CONTROLLER TUNING CONTROL LOOP OPTIMIZATION · • The fundamental trade-off in control loop tuning...

CONTROLCONTROLLERLER TUNINGTUNINGCONTROLCONTROLLERLER TUNINGTUNINGCONTROL LOOP OPTIMIZATIONCONTROL LOOP OPTIMIZATION

© Laboratory for Automatics and Measurement, Faculty of Chemical Engineering and Technology University of Zagreb

OUTLINEOUTLINEOUTLINEOUTLINE

• Control loop dynamics

B i i i l f t ll t iB i i i l f t ll t i•• Basic principle of controller tuningBasic principle of controller tuning

• Controller parameter optimizationController parameter optimization

• The problems with control loop performance

• Tips for controller optimal tuning


LEARNING OBJECTIVESLEARNING OBJECTIVESLEARNING OBJECTIVESLEARNING OBJECTIVES

When you have completed this unit you should:When you have completed this unit, you should:

• Have developed insight into the fundamental concept of tuning feedback controllers;

•• Be able to calculate the tuning parameters for a Be able to calculate the tuning parameters for a f db k t ll i Zi lf db k t ll i Zi l Ni h l lti tNi h l lti tfeedback controller using Zieglerfeedback controller using Ziegler--Nichols ultimate Nichols ultimate periodperiod;;

B bl t l l t th t i t f• Be able to calculate the tuning parameters for a feedback controller using the process reaction curve method.

•• UnderstandUnderstand thethe importanceimportance ofof controllercontroller tuningtuning..


WHATWHAT MEANSMEANS GOOD TUNED CONTROLLERGOOD TUNED CONTROLLER??WHAT WHAT MEANS MEANS GOOD TUNED CONTROLLERGOOD TUNED CONTROLLER? ?

• A feedback control system is of little value if it is improperly tuned;y p p y ;

• It is important for chemical engineers to understand how the controller in a feedback control system should be tuned.y

• To tune a controller you need to determine the optimum values of the controller gain (KC), integral time (τi) i and derivative time (τd);C i) d

• The first problem you encounter when tuning controllers is determining what is good control – it does differ from one process to the other process;

• Good control usually means fast reaction fast reaction and fast response fast response on disturbances and set point (SP) changes, as small as possible overshootovershoot, stability stability and robustness robustness (flexibility on changing in process condition).


COMMON PROBLEMS INCOMMON PROBLEMS IN CONTROL LOOPSCONTROL LOOPSCOMMON PROBLEMS IN COMMON PROBLEMS IN CONTROL LOOPSCONTROL LOOPS

ContinuousContinuous PVPV oscillation aroundoscillation around SPSPContinuous Continuous PVPV oscillation around oscillation around SPSP

PVPV deviation from the deviation from the SPSP

Sluggish Sluggish PV PV response after a response after a SP SP changechange

Overshoot and longOvershoot and long--term term PVPV oscillation after a oscillation after a SP SP changechange


SPEED VERSUS STABILITYSPEED VERSUS STABILITYSPEED VERSUS STABILITYSPEED VERSUS STABILITY

• The fundamental trade-off in control loop tuning is between a control loop’s speedspeed and stabilitystability;control loop s speed speed and stabilitystability;

• If you increase increase speed of responseincrease speed of response to a SP change or disturbance, the loop becomes less stable. If i d th d th t l l ill t ll• If you increased the speed more, the control loop will eventually become completely unstable;

• If a control loop is tuned for stability its speed of response suffers.


ROBUSTNESSROBUSTNESSROBUSTNESSROBUSTNESS

• Process characteristics can be influenced by production rate, valve characteristic, eqipment in service, feedstock composition, operating conditions, etc.

• Control loop robustness is defined as the amount of change in• Control loop robustness is defined as the amount of change in process characteristics the loop can tolerate before it become unstable;

• Instabilty can be caused with increased process gain, increased dead time and decreased time constant;If t l l i t d f t bilitt bilit it b t ill b hi h• If control loop is tuned for stabilitystability, its robustness will be high, and it can tolerate substantial changes in process characteristics;

• If a control loop is tuned for speedspeed, it will have low robustness and can easily become unstable.


