Advances In PID Control
Advances in PID ControlKarl Johan ÅströmDepartment of Automatic Control, Lund UniversityMarch 10, 2018
Introduction Awareness of PID and need for automatic tuning: The idea - Automatic generation of good input signalsThe patents Tore KJ: Sweden 83, USA 85, .Commercial exploitation NAF Control, Sune Larsson, Ideon: Tore, Båth, SDM 20(84), ECA 40 (86)Ahlsell, Alfa Laval Automation, Satt Control, ABBFisher Controls, Advisory board 88-92, board of directors90-92. Fisher Controls Rosemount [ EmersonProduct development - From 2kbytes to Mbytes KJs Telemetric Experience 79-80, WestreniusEuroterm and Mike SommervilleGain scheduling, continuous adaptationResearch: papers, MS, Lic & PhDResearch GoalsUnderstand PID control and its useHow good models are required?How to find tuning rules - computation dependent This lecture: What have we learned?
Tore – 40 Years of Collaboration Phd student 1978, PhD 1983;New Estimation Techniques forAdaptive Control Relay auto-tuning - patent 1983 NAF 1985-89 Back to the department at LTH1999PID control
Recent PhD Students Kristian Soltesz 2013 On automation in AnesthesiaVanessa Romero 2014 CPU Resource Management andNoise Filtering for PID ControlOlof Garpinger 2015 Analysis and Design ofSoftware-Based Optimal PID ControllersMartin Hast 2015 Design of Low-Order Controllers usingOptimization TechniquesJosefin Berner 2017 Automatic Controller Tuning usingRelay-based Model IdentificationFredrik Bagge Carlson 201X Side projects: OptimizationJulia programming
The Magic of FeedbackFeedback has some amazing properties, it can make good systems from bad components,make a system insensitive to disturbances and componentvariations,stabilize an unstable system,create desired behavior, for example linear behavior fromnonlinear components.The major drawbacks are that feedback can cause instabilities sensor noise is fed into the systemPID control is a simple way to enjoy the Magic!
The Amazing Property of Integral ActionConsider a PI controlleru ke kiZt0e(τ )dτAssume that all signals converge to constant values e(t) e0 ,Rtu(t) u0 and that 0 (e(τ ) e0 )dτ converges, then e0 must be zero.Proof: Assume e0 , 0, thenu(t) ke0 kiZt0e(τ )dτ ke0 kiZ0t e(τ ) e0 dτ ki e0 tThe left hand side converges to a constant and the left hand sidedoes not converge to a constant unless e0 0, furthermoreZ e(τ ) e0 dτu( ) ki0A controller with integral action will always give the correct steadystate provided that a steady state exists. Sometimes expressed as itadapts to changing disturbances.
Predictions about PID Control 1982: The ASEA Novatune Team 1982 (Novatune is auseful general digital control law with adaptation):PID Control will soon be obsolete 1989: Conference on Model Predictive Control:Using a PI controller is like driving a car only looking at therear view mirror: It will soon be replaced by ModelPredictive Control. 2002: Desborough and Miller (Honeywell):Based on a survey of over 11 000 controllers in the refining,chemicals and pulp and paper industries, 98% of regulatorycontrollers utilise PID feedback. The importance of PIDcontrollers has not decreased with the adoption ofadvanced control, because advanced controllers act bychanging the setpoints of PID controllers in a lowerregulatory layer.The performance of the system dependscritically on the behavior of the PID controllers. 2016: Sun LiA recent investigation of 100 boiler-turbine units in theGuangdong Province in China showed 94.4% PI, 3.7% PIDand 1.9% advanced controllers
Entech Experience & Protuner ExperiencesBill Bialkowsk Entech - Canadian consulting company for pulpand paper industry Average paper mill has 3000-5000 loops,97% use PI the remaining 3% are PID, MPC, adaptive etc. 50% works well, 25% ineffective, 25% dysfunctionalMajor reasons why they don’t work well Poor system design 20% Problems with valve, positioners, actuators 30% Bad tuning 30%Process Performance is not as good as you think. D. Ender,Control Engineering 1993. More than 30% of installed controllers operate in manual More than 30% of the loops increase short term variability About 25% of the loops use default settings About 30% of the loops have equipment problems
PID versus More Advanced ControllersPresentErrorPastFuturet u(t) kp β ysp (t) yf (t) kiZt0t TdTime dy dyf spysp (τ ) yf (τ ) dτ kd γ dtdt PI does not predict PID predicts by linear extrapolation, Td prediction horizon Advanced controllers predict using a mathematical model
Publications in Scopus6Pubications per 0200020102020Number of publications by year for control (blue), PID (red) andmodel predictive control (green) from Scopus search for thewords in title, abstract and keywords.
