research article analysis of liquid zone control valve...

Hindawi Publishing CorporationJournal of EngineeringVolume 2013 Article ID 450161 12 pageshttpdxdoiorg1011552013450161

Research ArticleAnalysis of Liquid Zone Control Valve Oscillation Problem inCANDU Reactors

Elnara Nasimi and Hossam A Gabbar

University of Ontario Institute of Technology 2000 Simcoe Street North Oshawa ON Canada L1H 7K4

Correspondence should be addressed to Hossam A Gabbar hossamgabbaruoitca

Received 14 November 2012 Revised 15 March 2013 Accepted 2 April 2013

Academic Editor Ibrahim Asi

Copyright copy 2013 H A Gabbar and E NasimiThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper looks at the existing challenges with steady-state Liquid Zone control at some CANDU (CANada Deuterium Uranium)stations wheremdashcontrary to expectations for equilibriumflowmdashLiquidZoneControl Valve oscillations have proven to be a chronicunanticipated challenge Currently the exact causes of this behaviour are not fully understood although it is confirmed that theControl Valve oscillations are not due to automatic power adjustment requests or zone level changes due to process leaks Thisphenomenon was analysed based on a case study of one domestic nuclear power station to determine whether it could be attributedto inherent controller properties Next a proposal is made in an attempt to improve current performance with minimal changes tothe existing system hardware and logic using conventional technologies Finally a proposal was made to consider Model PredictiveControl-based technology to minimize the undesirable Control Valve oscillations at steady state based on the obtained simulationresults and discussion of other available alternatives

1 Introduction

In CANDU nuclear power plants reactor neutron poweris measured and calibrated to the thermal power beingproduced Operation of reactivity control devices such asLiquid Zone light water-filled compartments andmechanicalcontrol rods is used to reduceeliminate power error

This paper describes efforts of a project that looked into aspecific case of LiquidZone (LZ)ControlValve (CV) problemwhere a controller performance resulted in undesirable CVoscillations leading to excessive wear and tear of the valveIn addition to equipment reliability this impacts the overallflux control stability and presents challenges for operationengineering and maintenance at the plant The focus of thisproject was to analyze the existing condition and proposealternatives to the existing control scheme in an attempt toresolve the existing condition and introduce a new intelligentcontroller based on modern advanced technologies

11 Literature Review One of the main obstacles for theintroduction of intelligent digital control for nuclear powerplants appears to be the historical assumption that the old

analogue controllers are more reliable safer and easier tomaintain than the new digital programmable controllersThere is a perception among both the plant personnel as wellas general public that the old analogue and electromechanicalsystems should remain the preferred method for implement-ing reactor control

This issue is quite prominent among certain special-ists and hugely pronounced among general populationSome sources mention that despite the fact that the newsophisticated intelligent control systems are more suitablefor the demands of todayrsquos industry the challenge of con-vincing all stakeholders that they can provide the requireddegree of reliability validation and verification still remains[1]

Studies done as early as 1989 [2] show that for nuclearreactors and steam generators where operating parame-ters change randomly a development of synthesis methodsrather than standard PID-controllers (Proportional-Integral-Derivative) is needed which can be easily accomplishedby using intelligent control systems built on the basis offuzzy logic and artificial neural networks with genetic algo-rithms Other studies [3] showed that there has already

2 Journal of Engineering

been a significant effort made in the area of automatic andfault-tolerant control research and development that can beapplied for operating power plants