CONTROL LOOP SPEED OF THE RESPONSECONTROL LOOP SPEED OF THE RESPONSE

• Due to the dynamic characteristics of the process andcontrol loop actual deviation from SP can not be removed

CONTROL LOOP SPEED OF THE RESPONSECONTROL LOOP SPEED OF THE RESPONSE

control loop actual deviation from SP can not be removedinstantly;

• The control loop can always be adjusted for a slower response but can not always be adjusted for faster responseresponse, but can not always be adjusted for faster response because it will become unstable;


CONTROLLER TUNING PROCEDURECONTROLLER TUNING PROCEDURECONTROLLER TUNING PROCEDURECONTROLLER TUNING PROCEDURE

• In controller tuning the term PROCESS includes all elements between the output of the controller (OP) and the input to the controller (PV);the output of the controller (OP) and the input to the controller (PV);

T ti i th t ll it i t d t i th• To optimize the controller it is necessary to determine the following process parameters: process gain (K),


p g ( ),dead time (Θ), time constant (τ) ili integrating rate (ri)

CONTROLLERCONTROLLER TUNINGTUNING PARAMETERPARAMETER OPTIMIZATIONOPTIMIZATION

CVCVDVDV

CONTROLLER CONTROLLER TUNING TUNING –– PARAMETER PARAMETER OPTIMIZATIONOPTIMIZATION

PROCESPROCESSSMVMV

Time constant Time constant -- ττProcess (steady state) gainProcess (steady state) gain-- kk

Dead time Dead time -- θθ

TransducerTransducerFinal controlFinal controlelementelement

PV PV Controller gainController gain-- kkccIntegral time Integral time -- ττii

D i ti tiD i ti ti

ALGORITHMALGORITHMALGORITHMALGORITHMeeOPOP

Derivative time Derivative time -- ττdd


SPSPCONTROLLERCONTROLLER

CONTROL LOOPCONTROL LOOP TUNING METHODSTUNING METHODS

11 TrialTrial andand error tuningerror tuning

CONTROL LOOP CONTROL LOOP TUNING METHODSTUNING METHODS

1.1. TrialTrial--andand--error tuningerror tuning

-- an iterative tuning method based on making small changes to an iterative tuning method based on making small changes to t ll tti d it i th i ff t th lt ll tti d it i th i ff t th lcontroller setting and monitoring their effect on the loopcontroller setting and monitoring their effect on the loop

2.2. Standard (traditional) tuning methodsStandard (traditional) tuning methods

-- ZieglerZiegler--Nichols Nichols method appeared in 1942;method appeared in 1942;-- CohenCohen--CoonCoon method published roughly decade after;method published roughly decade after;

Most other methods are modifications of the above methods;Most other methods are modifications of the above methods;-- Most other methods are modifications of the above methods;Most other methods are modifications of the above methods;

3.3. Automatic tuning Automatic tuning ((selfself--tuningtuning))

-- Simple methods embedded in controllers (Simple methods embedded in controllers (autotuning functionautotuning function););-- Dedicated software package for loop analysis and optimization.Dedicated software package for loop analysis and optimization.


CONTROL LOOP TUNING PROBLEMSCONTROL LOOP TUNING PROBLEMSCONTROL LOOP TUNING PROBLEMSCONTROL LOOP TUNING PROBLEMS

• Some loops cannot be tuned by any approach;;• Common problems that render a loop untunable are as follows::

11 Deficiencies in the process and instrumentation (P&I) diagram1.1. Deficiencies in the process and instrumentation (P&I) diagram

2.2. Process Process nonlinearitesnonlinearites

3.3. Problems with the final control element (especially valves).Problems with the final control element (especially valves).

