1. ChE / MET 433
19 Mar 12
30 Mar 07
2 Apr 08
27 Mar 09

2. 19 Mar 12 Ziegler-Nichols (ZN I) (QDR or QAD Tuning)
ChE / MET 433
19 Mar 12 Ziegler-Nichols (ZN I) (QDR or QAD Tuning)
(Ultimate Gain)
30 Mar 07
2 Apr 08
27 Mar 09 + + + -

3. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

4. Ziegler Nichols I (Ultimate Gain Method)
Procedure, done closed loop (on-line):
P-Only (switch off integral & derivative modes)
Controller in Auto mode (closed loop)
Adjust Kc
“bump” process with small setpoint change
Find Kc where loop response is undamped

5. Dynamic Changes as Kc is Increased for a FOPDT Process

6. Ziegler Nichols I (Ultimate Gain Method)
Procedure, done closed loop (on-line):
P-Only (switch off integral & derivative modes
Controller in Auto mode (closed loop)
Adjust Kc
“bump” process with small setpoint change
Find Kc where loop response is undamped
Record Kc (call it Kcu – the ultimate gain)
Measure Tu (the ultimate period)
Use Table to get tuning constants
Adjust controller settings to calculated values
Test to see if need to make fine adjustments

7. Quarter-decay-ratio response (sometimes called QAD)

8. Ziegler Nichols I (Ultimate Gain Method)
Response to disturbance should be close to QDR (QAD)
Advantages:
Don’t need to know mathematical models
Easy to use
Use on any process you can get to oscillate
Disadvantages:
Must force loop / process to oscillate (operating close to unstable)
Tuning constants not unique, except for P-only

9. Quarter Decay Ratio (QAD)
Advantages:
Good for load disturbances
Prevents large initial deviations w/o too much oscillations
Gives good “Ball Park” values; leading to fast responses for most processes
Disadvantages:
For SP changes, may overshoot too much
Parameters for PI, PID, not unique
May be too aggressive for cases where K or to change.

10. PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
Launch Loop Pro Trainer
Select Case Studies
Select Gravity Drained Tanks
Press the pause button
Adjust controller output to 50%
Press run (continue) button and let run till achieve steady state
Click the rescale button to re center the plot
Adjust controller output to achieve a level in tank 2 of 2 meters
Click the controller button and turn to PID control (P-Only)
You may have to turn the Integral part off; and Kc = 4 %/m
Press run button and adjust the disturbance up and down 0.5 l/min
Then adjust the set point up and down 0.5 m
Observe how the system behaves.

11. PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
Launch Loop Pro Trainer
Select Case Studies
Select Gravity Drained Tanks
Now, double Kc and observe effect.
Double it again…
Try it at Kc = 2 %/m

12. PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
Now turn on the Integral term (tI should be 4.0 min) and do the same adjustments, observing the behavior of the system.
You may need to adjust the History to see the full change.
Change tI and observe the effect.
Make sure you are back to the original settings (SP = 2m, Level at 2 m, etc) when you start and end with the PI controller.
Note.. double Tau I to 8 min… then work Tau I down to 0.5 min…or lower … and observe

13. PS Exercise: Tuning Two Tanks in Series
Loop Pro Trainer (process simulator):
Now turn on the Integral term (tI should be 4.0 min) and do the same adjustments, observing the behavior of the system.
You may need to adjust the History to see the full change.
Change tI and observe the effect.
Make sure you are back to the original settings (SP = 2m, Level at 2 m, etc) when you start and end with the PI controller.
Now let’s tune the controller.
Use the Ziegler Nichols I method to find Kcu and Tu.
Tune the controller for:
P – only control
And then for PI control.

14. Loop-Trainer
Kcu ~ 72, delta R = 4 –> 4.5

15. Kcu ~ 72, delta R = 4 –> 4.5…set Kc = 1/2Kcu = 36

16. ChE / MET 433
21 Mar 12
30 Mar 07
2 Apr 08
27 Mar 09

17. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

18. PS Exercise: Tuning Two Tanks in Series
Different opinions:
Different correlations will give different constants in the controller equations. D. Cooper suggests if one is uncertain, to start conservative, i.e. with the smallest controller gain and the largest integral (reset) time, thus, giving the least aggressive controller. Final controller tuning may best be performed on-line by trial and error, using experience and knowledge of the process, to obtain the desired controller performance.
To changes in the setpoint or load disturbances:
if the process response is sluggish; Kc is too small and/or I is too large.
if the process response is too quick and perhaps oscillating is not desired; Kc is too large and/or I is too small.
Ziegler-Nichols may be too aggressive for many ChE applications. Luyben (Plantwide Dynamic Simulators in Chemical Processing and Control, Wiley, 2002) suggests for PI controller Kc = Ku / 3.2 and I = 2.2 * Tu .