Intelligent control systems with fault diagnostic capabili-ties have been deployed in other safety-critical industries andapplications such as aerospace chemical process and med-ical industries for quite some time now Novel approachesfor fault diagnosis and control reconfiguration for complexsystems as well as trends and perspectives of intelligentcontrol in manufacturing systems are widely discussed [4ndash6] The use of fuzzy logic and neural network approachto intelligent reactor controller design appears to be theoverall trend in the industry today regardless of the typeof the reactor design or country of origin The 2003 OakRidge National Laboratory report for the US Departmentof Energy [7] states that the main focus in the controlcommunity is to integrate functions of intelligent systemssuch as fuzzy logic neural networks genetic algorithmsand knowledge-based systems with the conventional controlsystems to perform complex tasks more easily Other studiesidentify a WWPR-type (Water-Water Power Reactor) reactorcore using a multi-nonlinear autoregressive with exogenousinputs (NARX) structure that makes use of neural networkswith different time steps and a heuristic compound learningmethod with off- and online batch learning [8ndash11] Resultsof these studies show that the proposed controller is verywell able to control the reactor core during load followingoperations using optimum control rod group manoeuvreand variable overlapping strategy Power control stability ofthe Belgian Reactor 1 (BR1) at the Research Centre for theApplications of Nuclear Energy (SCK-CEN) was improvedby using a fuzzy logic control scheme [12] and showed goodpotential compared with human control room operators ForGeneration-3 CANDU-based plants requirements for useof control computers in shutdown and other safety systemswere identified as early as 1980s [13] but in most operatingunits only minimal changes have been implemented todate

2 Liquid Zone Control (LZC) System

21 Project Methodology This paper describes efforts of apreliminary study where a specific case of a known LiquidZone Control Valve problem was looked at First historicalplant data and troubleshooting results were obtained andanalysed to define the problemanddevelop a projectmethod-ology It is important to point out that although this conditionhas been experienced at several reactor units at some timeengineering analysis and troubleshooting activities have notproduced conclusive findings identifying the root causes ofthis phenomenon Furthermore since this condition appearsintermittent in nature and affects different units at varioustimes no comprehensive in-depth study has been conductedto review this issue from multidiscipline point of view Thisproject set out to conduct some preliminary analysis and setup a framework for a detailed research study that may bebeneficial for this case In order to comply with allocatedtime and scope constraints it was necessary to make somesimplification and use assumptions for unknown parameters

Powersetpoint

Bulkpower

Powermeasurement

Bulk powererror

LZC control

LZC system

routine

Figure 1 Simplified reactor control scheme in CANDU whereLiquid Zone Control system is shown as a means for fine reactivitycontrol and reduction of power error

First the existing LZ control system design was analysedand a simplified model was set up in MatLab Simulink 77R2008 [14]

Next step response simulation was conducted to deter-mine whether the modeled system response matches historicplant data This step was important to ensure that simplifica-tions and assumptions made during initiation of the projectare acceptable and do not have a significant impact on themodel accuracy

Next an attempt was made to look at how the modelperformance can be improved with minimal changes tothe existing components and using only conventional PIcontroller technology that is already available at the plant inquestion

Lastly other available technologies and methods basedon modern intelligent control techniques were looked at toevaluate their potential for the selected case study for exam-ple fuzzy logic and neural network-based control schemesThemain emphasis wasmade on evaluatingModel PredictiveControl-based (MPC) controller integrationwith the originalsystem model Although further and more detailed studiesare required to produce comprehensive results some prelim-inary tests were done to check the proposed modified systemresponse with the same step input disturbance

Finally project conclusions feasibility of the proposedchanges and proposals for future work are shown in the lastsection of this paper These steps are shown in Figure 2 as aproject task breakdown structure diagram

22 Liquid Zone Control System Description In a typicalCANDU reactor Liquid Zone system is comprised of 14light-water filled compartments distributed throughout thereactor core Light water in the LZ compartments acts as aneutron absorber and thus Reactor Regulating System (RRS)automatically modulates zone levels by adjusting inflowsfor bulk and spatial neutron flux control Individual zonepower is measured using both neutronic and thermal powermeasurements and compared to the setpoint A simplifiedreactor control scheme inCANDU is shown in Figure 1 Zone

Journal of Engineering 3

Develop process model in Simulink

Simulate system response to unit

System optimization

Alternative 1minimum changes to

Analyse system structure and

Establish mathematical model

Confirm that the model response matchesplant data

Alternative 2no changes to existinghardware intelligent

controller

MPC

Comparison of results

Other alternatives fuzzy logic neural network(NN)