44 Measurement noiseMeasurement noise4.4. Measurement noiseMeasurement noise

5.5. Large dead times

6.6. Control loop interactionControl loop interaction

77 I ti f d l


7.7. Improper nesting of cascade loops

11 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD1 1 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD

• An iterative tuning method based on making small changingto the controller setings and monitoring effect on the loop;

• It is the most popular, but unfortunately it is the least effectivep p , yof all tuning method;

• It is suitable for fast and simple standard control loops withthe following characteristics: g

deaddead timetime + time time constantconstant < 5 to10 min

• It is not suitable for slow (sluggish) and the complex controlschemes:

deaddead timetime + timetime constantconstant > 30 mindeaddead time time + time time constantconstant > 30 min


11 -- TRIAL AND ERROR METHODTRIAL AND ERROR METHOD1 1 -- TRIAL AND ERROR METHODTRIAL AND ERROR METHOD

CCoonnttrrooll lloooopp FFCC PPCC LLCC TTCC AACCppCCoonnttrroolllleerr ttyyppee PPII PPII PP,, PPII PPII,, PPIIDD PPIIDD PP [[%%//%%]] 00,,11--33 11--2200 00,,22--1100 00,,55--1100 00,,11--55 II [[mmiinn]] 00,,11--66 00,,55--2200 1155--11000000 55--110000 1100--220000

DD [[mmiinn]] -- 00--22 rraarreellyy

00,,55--44 rraarreellyy 00..55--33 00,,55--44

SSeettttlliinngg ttiimmee [[mmiinn]] 00,,55--22 00,,55--66 ------ 1155--9900 6600--772200 N i ft l ti l i llNNooiissee oofftteenn rraarreellyy ssoommeettiimmeess rraarreellyy ooccccaassiioonnaallllyy NNoonnlliinneeaarriittyy qquuaaddrraattiicc lliinneeaarr lliinneeaarr eexxiissttss eexxiissttss

• The method works on the principle of making a change to one• The method works on the principle of making a change to one of the controller parameter (e.g. control gain) and seeing whateffect it has on the loop’s performance;If the change made the loop perform better keep on chaging in• If the change made the loop perform better, keep on chaging inthe same direction. If it made the loop perform worse, change it in the opposite direction.Aft h h it th ff t f th h th


• After each change, monitor the effect of the change on theloop’s performance.

11 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD

• Once you have reached an optimum value for the first t ( t ll i ) b i th ith th

1 1 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD

parameter (controller gain) begin the same process with thenext controller setting (integral time);

• Once you have the optimum for the second parameter• Once you have the optimum for the second parameter, revisit the first parameter because its optimum value mightbe different now that the second setting has been adjusted;

• If you are adventorous and have enough time, you can alsochange the third controller parameter (derivative time) andinteratively go back to the other two until you finally have an

ti ll t d t lloptimally tuned controller;

• Table on th next slide represents guidance on trial-and-errortuningtuning.


11 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD1 1 –– TRIAL AND ERROR METHODTRIAL AND ERROR METHOD

OOBBSSEERRVVAATTIIOONN

Loop seems sluggish Loop oscillates or overshoots set pointp

CCoorrrreeccttiivvee aaccttiioonn

Control gain Increase DecreasegProportional band Decrease Increase

Integral time Decrease Increase

(min or sec) Integral gain (repeat / min or sec) Increase Decrease

Derivative time or derivative gain (min or sec)

Try a small decrease. If condition worsens, increase.

Try a small increase If condition worsens, decrease.