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuners7. Summary
RequirementsndyspFymΣeControllerCuΣ 1PxProcess Attenuate load disturbances d Do not inject too much measurement noise n Robustness to model uncertainty ΣSetpoint response - Can be dealt with separately byfeedforward F – (2 DOF, setpoint weighting, I-PD)y
I–PD Controller with filtering and antiwindupFilteryGf (s) ẏfkd yfkprΣekiuff ActuatorModelΣΣ1sµu ΣesktThe filter (can be combined with antialias filter) d x1010x1 y, Tf 2 Tf 1 x2Tf 2dt x2has the states x1 yf and x2 dyf /dt. The filter thus givesfiltered versions of the measured signal and its derivative. Thesecond-order filter also provides good high-frequency roll-off.
Tune for Load Disturbances - Shinskey 1993“The user should not test the loop using setpoint changes if the set point is to remainconstant most of the time. To tune for fastrecovery from load changes, a load disturbance should be simulated by stepping thecontroller output in manual, and then transferring to auto. For lag-dominant processes,the two responses are markedly different.”Process control: Tune kp , ki , kd and Tf for load disturbances,measurement noise and robustness, then tune β , and γ forsetpoint response. u(t) kp β r (t) yf (t) kiZt01Y (s)Yf (s) 1 sTf s2 Tf 2 /2 dr dy fr (τ ) yf (τ ) dτ kd γdtdt
Assessment of Disturbance ReductionCompare open and closed loop systems!Ycl1 SYol1 PCGeometric interpretation: Disturbances with frequencies outsideare reduced. Disturbances with frequencies inside the circle are amplified by feedback, the maximumamplification is Ms .Disturbances with frequenciesless than sensitivity crossoverfrequency ω sc are reduced byfeedback. 1ω msω sc
Load Disturbance AttenuationTransfer function from load disturbance d to process outpur y (P(0) K )Gyd sP(s)ssP SP (( K (1 PCs Kkis KkikiP 2(s 1) 4 PI: kp 0.5, ki 0.250pGxd (ω )p10 110 210 210 1100ω10110
Criteria and FOTD ModelTraditionally the criteriaZ Z Z IE e(t)dt ,IAE IE2 pe(t)pdt ,e2 (t)dt00Z0 Z 22ITAE t pe(t)pdt ,QE (e (t) ρ u (t))dt00Notice that for a step u0 in the load disturbance we haveZ 1u( ) kie(t)dt ,IE ki0The FOTD modelP(s) Ke sL ,1 sTτ L,L T0 τ 1Lag dominant τ small (τ 0.3) and delay dominant dynamics τclose to 1
Measurement Noise InjectionndCPIDuxΣΣPy GgProcessControllerController transfer functionGf 11 sTf s2 Tf2 /2CPID (s) kp ki kd s,sC CPID GfTransfer function from measurement noise n to control signal u Gun (s) ki kp s kd s2sC SC ( 1 PCs Kki s(1 sTf (sTf )2 /2)Only controller parameters and K P(0)
Bode Plots of Noise Transfer Function GunLag dominated11PI1000 1010 1 110 2100102104110 21001021000 10 101021041021010 110 2100101010101011010 210110PID101010 11010 Delay dominatedBalanced10 210010210410 210010210Validity of approximation (error in mid frequency range Mspeak)Differences PI/PID lag dominated/delay dominated
Stochastic Modeling of Measurement NoiseMeasurement noise stationary with spectral density Φ(ω )Z Z 222σu pGun (i ω )p Φ(ω )d ω , σ yf pGf (i ω )p2 Φ(ω )d ω s2ki kp s kd(s Kki )(1 sTf (sTf )2 /2)!2 2k k2kkkidpiσ u2 ( π 2 d3 Φ0 , KTfTfGun (s) ( σ y2f πΦ0TfNoise gain kn σ u /σ yf and SDU (standard deviation of u withwhite measurement noise Φ0 1)sk2σuki Tfknw kp2 2ki kd 2 d2(σ yfKTfv!u2 2k k2u kikkidpdπ Φ0 1 [ SDU t 2 3KTfTf
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuners7. Summary
