chapter 9 pid tuning methods. overall course objectives develop the skills necessary to function as...
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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, I, and D.
• 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
Time
B
C
Decay Ratio = C/B
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
0 1 2 3 4 5 6 7Time (days)
Pro
duct
Com
posi
tion Upper Limit
Lower Limit
Classical Tuning Methods
• Examples: Cohen and Coon method, Ziegler-Nichols 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, f.
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
y
Time
d1
d2
d3
d3 > d2 > d1
• 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, p, and p which a linear analysis does not consider.
Controller Reliability Example: CSTR with CA0 Upsets
-2
0
2
4
0 40 80 120 160Time (seconds)
T' (
K)
CA0=-0.5
CA0=0.5
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
DPlug Flow Reactor
Tuning Criterion Selection
Product
FeedLC
Product
Product
Product
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
1.9
2
2.1
2.2
2.3
0 50 100 150 200Time (seconds)
Lev
el
DR=1/6
Critically Damped
DR=1/10
• 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
Time
y s
ab
c
Field Tuning Approach
• Decrease Kc by 10%.
• Make initial estimate of I (i.e.,I=5p).
• Reduce I until offset is eliminated
• Check that proper amount of Kc and I are used.
Time
y s
a
b
c
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 I=
ZN×FT
ATV Test
Time
a
h
c
ys Pu
y0
c0
• 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
• Calculate Ku from ATV results.
• ZN settings
• TL settings
a
hKu
4
2.1/45.0 uZNIu
ZNc PKK
45.0/31.0 uTLIu
TLc PKK
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
1.9
2
2.1
2.2
2.3
0 20 40 60Time (hours)
Mol
e P
erce
nt Open Loop Test
ATV Test
• Much faster than open loop test.
• As a result, it is less susceptible to disturbances
• Does not unduly upset the process.
Online Tuning
0
1
2
3
0 500 1000 1500 2000Time (minutes)
Mol
e P
erce
nt
FT=1.6
FT=0.8
FT=0.4
• Provides simple one-dimensional tuning which can be applied using setpoint changes or observing controller performance over a period of time.
ATV Test Applied to Composition Mixer
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200Time (minutes)
Con
cent
rati
on (
gmol
es/l)
CST Composition Mixer Example
• Calculate Ku
• Calculate ZN settings
• Apply online tuning
Online Tuning for CST Composition Mixer Example
0.68
0.72
0.76
0 100 200Time (minutes)
Con
cent
rati
on
• FT=0.75
• FT=0.5
0.64
0.68
0.72
0.76
0 100 200Time (minutes)
Con
cent
rati
on
Control Performance for Tuned Controller
0.74
0.76
0.78
0 50 100 150 200Time (minutes)
Con
cent
rati
on (
gmol
es/l)
Critically Damped Tuning for CST Composition Mixer
0.68
0.72
0.76
0 100 200Time (minutes)
Con
cent
rati
on
Comparison Between 1/6 Decay Ratio and Critically Damped
Tuning
0.74
0.76
0.78
0 50 100 150 200Time (minutes)
Con
cent
rati
on (
gmol
es/l)
CriticallyDamped
Demonstration: Visual Basic Simulator
ATV based tuning
PID Tuning Procedure
• Tune PI controller using field tuning or ATV identification with online tuning.
• Increase D until minimum response time is obtained. Initially set D=Pu/8.
• Increase D 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
100
105
110
115
120
0 50 100Time (seconds)
Te
mp
era
ture
(ºF
)
Comparison of PI and PID
Time
PID
PI
• 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
• 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.
MAX
MAXc L
FK
Initial Settings for Level Controllers for PI Control
• Ac is cross-sectional area to tank and 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.
c
cI
MAX
MAXc
K
A
L
FK
4
736.0
Initial Settings for Level Controllers
• Use online tuning adjusting Kc and I 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 I.
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, t
• t 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: t < 0.05(p+p)
• For certain processes, t 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
Time
y
continuous
t=0.5
• p =0.5• When the controller
settings for continuous control are used with t=0.5, instability results.
• Results shown here are based on retuning the system for t=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.
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