1.9
0
20
40
Time (hours)
60
• Much faster than open loop test.
• As a result, it is less susceptible to disturbances
• Does not unduly upset the process.
Online Tuning
3
Mole Percent
FT=0.8
2
1
FT=1.6
FT=0.4
0
0
500
1000
1500
Time (minutes)
2000
• Provides simple one-dimensional tuning which
can be applied using setpoint changes or observing
controller performance over a period of time.
Concentration (gmoles/l)
ATV Test Applied to
Composition Mixer
1
0.9
0.8
0.7
0.6
0.5
0
50
100
150
Time (minutes)
200
CST Composition Mixer
Example
• Calculate Ku
• Calculate ZN settings
• Apply online tuning
Concentration
Online Tuning for CST
Composition Mixer Example
0.76
• FT=0.75
0.72
0.68
Concentration
0
100
Time (minutes)
200
0.76
0.72
• FT=0.5
0.68
0.64
0
100
Time (minutes)
200
Concentration (gmoles/l)
Control Performance for Tuned
Controller
0.78
0.76
0.74
0
50
100
150
Time (minutes)
200
Concentration
Critically Damped Tuning for
CST Composition Mixer
0.76
0.72
0.68
0
100
Time (minutes)
200
Concentration (gmoles/l)
Comparison Between 1/6 Decay
Ratio and Critically Damped
Tuning
0.78
Critically
Damped
0.76
0.74
0
50
100
150
Time (minutes)
200
Demonstration: Visual Basic
Simulator
ATV based tuning
PID Tuning Procedure
• Tune PI controller using field tuning or ATV
identification with online tuning.
• Increase tD until minimum response time is
obtained. Initially set tD=Pu/8.
• Increase tD and Kc by the same factor until
desired response is obtained.
• Check response to ensure that proper
amount of integral action is being used.
Comparison between PI and PID
for the Heat Exchanger Model
Temperature (ºF)
120
115
110
105
100
0
50
Time (seconds)
100
Comparison of PI and PID
PID
PI
Time
• The derivative action allows for larger Kc which in
turn results in better disturbance rejection for
certain processes.
Demonstration: Visual Basic
Simulator
PID Tuning Example
Initial Settings for Level
Controllers for P-only Control

 FMAX
Kc 

LMAX
• Based on critically damped
response.
• FMAX is largest expected
change in feed rate.
• LMAX is the desired level
change under feedback
control.
• Useful as initial estimates
for slow responding level
control systems.
Initial Settings for Level
Controllers for PI Control

 0.736FMAX
Kc 

LMAX
4 Ac r
tI 
 Kc
• Ac is cross-sectional area to
tank and r is liquid density.
• FMAX is largest expected
change in feed rate.
• LMAX is the desired level
change under feedback
control.
• Useful as initial estimates
for slow responding level
control systems.
Initial Settings for Level
Controllers
• Use online tuning adjusting Kc and tI with
FT to obtain final tuning.
• Remember that Kc is expressed as
(flow rate/%); therefore, height difference
between 0% and 100% is required to
calculate tI.
In-Class Example
• Calculate the initial PI controller settings
for a level controller with a critically
damped response for a 10 ft diameter tank
(i.e., a cylinder placed on its end) with a
measured height of 10 ft that normally
handles a feed rate of 1000 lb/h. Assume
that it is desired to have a maximum level
change of 5% for a 20% feed rate change
and that the liquid has a density
corresponding to that of water.
Control Interval, Dt
• Dt is usually 0.5 to 1.0 seconds for regulatory
loops and 30 to 120 seconds for supervisory loops
for DCS’s.
• In order to adequately approach continuous
performance, select the control interval such that:
Dt < 0.05(qp+tp)
• For certain processes, Dt is set by the timing of
analyzer updates and the previous formula can be
used to assess the effect on control performance
Effect of Control Interval on
Control Performance
y
continuous
D t=0.5
Time
• qp =0.5
• When the controller
settings for continuous
control are used with
Dt=0.5, instability results.
• Results shown here are
based on retuning the
system for Dt=0.5
resulting in a 60%
reduction in Kc.
Overview
• Controller tuning is many times a
compromise between performance and
reliability.
• Reliability is determined by process
nonlinearity and the disturbance type and
magnitude.
• The controller tuning criterion should be
based on controller reliability and the process
objectives.
Overview
• Classical tuning methods, pole placement
and IMC tuning are not recommended
because they are based on a preset tuning
criterion and they usually require a process
model.
• Tune fast loops should be tuned using field
tuning and slow loops using ATV
identification with online tuning.