Load Disturbance Attenuation and Robustness Performance (IAE 1/ki blue) and robustness (Ms , Mt red)IE level curves are horizontal lines (P(s) (s 1) 1.30.1000.10.2kp0.30.40.5Little difference IE and IAE for ki 0.4 and robust systems Ms 1.6Approximately: ki gives performance and kp sets robustness
Load Disturbance Attenuation and Noise InjectionProcess: P(s) 1e s1 0.1sτ 0.09 lag dominated! 1kController: C kp i kd s s1 sTf (sTf )2 /2MIGO design without filtering: kp 2.78, Ti 47.2, Td 11.6Filter time constants:Tf [0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 50 100]2IE10110010010121010kn
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuners7. Summary
Design ProcessModels - Essentially monotone step responsesZiegler-Nichols - Two parametersThe FOTD model - Three parameters K , L, T G(s) K e sL1 sT Normalized time delay τ L , 0 τ 1L T Lag (small τ ) and delay dominated dynamics τ close to oneMore complex modelsThe test batch - essentially monotone dynamics Heritage of Eurotherm and Mike Sommerville 123 processes10.8y0.60.40.20 0.200.511.52x2.533.5Design controllers and match to model parameters4
Constrained Optimization Modeling & control designCriteriaLoad disturbanceattenuation IE, IAERobustness Ms MtMeasurement noise SDUNoise gain kn Loop transfer functionGl PGf kp ki kd sslinear in parameters Convex-concave methods0ℑ L(i ω ) 1 2 2 1ℜ L(i ω )Many l/0
PI Control: Minimize IAE, Ms , Mt 1.4akp vs τKkp vs τ210110110010010 110 100.20.40.60.81Ti /T vs τ21000.200.40.60.810.81Ti /L vs τ11010010 21010 10 0.20.40.60.811000.20.40.6The two parameter Ziegler-Nichols does not work (reddashed right figures)!Tuning of PI controller can be done with a three parameterFOTD model model
Some Tuning Rules Ziegler-Nichols stepkp 0.9,Kv Lki 0.27,K v L3Ti L/0.3 Ziegler-Nichols frequencykp 0.45ku ,ki 0.54ku,TuTi Tu /1.2 Lambda Tuning - Tcl T , 2T , 3Tkp T,K (Tcl L)ki 1,K (Tcl L)Ti T Skogestad SIMC Like Lambda but Ti min(T , 4(Tcl L)) Skogestad SIMC kp T L/3,K (Tcl L)Ti min(T L/3, 4(Tcl L)) AMIG0 (Ms , Mt 1.4)kp T0.15 LT 0.35 ,K(L T )2 KLTi 0.35L 13LT 2T 2 12LT 7L2
Tuning – Lag-Dominated DynamicsLagdominant201.9S S 181614ki121.610864200 S S AS S 21.81.71.51.41.31.2λ24kp6810Lambda tuning has very low gainsS and S give similar tuningLambda tuning gives constant integral time Ti kp /ki
Tuning – Balanced 0.10.05λSS 1.5ASS λ1.3SS λ0.21.71.41.11.2000.20.40.6kp0.811.2 Tuning methods S , A and λ gives similar results All controllers have constant integral time Ti kp /ki
Tuning Delay-Dominated DynamicsDelay 0.2SS 1.21.6AS 1.4S S 1.50.11.3ZN00 0.050.10.150.2kp0.250.30.350.4Lambda tuning too high integral gainObvious why Skogestad modified his methodAll controllers have constant integral time Ti kp /ki
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuners7. Summary
Difficulties with Derivative Action Shapes of stability region - don’t fall off the cliff10.8ki0.60.40.2000.51kp Filtering necessary1.500.511.5kd22.533.5
Temperature Control P(s) e11.54sIE 0.086, IAE 0.10CPI (s) 2.94 s48.25 0.46ssIE 0.021, IAE 0.031CPID (s) 7.40 System output, y (t)10.20.10123ℑ L(i ω )00 1Control signal, u(t) 20.50 3 3 0.5 1 1.5 2 1ℜ L(i ω )012301
IE or IAE for P (s 1) 3CIEIAECκIAECIAEIAE16.62 6.26s 3.31 s 0.743.20 3.61 3.34ss 0.573.33 3.81 4.25ss 0.530.50 0.5 1 1.5 2 2.5 3 3 2.5 2 1.5 1 0.500.50.20.150.10.050 0.05 0.1024681012141618201