(min or sec)

TRIAL AND ERRORTRIAL AND ERROR –– P CONTROLLERP CONTROLLERTRIAL AND ERROR TRIAL AND ERROR –– P CONTROLLERP CONTROLLER

The impact of controller gain changes on P-only controller


TRIAL AND ERROR METHODTRIAL AND ERROR METHOD –– PI CONTROLLERPI CONTROLLERTRIAL AND ERROR METHOD TRIAL AND ERROR METHOD –– PI CONTROLLERPI CONTROLLER

The impact of controller gain on PI controller

The impact of integral time changes on PI controller


TRIAL AND ERROR METHODTRIAL AND ERROR METHOD –– PID CONTROLLERPID CONTROLLERTRIAL AND ERROR METHOD TRIAL AND ERROR METHOD –– PID CONTROLLERPID CONTROLLER

The impact of derivative time changes on PID controller

Vrijeme (min)


22 –– STANDARD (TRADITIONAL) TUNING METHODSSTANDARD (TRADITIONAL) TUNING METHODS

OO l th dl th d

2 2 –– STANDARD (TRADITIONAL) TUNING METHODSSTANDARD (TRADITIONAL) TUNING METHODS

•• OpenOpen--loop methodsloop methods

ZieglerZiegler--Nichols reaction curve methodNichols reaction curve methodZieglerZiegler Nichols reaction curve methodNichols reaction curve methodCohenCohen--Coon Coon method method LambdaLambda testtest

•• ClosedClosed looploop methodsmethods•• ClosedClosed--looploop methodsmethods

ZieglerZiegler--NicholsNichols continouscontinous oscillationoscillation methodmethodZieglerZiegler NicholsNichols continouscontinous oscillationoscillation methodmethodReleyReley methodmethod


22 –– CONTROLLER TUNING PROCEDURECONTROLLER TUNING PROCEDURE2 2 –– CONTROLLER TUNING PROCEDURECONTROLLER TUNING PROCEDURE

Step Step 11 –– Process testingProcess testingpp gg• It is necessary to cause OP step change ((stepstep testtest))..

StepStep 22 –– Process dynamics analysisProcess dynamics analysisStep Step 22 Process dynamics analysisProcess dynamics analysisa.a. Standard Standard methodsmethods are based on response graphical analysis for

determination of controller parameters;;b.b. Automatic Automatic tuningtuning (selfself--tuningtuning) using test which introduced smaller

disturbance in control loop and process;cc ComputionalComputional(numericnumeric) methods in dedicated software for controllerc.c. ComputionalComputional(numericnumeric) methods in dedicated software for controller

parameter determination based on control loop history database.

StepStep 33 –– Controller parameter calculationController parameter calculationStep Step 33 –– Controller parameter calculationController parameter calculation• For particular controller (P, PI, PID, etc.) empirical relationship is

applied to determine optimal controller setting;


• By using specialized software the controller parameters are optimized applying numerical optimization methods.

ZIEGLERZIEGLER--NICHOLS CLOSED LOOP METHODNICHOLS CLOSED LOOP METHODZIEGLERZIEGLER--NICHOLS CLOSED LOOP METHODNICHOLS CLOSED LOOP METHOD

• J.G. Ziegler and N.B. Nichols published in 1942 two empiricalJ.G. Ziegler and N.B. Nichols published in 1942 two empirical methods for PID controller tuning;

• One method is called process reactionprocess reaction--curve methodcurve method, and fanother method of critical oscilation is called ultimateultimate--cycling cycling

methodmethod;

Th h l l i i d li• They put the control loop in sustained cycling;

• Based on the period and amplitude of oscillation they determined controller parameters;determined controller parameters;

• For modern heat-integrated processes this method is not practialpractial.

For many loops, the severity of such a test is unacceptable.


y p , y p

ZZ––N CLOSED LOOP METHOD TUNING PROCEDUREN CLOSED LOOP METHOD TUNING PROCEDURE

TUNING PROCEDURETUNING PROCEDURE::

ZZ––N CLOSED LOOP METHOD TUNING PROCEDUREN CLOSED LOOP METHOD TUNING PROCEDURE

1. Put the controller in automatic mode. Remove integral andderivative modes;derivative modes;

2. Increase the controller gain until the loop cycles continuously( PV and OP oscillations are visible);( PV and OP oscillations are visible);

3. 3. Note the period of cycleperiod of cycle (time) PU (ultimative period)and ultimate gain ultimate gain KCU which causes this oscillation;

4. Substitute the values of the ultimate gain and the ultimate4. Substitute the values of the ultimate gain and the ultimateperiod into the tuning equations (table on the following slide!)