Solution

current challenges

step input

hardware using existing PI controller

Figure 2 Project task breakdown structure

levels are adjusted individually to minimize the power errorand to ensure that each zone is producing the same powerand ideally during steady-state operation with no powermaneuvers Liquid Zone levels are expected to remain steadywith no RRS control demand

23 Performance Requirements A simplified block diagramof Liquid zone control is shown in Figure 3 Circulationof light water through all 14 Liquid Zone compartments isachieved by continuous water flow through the zones toensure cooling to the zone control compartments Waterlevels are adjusted by RRS by adjusting inlet Control Valves

(CVs) so that a constantΔ119875 ismaintained across the zones Inthis case study only one (1) valve will be considered in orderto simplify the analysis According to the original designdocumentation reviewed during early stages of this study theCV in questionwill be assumed to be a linear diaphragmvalveas shown in Figure 4

The valve is assumed to have a flow restriction of 091 Lsmaximumwith a 005 sec deadband with a natural frequencyof 1Hz and a damping ratio of 1

Since the focus of this study is the controller itself noparametrical studies were conducted on valve design orproperties


Delay tank

Constant Δ119875control

He balance header

LZC inlet CV

LZC compartment

LZC pump

Figure 3 Simplified block diagram of LZ control only 1 of 14 light-water compartments is shown

24 Existing System Principle of Operation During steady-state operation with no RRS power adjustment demandand no zone level changes there should be equilibriumbetween inflow and outflow to the zones For cases where thecontroller responds to either real or indicated power errorLIFT term is calculated using (1) For steady-state operationwith no rate term (DLIF = 0) this can be expressed as

LIFT = BIAS plusmn BLIF (1)

where BIAS lift which causes inflow = outflow RLIF relativelift = BLIF + DLIF BLIF bulk lift = bulk power controlterm and DLIF differential lift = spatial control term for fluxtilts

In this case the value of BLIF will depend on the effectivepower error Ep as shown below

BLIF = Kp lowast Ep (Power Error)

Ep = KB (PLOG minus PDLOG) + KR (RI minus RD) (2)

where Ep effective power error PLOG measured reactorpower PDLOG demandpower setpoint KB normalized fluxloop control gain (=1 at gt25 FP) KR flux loop derivativegain (=05) RI indicated log rate median ion chamber lograte signal and RD demanded reactor power maneuveringrate

Since the focus of this study is on unanticipated steady-state oscillations at full power the following assumptionscan be made RP gt 25 so KB = 10 RD = 00 steadystate no power maneuvering (PLOG-PDLOG) = 0 systemat setpoint

Ep = +KR (RI) = 05 (RI) (3)

Since BIAS in (3) is a constant value this is similar toproportional-only mode where

output = gain lowast (measured variable minus setpoint) (4)

Thus for the purpose of this study the existing steady-state LZ controller will be considered to be proportional-only no adjustments for flux tilts or zone level tilts and noantifloodantidrain restrictions as shown in Figure 5

25 Current Challenges Based on the system design and per-formance requirements the following assumptions should betrue for steady state with no flux or zone level tilts

BLIF = DLIF = 0

LIFT = BIAS = Const (= 0455) (5)

Therefore at steady state with no RRS demand for zoneadjustments the zones should remain in a state where inflowis equal to outflow which is achieved by a constant value ofthe BIAS term (set to 0455 in this case)

In practice as was seen in this case study it is commonto see steady-state LZC CV oscillations This behaviour wasconfirmed by running simulation on the LZ Controller andValve model shown in Figure 6

The controller response to a unit step change resultsin a high degree of oscillation exceeding plusmn15 which isconsistent with the field observations of cases where thezone oscillations of up to a total of 20 (plusmn10) have beennoted in worst case scenarios This condition appears tobe intermittent in nature with random occurrence whereexact causes are not fully understood despite engineeringanalysis and troubleshooting efforts conducted at the plantIt has been confirmed that the CV oscillations are not dueto RRS power adjustment requests or zone level changes dueto process leaks Some of these transients are attributed tolevel transmitter (LT) drifts signal noise or impulse linemoisture build-upThe lack of understanding the exact causeof this behaviour adversely affects operatorsrsquo confidence inthe field instrumentation (as a potential source of erroneousreadings) Similar to control valves design and performanceof LZ level transmitters will not be considered other than as acomponent adding to the overall noise (disturbance) that thecontroller must mitigate while maintaining robustness andspeed of response

