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

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 + + + -

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

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

Dynamic Changes as Kc is Increased for a FOPDT Process

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 7-1.1 to get tuning constants Adjust controller settings to calculated values Test to see if need to make fine adjustments

Quarter-decay-ratio response (sometimes called QAD)

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

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.

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.

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

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

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.

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

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

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

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

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 .

Step Change Responses: Kc tI

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

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

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

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

Open-Loop Step Test……..FOPDT

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

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

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

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

Open-Loop Step Test……..FOPDT: Smith & Corripio Method Estimation of Fit 3 suggested for non-integrating processes: Fit 3: 7-2.16 p 239

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)

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

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)

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

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

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

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

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

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: 7-2.17 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)

Time Integral Performance Criteria

Time Integral Performance Criteria

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

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?

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

Import POLYMATH run DATA for step change…

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

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

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 away??@@

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

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 away??@@

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

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?

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”..

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

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

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)

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

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)

PS EX: Find PI Parameters using the ATV Method

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: http://www.watlow.com/downloads/en/manuals/945e_a.pdf

Example single point industrial controllers: http://www05.abb.com/global/scot/scot203.nsf/veritydisplay/92a7e32993766c8bc12573480041630a/$file/ss_c250_7.pdf

http://www05. abb. com/global/scot/scot203 http://www05.abb.com/global/scot/scot203.nsf/veritydisplay/06311f5d1502d0d08025704d00393533/$file/im_c250_5.pdf

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

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)

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)

Kc and I levels good? Kc tI

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

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

Higher Order Process

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

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