PID Control: Minimize IAE, Ms , Mt 1.4Kkp vs τ210210111010001010 110 100.20.40.60.81Ti /T vs τ1100.60.810.810.81010 2 100.20.40.60.81Td /T vs τ11010000.20.40.6Td /L vs τ11001010 1 11010 2 0.4Ti /L vs τ1 1 0.21010 0100101021010aK kp KL/T vs τ 200.20.40.60.811000.20.40.6Tuning rules based on FOTD can be found for τ 0.3More complex models for lag dominated dynamicsKKLimiting cases 1 sTe sLe sL and (1 sT/2)2
Modeling for PI & PID ControlAMIGO Tuning - complete testbatchki [PID]/ki [PI] vs τ21011001000.10.2circles: P(s) 0.30.4Ke sL ,1 sT0.50.60.7squares: P(s) 0.80.91Ke sL(1 sT )2FOTD OK for τ 0.4 better model required for smaller τ !Derivative action small improvement for τ 0.8
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuning7. Summary
Relay Auto-tuning1y0.50 0.5 1051015t202530Relay feedback creats oscillation at ω 180 !Automation of ZN frequency response method modified ZN tuning rules
The First Industrial Test 1982
Temperature Control of Distillation Column
Commercial Autotuners One-button autotuningThree settings: fast, slow,delay dominatedAutomatic generation of gainschedulesAdaptation of feedback gainsAdaptation of feedforwardgainMany versionsSingle loop controllersDCS systems RobustExcellent industrialexperienceLarge numbers
Industrial SystemsFunctions Automatic tuning AT Automatic generation of gain scheduling GC Adaptive feedback AFB and adaptive feedforward AFFSample of products NAF Controls SDM 20 - 1984 DCS AT, GS SattControl ECA 40 - 1986 SLC AT, GS Satt Control ECA 04 - 1988 SLC AT Alfa Laval Automation Alert 50 - 1988 DCS AT, GS Satt Control SattCon31 - 1988 PLC AT, GS Satt Control ECA 400 -1988 2LC AT, GS, AFB, AFF Fisher Control DPR 900 - 1988 SLC Satt Control SattLine - 1989 DCS AT, GS, AFB, AFF Emerson Delta V - 1999 DCS AT, GS, AFB, AF ABB 800xA - 2004 DCS AT, GS, AFB, AFF
Next Generation of AutotunersObservations A sine-wave input permits estimation of only twoparametersPI controllers can be designed based on an FOTD modelLittle difference between PI and PID for processes withdelay dominated dynamics Improvement by derivative action a factor 2 for τ 0.45 PID controllers require better modeling if τ 0.4 Separate real delays from higher order dynamics Suitable model classesRequirement on an auto-tuner Good excitation - modify relay and experiments Short experiment time - do not wait for steady state Other types of inputs - asymmetric relay additional inputs Trade-off buttons - performance & robustness related
ModelsTwo parameter modelsP(s) b,s aP(s) K e sLThree parameter modelsb, a1 s a2Ke sLP(s) (1 sT )2P(s) s2P(s) be sL ,s aP(s) Ke sL1 sTFour parameter modelsP(s) s2b1 s b 2, a1 s a2P(s) s2be sL a 1 s a2Five parameter modelP(s) s2b1 s b 2e sL a 1 s a2
2510012131415 1161025100 5u11010203040 1501025100 510121416Time [s]1820Figure from Josefin Berneryu 510y10 122yuTypical Experiments
Better Excitation with Asymmetric Relay U 2 R U 20.080.060.040.020.000123 Symmetric relay blue Asymmetric relay red45ω [rad/s]6Figure from Josefin Berner78910
Chirp Signal – Broadband Excitationu(t) (a b t) sin (c d t)tFrequency varies between a and c d tmax amplitude betweena b tmax4u(t)20 2 tice both high and low frequency excitation
Asymmetric Relay and ChirpAsymmetrical relay experiment combined chirp signalexperiment Double experiment time. Constant amplitude,L 0.01, w 15 (1 0.5 t), tmax 2.7,0.15 ω L 0.35 Relay onlyRelay and ChirpP(s) b exp( sL)/(s2 a1*s a2)b exp( sL)/(s2 a1 s a2)001010 1 11010 210 2 210 110010110210010 210 90 90 180 180 270 210 1100101102100 110010110210 270 210 110010110210