26 The Need for Intelligent Control There are several keychallenges that spurious zone oscillation during steady stateis present First this raises concerns about RRS capability torespond to real changes when CV manipulation is requiredfor power manoeuvres Hardware-wise the unanticipatedCV oscillation accelerates wear and tear of the mechanicalcomponents and increases their rate of failure thus resultingin increased demands on maintenance resources and costsAdditional unscheduled calibrations and drift checks for allcomponents of RRSLZ control circuits add to maintenanceburden and increase risk of inadvertent system upsets andpotential emergency shutdowns during reactor operation


BLIF

Valve deadband time(005 s)

119883998400 = 119860119909 + 119861119906119884 = 119862119909 + 119863119906

LZ valve(second order)

1119911 091 + minus

Linear valve

Valve bias flow0455 (Ls)

0455

(max 091 Ls)

Figure 4 Simplified LZ Control Valve set-up

Sensor and linedisturbance

for steady state

PID

(currently in usefor steady state)

Deadband005 s

LZC CV2nd order valve

091 max

0455

Constantbias to maintain outflow

Scope 1+

minus

+

minus

11199042 + 2119904 + 1

119870minus

119875-only controller

Figure 5 Existing LZ Controller and Valve set-up in Simulink

In addition to these equipment reliability issues steady-state zone level transients challenge overall reactor fluxcontrol and stability which presents significant burden tooperators engineering andmaintenance as it sets ground forquestioning the overall RRSLZ control scheme and accuracyof system design and behaviour model

In this study an initial attempt was made to look intopotential changes to the existing system that would requireonly most minimal changes to the existing hardware andcontrol logic A set up for the optimized LZ controlleris shown in Figure 7 and controller response is shown inFigure 8 Saturation control and rate limiter were added tothe model so that the first derivative of the signal is passingthrough it to ensure that the output changes not faster thanthe specified limit and the controller output never reaches theactuator limits

The proposed improved controller set-up was testedagainst the same unit of disturbance as in the first case

The results of this experiment showed that these modifi-cations resulted in conservative bounds and some improve-ment in controller performance Noticeably the magnitudeof oscillations (up to plusmn2) has improved but did not entirelyeliminate the undesirable valve cycling thus failing to satisfythe criteria for required improvements

More importantly the original LZ Fisher amp Porter 3000controllers used at a facility selected for a case study areobsolete and are no longer supported by vendors and thusimplementation of these changes is unlikely to be beneficial in

terms of cost savingsThe recently installed replacement ABB5000-series controllers were also analysed as an alternativesolution for the obsolescence problem but have shown tohave an unusual failure mode (memory failure followingClass-II power and battery failure) that had not been fullyanalysed or understood prior to installation AdditionallyABB 5000 series is near obsolete and is not going to presenta viable long-term solution for the future thus the initialproposal is not recommended for further detailed studyand a different approach based on a modern technology isrequired

This study proceeded to look at feasibility of implemen-tation of such controller based on Model Predictive Control(MPC) [15] principles Several other controlmethods such asfuzzy logic and neural network-based controllers [16] wereexamined to determine whether they can provide suitablealternatives as well This is described in more detail in thesubsequent sections

3 Proposed Controller with MPC

In order to address the needs for a sustainable long-termsolution to the existing LZ control challenges severalalternative technologies were considered Model-Predictive-Control- (MPC-) based model was designed and tested firstin order to see whether intelligent control algorithm canpresent a suitable solution This is described in the followingsections


Figure 6 Existing LZ CV response to unit step change the magnitude of controller response is shown over 100 sec interval

