Report

ChE / MET 433 19 Mar 12 1 ChE / MET 433 19 Mar 12 Ziegler-Nichols (ZN I) (QDR or QAD Tuning) (Ultimate Gain) Ls GL ?? GP ?? Rs + E s M (s ) Gc GP GL + + C s 2 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 3 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 o “bump” process with small setpoint change o Find Kc where loop response is undamped 4 Dynamic Changes as Kc is Increased for a FOPDT Process Time Time Time K CU ultimate gain Time Time Time 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 o “bump” process with small setpoint change o Find Kc where loop response is undamped • Record Kc (call it Kcu – the ultimate gain) TU • 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 6 Quarter-decay-ratio response (sometimes called QAD) 7 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 8 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. 9 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. 10 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 11 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. 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. 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. 13 Loop-Trainer Kcu ~ 72, delta R = 4 –> 4.5 14 Kcu ~ 72, delta R = 4 –> 4.5…set Kc = 1/2Kcu = 36 15 ChE / MET 433 21 Mar 12 16 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 17 PS Exercise: Tuning Two Tanks in Series Different opinions: 1. 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 tI is too large. • if the process response is too quick and perhaps oscillating is not desired; Kc is too large and/or tI is too small. 2. 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 tI = 2.2 * Tu . 18 Step Change Responses: Kc tI 19 c (t ) or %CO m Kc too large Is Kc or tI too high? Lag Properly tuned controller cy(s t ) or PV cm(t ) or %CO Time Lag ycs(t ) or PV c (t ) or %CO m Time Lag ycs(t ) or PV tI too large Time 20 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules; FOPDT fit to Open Loop Step Test • Ziegler-Nichols Open Loop (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 21 Ziegler Nichols II (ZN II) Fit response to FOPDT model Ls GL ?? GP ?? Rs + E s M (s ) Gc GP GL + + C s - K e to s GP t s 1 KV , KT , K P all in K 22 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 K e to s fit t s 1 K process SS gain t effective process time constant to effective process dead time 23 Open-Loop Step Test……..FOPDT 24 Open-Loop Step Test……..FOPDT: Loop Pro Method K K K 25 Open-Loop Step Test……..FOPDT: Loop Pro Method t t t t t 26 Open-Loop Step Test……..FOPDT: Loop Pro Method to to to 0.3 min 27 Open-Loop Step Test……..FOPDT: Smith & Corripio Method cs c(t ) m K cs m m(t ) 28 Open-Loop Step Test……..FOPDT: Smith & Corripio Method Estimation of t & to Fit 3 suggested for non-integrating processes: @ 0.632cs @ 0.283cs cs t 3 2 t2 t1 to t 2 t t1 Fit 3: 7-2.16 p 239 t2 29 Open-Loop Step Test……..FOPDT: Smith & Corripio Method Estimation of t & to Fit 1 suggested for integrating processes. Fin if Fin A u (t ) Fin What happens to h ?? h Fout = constant integrating process h non-integrating process (self-regulating) Fout h 30 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 K e to s fit t s 1 K process SS gain t effective process time constant to effective process dead time t 0.1 o 0.5 t 31 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) 32 PS Exercise: Compare “Loop Pro” and “Fit 3” FOPDT Methods 33 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 34 ChE / MET 433 23 Mar 12 35 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 36 Time Integral Performance Criteria •disturbance/load change Integrate error from old SP c(t ) SP (old ) •setpoint change c(t ) new SP Integrate error from new SP 37 Time Integral Performance Criteria Smith/Murrill developed unique tuning relationships •IAE (Integral of the Absolute value of the Error) IAE e(t ) dt Eqn: 7-2.17 p 245 0 •ITAE (Integral of the Time-weighted Absolute value of the Error) ITAE t e(t ) dt 0 •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) 38 Time Integral Performance Criteria 39 Time Integral Performance Criteria 40 PS EX: Find PI Parameters for IAE Criteria 41 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? 42 In-Class EX: Loop Pro Demo Fitting 43 44 ChE / MET 433 26 Mar 12 45 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 46 Single step Step Testing Thoughts + 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 47 Doublet Test Step Testing Thoughts + 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 48 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 49 Step Testing Comparisons PRBS Doublet 50 PS EX: Find PI Parameters for IAE Criteria 51 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 52 ChE / MET 433 28 Mar 12 53 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 54 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) c(t ) sp m(t ) * Åström and Hägglund (1983); * Luyben & Luyben (1997) 55 Auto-Tune Variation (ATV) 4h Ku a K ZN c 0.45 K u K cTL 0.31Ku t ZN I Pu / 1.2 t ITL Pu / 0.45 • Calculate Ku from ATV results.* • ZN settings • TL settings** (less aggressive and recommended for more sluggish processes) * Riggs & Karim (2006) ** TL = Tyreus & Luben 56 Auto-Tune Variation (ATV) Relay feed back test or ATV + Keeps process close to normal operation + More efficient for process with long time constant. Mole Percent 2.3 2.2 Open Loop Test 2.1 ATV Test 2 1.9 0 20 40 Time (hours) 60 Riggs & Karim (2006) 57 PS EX: Find PI Parameters using the ATV Method 58 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 59 Example single point industrial controllers: 60 61 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 62 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 ys c a b Time * J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006) 63 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. c b ys • • • • a Time * J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006) 64 Kc and Kc tI levels good? tI 65 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 66 Rules of Thumb * * D.A. Coggan, ed., Fundamentals of Industrial Control, 2nd ed., ISA, NC (2005) 67 Higher Order Process 68 Feedback Controller Tuning: (General Approaches) 1) Simple criteria; i.e QAD via ZN I, tr, etc • easy, simple, do on existing process • multiple solutions 2) Time integral performance criteria • ISE integral square error • IAE integral absolute value error • ITAE integral time weighted average error 3) Semi-empirical rules • FOPDT (ZN II) • Cohen-Coon 4) ATV, or Autotuning 5) Trial and error 6) Rules of thumb 69 ChE / MET 433 70