19. Step Change Responses:Kc tI

20. Properly tuned controller
Is Kc or tI too high?
Kc too large
Properly tuned controller
tI too large

21. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules; FOPDT fit to Open Loop Step Test
Ziegler-Nichols Open Loop (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

22. Ziegler Nichols II (ZN II) Fit response to FOPDT model+ + + -
30 Mar 07
2 Apr 08
27 Mar 09

23. Ziegler Nichols II (FOPDT fit)
Procedure, usually done open loop:
Put controller in Manual mode
Manually make step change in controller output
Observe (record) data and fit to FOPDT model

24. Open-Loop Step Test……..FOPDT

25. Open-Loop Step Test……..FOPDT: Loop Pro Method

26. Open-Loop Step Test……..FOPDT: Loop Pro Method

27. Open-Loop Step Test……..FOPDT: Loop Pro Method

28. Open-Loop Step Test……..FOPDT: Smith & Corripio Method

29. Open-Loop Step Test……..FOPDT: Smith & Corripio Method
Estimation of
Fit 3 suggested for non-integrating processes:
Fit 3: p 239

30. Open-Loop Step Test……..FOPDT: Smith & Corripio Method
Estimation of
Fit 1 suggested for integrating processes.
What happens to h ?? h
= constant
integrating process h
non-integrating process
(self-regulating)

31. Ziegler Nichols II (FOPDT fit)
Procedure in open loop:
Put controller in Manual mode
Manually make step change in controller output
Observe (record) data and fit to FOPDT model

32. Cohen-Coon: Procedure same as for ZN II (open loop step test):
The Ziegler-Nichols rules are more sensitive to the ratio of dead time to time constant, and work well only on processes where the dead time is between 1/4 and 2/3 of the time constant.
The Cohen-Coon tuning rules work well on processes where the dead time is between 1/10 and 4 times the time constant.
“Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going unstable if the process gain or dead time doubles in value.” Smuts suggests reducing Kc by ½ to avoid problems later on.
* Jacques F. Smuts, Process Control for Practitioners, Opticontrols, Inc (2011)

33. PS Exercise: Compare “Loop Pro” and “Fit 3” FOPDT Methods
Find Tau, K, and to by both methods. Compare.

34. PS Exercise: Use The Step Test (ZN II, or Open Loop FOPDT Fit) to Tune The PI Controller
Launch Loop Pro Trainer
Select Case Studies
Select Gravity Drained Tanks
Press the pause button
Adjust controller output to 51%
Tune controller for operation around a tank level of 2 meters

35. ChE / MET 433
23 Mar 12
30 Mar 07
2 Apr 08
27 Mar 09

36. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

37. Time Integral Performance Criteria
disturbance/load change
setpoint change
Integrate error from old SP
Integrate error from new SP

38. Time Integral Performance Criteria
Smith/Murrill developed unique tuning relationships
IAE (Integral of the Absolute value of the Error)
ITAE (Integral of the Time-weighted Absolute value of the Error)
Eqn: p 245
Determine type of input/forcing function (i.e. purpose of controller)
maintain c(t) at setpoint (“Regulator” controller)
c(t) track setpoint signal (“servo” control)

39. Time Integral Performance Criteria

40. Time Integral Performance Criteria

41. PS EX: Find PI Parameters for IAE Criteria
For disturbance change

42. PS EX: Find PI Parameters for IAE Criteria
Launch Loop Pro Trainer
Select Case Studies
Select Gravity Drained Tanks
Put your PI tuning parameters into the simulator controller and check tuning.
Do the parameters need to be adjusted?

