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.