119875-only controllerSensor and line

disturbancefor steady state 1

PID

with optimization

Deadband005 s 1

RateSaturationlimits LZC CV

2nd order valve 1091 max 1

0455

Constantbias to maintain outflow 1

Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1

Figure 7 Optimized LZ controller set-up in Simulink

As discussed earlier the main driver for implementationchanges to the existing LZ steady-state control was to mini-mize or eliminate the undesirable CV oscillations There arehowever other general performance requirements that thenew controller must satisfy in order to present an acceptablealternative to the existing system These are summarized asfollows

(i) Closed-Loop Stability The new MPC controller mustmaintain the system output bounded to avoid reach-ing actuator limits and saturation and minimizeovershot

(ii) Fast ResponseThenewMPCcontrollermust suppressor reject changes in the reference disturbances in theloop

(iii) Robustness The new MPC controller must havesufficient margin to allow for modeling errors orvariations in system dynamics

31 Control Design Principles of Model Predictive Controlwere used to develop the new LZC control algorithm andset up a model MPC control algorithm is based on iterativeprediction of future plant states based on the presently mea-sured information for example Level Transmitter indicationat time interval 119896 as well as known measured disturbancesBased on known constrains and control objectives the alter-native future states or the so-called trajectories are calculatedThe next step would be to develop an optimization costfunction 119869 over the receding prediction horizon

119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)


Figure 8 Response of the optimized LZ controller to a unit disturbance the magnitude of controller response is shown over 100 sec interval

and so forth

Weighting coefficients119908119909119894 = for 119909119894

Constrainsactual constrainsvalve deadband

Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

Control input Actual

Plantmeasurements 119909119894

Error feedback into modelto update future predictions

Model

120576(119896)

119908119906119894 = for changes in 119906119894

Prediction horizon 119875

119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)

Figure 9 MPC block diagram

where 119909119894= controlled variable for example LZ level 119903

119894= ref-

erence variable for example BIAS (0455) 119906119894= manipulated

variable (eg control valve CV) 119908119909119894= weighting coefficient

for 119909119894 119908119906119894= weighting coefficient for changes in 119906

119894

Block diagram for this process is shown in Figure 9

Error 120576(119896) represents discrepancy between the physicalplant and its model and is used as feedback for the MPCcontroller to adjust future predictions

The MPC process is iterative that is once a selectedcontrol scheme is applied new measured values for plant


Start

Transfer toanother control

schemeEnd

Initializationcalculate controller gain Kp

No

No

Yes

Setpoint

Solve optimization

Setp

oint

s

Set all elements of predicted

Startcontroller

test

Setpoint trackingdisturbance rejection

Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894

Measure plant outputLT output 119909119894(119905)

Increment time interval119905 = 119905 + 1

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)

119908119909119894 = weighting coefficient for 119909119894119908119906119894 =weighting coefficient for changes in 119906119894

119903119894 = 0455

120576(119896)

Manipulate 119909119894

BLIF = KplowastEp (power error)Ep = KB(PLOG minus PDLOG) + KR(RI minus RD)

Figure 10 Proposed control design algorithm

response become availableThesemeasurements becomenewinputs into the control algorithm calculation and the processis repeated for the next time interval that is 119896 = 119896 + 1The flowchart in Figure 10 illustrates a step-by-step controlscheme for the proposed controller

Next the proposedMPC-based controller was integratedinto the previously created LZ CV system model in Simulink(MatLab Simulink 77 R2008 [14] on a standard student Win-dows PC computer) so that MPC controller would assume allof the performance functions of the existing PID controller

The subsequent modifications to the system with saturationand rate limiter were removed with the expectation thatthe new controller would be able to maintain the requiredsaturation control This model is shown in Figure 11

Controller parameters listed below were arbitrarilyselected to represent

(i) prediction and control horizons(ii) hard and soft constraints on manipulated variables

and output variables



for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md

bias to maintain outflow 2

LZC CV2nd order valve 2

+minus

Figure 11 MPC for LZ controller set-up in Simulink

(iii) weights on manipulated variables and output vari-ables

(iv) model for measurement noise and for unmeasuredinput and output disturbances

Once the model was finalized the new controller perfor-mance was tested by simulating closed-loop system responseTheoutput characteristicswere tested to check if performancecan be tuned to achieve the desirable balance betweencontroller robustness versus speed of response Since thescope of this study was to confirm feasibility of this approachno detailed parametric experiments were conducted untilmore research is conducted for this proposal