43. In-Class EX: Loop Pro Demo Fitting
Show how Loop Pro Trainer can be used to fit FOPDT

44. Import POLYMATH run DATA for step change…

45. ChE / MET 433
26 Mar 12
30 Mar 07
2 Apr 08
27 Mar 09

46. Step Testing Thoughts Single step; can be analyzed by hand
Pulse, doublet, pseudo-random binary sequence (PRBS) tests; require computer tools for analysis
Data collected should meet these criteria:
Process at steady state before data collected
Signal to noise ratio should be 10 or greater
Collected data should be done when no disturbances were present
After fitting, the model appears to fit the data visually

47. Step Testing Thoughts Single step
+ simple, graphical analysis can be done
long time away from desired operating level (DLO; or SP)
Data only on one side of DLO
Pulse (two step tests in rapid succession; 1 up and 1 back down)
+ only need to let measured process variable show a clear response
long time away from desired operating level (DLO; or SP)
Data only on one side of DLO
Single step: 35 – 40 min till hit SS change… long time to be

48. Step Testing Thoughts Doublet Test
+ two pulse tests; one up; one down; ending at beginning level
+ obtain data on both sides of DLO
+ relatively quickly return to normal operation level
+ a preferred method of some in industry for open loop tests
since done open loop; could be concern for certain systems

49. Step Testing Thoughts PRBS Test (pseudo-random binary sequence )
+ theoretically PV shouldn’t vary far from DLO
need a well defined, random test
should have some idea of process gain, time constant, and deadtime
might take longer than a doublet test
Single step: 35 – 40 min till hit SS change… long time to be

50. Step Testing Comparisons
Doublet
PRBS
Single step was ~35 min….. Shortened doublet is ~15 min!

51. PS EX: Find PI Parameters for IAE Criteria
Compare K, Tau, to, and Kc and Tau I to the single step test…..
Redo it but don’t let the PV achieve SS until the end. How does it compare?

52. Step Testing Thoughts Can do closed loop studies, and fit to FOPDT
Controller aggressive enough for 10 times S to N response
Data should begin and end at steady state
No load disturbances should occur
Do step, pulse, doublet changes to the set point.
Fit data to FOPDT; check tuning parameters on the process
Using an aggressive P-only controller may be better, since adding in Integral time changes order of the perceived “process”..

53. ChE / MET 433
28 Mar 12
30 Mar 07
2 Apr 08
27 Mar 09

54. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

55. Auto-Tune Variation (ATV)*
Relay feed back test or ATV
+ Keeps process close to normal operation
+ More efficient for process with long time constant.
General method:
determine reasonable h value to move FCE (3 – 10 % change)
Input the change +h
When PV starts to move, input change of –2h
When PV cross the set point, input change of +2h
When PV re-crosses the set point, input change of –2h
Repeat until constant oscillations of PV are maintained (~3-4 cycles)
Record amplitude (a) and period of oscillation (Pu)
* Åström and Hägglund (1983);
* Luyben & Luyben (1997)

56. Auto-Tune Variation (ATV)
Calculate Ku from ATV results.*
ZN settings
TL settings** (less aggressive and recommended for more sluggish processes)
* Riggs & Karim (2006)
** TL = Tyreus & Luben

57. Auto-Tune Variation (ATV)
Relay feed back test or ATV
+ Keeps process close to normal operation
+ More efficient for process with long time constant.
Much faster than open loop test.
As a result, it is less susceptible to disturbances
Does not unduly upset the process.
From Riggs.
Riggs & Karim (2006)

58. PS EX: Find PI Parameters using the ATV Method

59. Auto-Tune or Self-Tuning Controllers
General loop auto-tuning:
On demand or on-the-fly (continuous updating)
Can be simple step test or pulse doublet
Can be sophisticated self-tuning for difficult process
Example single point industrial controllers:

60. Example single point industrial controllers:

61. http://www05. abb. com/global/scot/scot203

62. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

63. Trial and Error (field tuning)*
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
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
* J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006)

64. Trial and Error (field tuning)*
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.
* J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006)

65. Kc and I levels good? Kc tI

66. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

67. Rules of Thumb *
* D.A. Coggan, ed., Fundamentals of Industrial Control, 2nd ed., ISA, NC (2005)

68. Higher Order Process

69. Feedback Controller Tuning: (General Approaches)
Simple criteria; i.e QAD via ZN I, tr, etc
easy, simple, do on existing process
multiple solutions
Time integral performance criteria
ISE integral square error
IAE integral absolute value error
ITAE integral time weighted average error
Semi-empirical rules
FOPDT (ZN II)
Cohen-Coon
ATV, or Autotuning
Trial and error
Rules of thumb

70. ChE / MET 433
30 Mar 07
2 Apr 08
27 Mar 09