PID Tuning Methods

1
Chapter 9

• PID Tuning Methods

2
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

3
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.

4
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

5
Decay Ratio for Non-Symmetric Oscillations
6
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.

7
Example of an SPC Chart
8
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)

9
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.

10
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.

11
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.

12
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.

13
Controller Reliability

• 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.

14
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.

15
Controller Reliability Example CSTR with DCA0
Upsets
16
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.

17
Tuning Criterion Selection
18
Tuning Criterion Selection
19
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.

20
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

21
Effect of Tuning Criterion on Control Performance

• The more aggressive the control criterion, the
  better the control performance, but the more
  likely the controller can go unstable.

22
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.

23
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

24
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

25
Field Tuning Approach

• Decrease Kc by 10.
• Make initial estimate of tI (i.e., tI5tp).
• Reduce tI until offset is eliminated
• Check that proper amount of Kc and tI are used.

26
An Example of Inadequate Integral Action

• Oscillations not centered about setpoint and slow
  offset removal indicate inadequate integral
  action.

27
Demonstration Visual Basic Simulator

• Field Tuning Example

28
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
• KcKcZN/FT tItIZNFT

29
ATV Test

• 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.

30
Applying the ATV Results

• Calculate Ku from ATV results.
• ZN settings
• TL settings

31
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.

32
Advantages of ATV Identification

• Much faster than open loop test.
• As a result, it is less susceptible to
  disturbances
• Does not unduly upset the process.

33
Online Tuning

• Provides simple one-dimensional tuning which can
  be applied using setpoint changes or observing
  controller performance over a period of time.

34
ATV Test Applied to Composition Mixer
35
CST Composition Mixer Example

• Calculate Ku
• Calculate ZN settings
• Apply online tuning

36
Online Tuning for CST Composition Mixer Example

• FT0.75
• FT0.5

37
Control Performance for Tuned Controller
38
Critically Damped Tuning for CST Composition Mixer
39
Comparison Between 1/6 Decay Ratio and Critically
Damped Tuning
40
Demonstration Visual Basic Simulator

• ATV based tuning

41
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 tDPu/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.

42
Comparison between PI and PID for the Heat
Exchanger Model
43
Comparison of PI and PID

• The derivative action allows for larger Kc which
  in turn results in better disturbance rejection
  for certain processes.

44
Demonstration Visual Basic Simulator

• PID Tuning Example

45
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.

46
Initial Settings for Level Controllers for PI
Control

• 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.

47
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.

48
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.

49
Control Interval, Dt

• Dt is usually 0.5 to 1.0 seconds for regulatory
  loops and 30 to 120 seconds for supervisory loops
  for DCSs.
• In order to adequately approach continuous
  performance, select the control interval such
  that Dt lt 0.05(qptp)
• 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

50
Effect of Control Interval on Control Performance

• qp 0.5
• When the controller settings for continuous
  control are used with Dt0.5, instability
  results.
• Results shown here are based on retuning the
  system for Dt0.5 resulting in a 60 reduction in
  Kc.

51
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.

52
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.