ZZ––N METHOD:N METHOD: ContinousContinous oscillationoscillation testtestZZ––N METHOD: N METHOD: ContinousContinous oscillationoscillation testtest

pera

ture

(°C

)Te

mlv

e op

enin

g(%

)

Time(min)

Val

P controller PI controller PID serial PID parallel Kc = 0.5*Kcu Kc = 0.45*Kcu Kc = 0.6*Kcu Kc = 0.75*Kcu

τi = Pu / 1 2 τi = 0 5*Pu τi = 0 625*Pu


τi Pu / 1.2 τi 0. 5 Pu τi 0.625 Pu τd = Pu / 8 τd = Pu / 10

OPEN LOOP METHODOPEN LOOP METHODOPEN LOOP METHODOPEN LOOP METHOD

• Execute the process test with the controller on manual modeExecute the process test with the controller on manual mode(open loop);

• Analyse PV-a response on the OP step change;

• OP change must be as small as possible so as not to• OP change must be as small as possible so as not to disturb the process too much, but larger than measurement noise and valve hysteresis;

• The problem can be appereance of disturbances or process load change during the open loop test;load change during the open loop test;


ZIEGLERZIEGLER––NICHOLSNICHOLS OPEN LOOP METHODOPEN LOOP METHOD

TUNING PROCEDURETUNING PROCEDURE

ZIEGLERZIEGLER––NICHOLS NICHOLS OPEN LOOP METHODOPEN LOOP METHOD

TUNING PROCEDURETUNING PROCEDURE::

1.1. Put the controller in Put the controller in manual mode manual mode and wait for and wait for PVPV to to stabilizestabilize;;

2.2. Make previously defined Make previously defined OPOP step changestep change;;

3.3. Graphically determine Graphically determine the slope the slope of the of the processprocess reactionreactioncurvecurve at the inflection point (maximum slope), and relatedat the inflection point (maximum slope), and relatedcurvecurve at the inflection point (maximum slope), and related at the inflection point (maximum slope), and related dead timedead time;;

44 Based on empirical relationshipBased on empirical relationship (( table on the following slide!table on the following slide!))4.4. Based on empirical relationship Based on empirical relationship ( ( table on the following slide!table on the following slide!))calculate calculate controller parameterscontroller parameters..


ZIEGLERZIEGLER––NICHOLSNICHOLS OPEN LOOP METHODOPEN LOOP METHODZIEGLERZIEGLER––NICHOLS NICHOLS OPEN LOOP METHODOPEN LOOP METHOD

pera

ture

(°C

)

TangentTe

mp (

Steady-state

ve o

peni

ng(%

)

Time (min)

Valv


Time (min)

ZZ––NN OPEN LOOP METHODOPEN LOOP METHOD

Reaction curve characteristicsReaction curve characteristics::

ZZ––N N OPEN LOOP METHODOPEN LOOP METHOD

LLRR –– Reaction lag [min][min]

–– Time elapsed from step change to the point where tangent intersect the baseline

RRRR –– Reaction rate Reaction rate ((reactionreaction raterate), [% / min]), [% / min]–– slope of the tangent

• The values are then substituted into the equations in the following table:

P controller PI controller PID serial PID parallel KC = ∆OP / (L *R ) K = 0 9*∆OP / (L *R ) Kc = 1 2*∆OP / (L *R ) KC = 1 5*∆OP / (L *R )


KC = ∆OP / (LR RR) Kc = 0.9 ∆OP / (LR RR) Kc = 1.2 ∆OP / (LR RR) KC = 1.5 ∆OP / (LR RR) τi = 3.33*LR τi = 2.0*LR τi = 2.5*LR τd = 0.5*LR τd = 0.4*LR

CONTROLLER TUNING CONTROL LOOP OPTIMIZATION · • The fundamental trade-off in control loop tuning...

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