Outline1. Introduction2. Requirements3. Tradeoffs4. PI Control5. PID Control6. Relay Auto-tuners7. Summary
SummaryInsight into PID control PI control can be designed based on FOTD modelImportance of lag and delay dominant dynamics andnormalized time delay τPI is sufficient for delay dominated processes τ 0.8Derivative action helps for τ 0.8Derivative action gives significant improvement for τ 0.4but improved models are requiredNext generation of relay auto-tuners Use system identification and model testing Use algorithms instead of simple tuning rules Admits tuning knob
controllers utilise PID feedback. The importance of PID controllers has not decreased with the adoption of advanced control, because advanced controllers act by changing the setpoints of PID controllers in a lower regulatory layer.The performance of the system depends critically on the behavior of the PID controllers. 2016: Sun Li
PID-controller Today most of the PID controllers are microprocessor based DAMATROL MC100: digital single-loop unit controller which is used, for example, as PID controller, ratio controller or manual control station. Often PID controllers are integrated directly into actuators (e.g valves, servos)File Size: 1MBPage Count: 79Explore furtherWhen not to use PID-controllers - Control Systems .www.eng-tips.comPID Controller-Working and Tuning Methodswww.electronicshub.org(PDF) DC MOTOR SPEED CONTROL USING PID CONTROLLERwww.researchgate.netTuning for PID Controllers - Mercer Universityfaculty.mercer.eduLecture 9 – Implementing PID Controllerscourses.cs.washington.eduRecommended to you b
typical unit negative feedback control system [4]. PID control theory is widely used in the field of industrial automation control. The basic principle is clear and concise. As a useful complement to PDCA theory, PID control theory has good feasibility.PID control theory uses PID control ideology to supplement and improve the correction
Standard PID Control A5E00204510-02 Finding Your Way Chapter 1 provides you with an overview of the Standard PID Control. Chapter 2 explains the structure and the functions of the Standard PID Control. Chapters 3 helps you to design and start up a Standard PID Control. Chapters 4 explains the signal processing in the setpoint .File Size: 1MB
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Plot System Responses . (time-domain response) or Bode plots (frequency-domain response). For 1-DOF PID controller types such as PI, PIDF, and PDF, PID Tuner computes system responses based upon the following single-loop control architecture: For 2-DOF PID controller types such as PI2, PIDF2, and I-PD, PID Tuner computes responses based upon .
Logic Controllers), DCS (Distributed Control System) or single loop or stand alone controllers. The PID principle is also the basic for many advances control strategies. In this paper a novel optimal PID controller tuning approach based on the HC12 is proposed. The optimal PID parameters design
PID Control Proportional-Integral-Derivative (PID) controllers are one of the most commonly used types of controllers. They have numerous applications relating to temperature control, speed control, position control, etc. A PID
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