4 Discussion of Results

41 Run Time Adjustment One of the main advantagesof MPC controllers is that controller performance can beimproved by manipulating controller parameters such asweights and constraints and simulating closed-loop systemresponse This method was used in an iterative process sothat the new controller performance can be tested against byrunning closed-loop simulations the linear plant model Runtime adjustment of output characteristics was performed todemonstrate that the controller is able to achieve the desirablebalance between robustness versus speed of response Shownin Figure 12 are the results for three scenarios where theratio of speed of response versus robustness is arbitrarilychosen to be 10 05 and 03 and response of MPC vs non-linear proportional only and optimized proportional-onlycontroller is shown in Figure 13

This confirmed that various options are available andcontrollerrsquos performance can be tuned based on the sys-tem performance requirements Next the MPC controllerperformance was compared to the nonlinear proportional-only PID controller described earlier In all cases the MPCcontroller rejected disturbance and attempted to return plantoutput to the desired setpoint while remaining within thepreset constrains It can be seen that when a higher speedof response was chosen the controller recovered in the leasttime but with a higher overshot In the third case wherea higher degree of robustness was required the controllerovershot was the smallest This however was achieved at theexpense of longer recovery time42 Proposed Implementation Based on the results obtainedduring this study MPC-based controller appears to be astrong alternative to the existing obsolete PID controllersespecially for older Nuclear power units and is recom-mended for consideration for future generations of CANDUnuclear power plants Implementation of hardware set-upfor the proposed model predictive control system on a PC-compatible hardware using Simulink Coder is shown inFigure 14

Comprehensive further work will be required to developand verify optimal cost and control sequence at each com-putation step and to extend the control scheme to encompassthe entire range of LZ operation for example integral controlrequired during power manoeuvres

Next ldquoCrdquo code from Simulink blocks can be used todeploy a supported target system for prototype testing todetermine if the proposed controller will have enough com-putational speed to address performance requirements for


0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18

2Plant output sum4 (pt 1)

Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)

Figure 12 MPC controller performance is shown for three cases where the ratio of speed of response versus robustness of theMPC controlleris adjusted to 10 (a) 05 (b) and 03 (c) Plant output is shown in blue versus the reference setpoint in grey

a larger more complex plant model One of the foreseeablechallenges that the current LZ control scheme set-up mayrepresent for MPC-based controller deployment could bethe need for synchronization of the individual systems Asmentioned earlier a typical CANDU LZ control is comprisedof 14 light water compartments each with its own associatedControl Valve Bulk and special level adjustment is calculatedby Reactor Regulating System (RRS) residing on the DigitalControl Computers (DCCs) It is critical to ensure that thenew controller is able tomaintain process variables at setpointin a MPC-DCC set-up

Additionally field installation of the proposed MPCcontroller will require extensive design verification by anindependent third party to ensure compliance with all appli-cable codes and standards and will require approval from theCanadian Nuclear Safety Commission

43 Comparative Analysis of Other Alternative TechnologiesFuzzy logic-based control methods were considered for this

project as an alternative means to enhance the currentlyobsolete LZ controllers at nuclear power stations Typicallyfuzzy logic is used in applications for complex system orbehaviours where relationships are unknown or unclearThis alternative was rejected since the system model isknown and understood Also negative feedback receivedfrom the current operations staff at a selected nuclear facilityon the use of ldquofuzzy logicrdquo term highlighted additionalchallenges that will need to be overcome in order to imple-ment this approach especially at older utilities It becameapparent that a large number of control room operators andsome maintenance personnel are not familiar with recentdevelopments in control technology The use of ldquofuzzyrdquoterm in fuzzy-logic methods was perceived to be equalto ldquounclearrdquo or ldquoconfusingrdquo and is therefore not readilyaccepted as ldquoappropriaterdquo to the critical control and safetyapplications in nuclear power plants Therefore should thismethod be selected in future work specifically for olderplants the researches must consider the required changes to


Figure 13 MPC controller (bottom graph) is shown against the nonlinear proportional-only controller (topmost) and optimizedproportional-only controller (middle) the magnitude of controller response is shown over 100 sec interval

Figure 14 Hardware setup for rapid prototyping of a modelpredictive controller on PC-compatible hardware using SimulinkCoder and xPC Target [14]

the existing operations and maintenance training programsand include provisions for education and familiarization ofpersonnel with this technology in order to eliminate culturalbarrier

Another alternative considered in this project for futureconsideration was Neural-Network- (NN-) based controllerIt was also rejected since the NN methods are most suitablefor applications where formal analysis is difficult or impos-sible due to complexity of pattern recognition and systemidentification and control In the case of LZ controllers wherepatterns and identification are simple and formal analysiscan be readily conducted this technology does not seem

to provide the best fit especially as it may require highcomputational resources Also from the cultural perspectivethe main principle of NN methods was perceived by certainoperators as overcomplicated and ldquonot technological enoughrdquodue to association with biological organisms based on apreconceived notions of ldquohuman factors = human errorrdquoThisfeedback was consistent with earlier findings in the literaturereview [1] where public acceptance is identified as one of themain ldquosoftrdquo criteria for nuclear industry

5 Conclusions

It has become clear that the old obsolete FampP 3000 controllersand the newly installed ABB 5000 series controllers cannotprovide a sustainable long-term solution for LZ control atexisting CANDU nuclear power plants and will have to bereplaced with a modern technology for the next generationof CANDU reactors This project was conducted as a pre-liminary feasibility study to evaluate the existing challengesand consider suitable alternatives The existing proportional-only steady-state control scheme was examined based onperformance history at a selected operating facility Anoptimized proportional controller was considered and earlytests showed a significant improvement in the magnitudeof steady-state error Despite the advantages of minimalchanges to the existing equipment and circuitry and ease ofimplementation this approach was not able to eliminate the


undesired oscillation of CV valves that was the main focus ofthis study Furthermore this controller would still be basedon the obsolete hardware and technology currently in serviceat production facilities and is not going to present a long-termsolution for the next generation of CANDU plants

An alternative MPC-based control scheme was imple-mented in Matlab Simulink and tested against the samedisturbance to emulate simplified plant conditions leadingto CV oscillations The MPC-based controller showed asignificant improvement both in terms of rejecting the dis-turbance and returning plant output to the desired referencepoint as well as minimizing oscillations on the CV valvesThis highlighted an important benefit of application of MPCcontroller technology for operating power plants whereprescribed plant constrains can be addressed For exampleactuator constraints and controllerrsquos performance can betuned in terms of speed of response magnitude of error orrobustness based on specific plant requirements

Two other alternatives namely fuzzy logic and neuralnetwork-based control schemes were investigated to deter-mine whether they could provide another suitable optionfor future study These alternatives were rejected for variousreasons such as complexity required computational powerand cultural perceptions

Based on these results it is proposed to consider furtherdetailed study for application of MPC-based controller forLiquid Zone control in CANDU reactors with model andprototype development and testing using historical plantdata Based on results of these studies field implementationand in-service tests can be conducted at one of the existingfacilities so that lessons learned could be incorporatedinto the future generation of CANDU reactor design as asustainable long-term solution based on widely available andsupported modern technology [17ndash20] It is anticipated thatthis project will involve high levels of financial costs andmultidisciplinary resources and thus futureworkwill dependon industry interest in advancing this proposal

References

[1] J G Williams and W C Jouse ldquoIntelligent control in safetysystems criteria for acceptance in the nuclear power industryrdquoIEEE Transactions on Nuclear Science vol 40 no 6 pp 2040ndash2044 1993

[2] D E GoldbergGenetic Algorithms in Search Optimizations andMachine Learning Addison-Wesley Reading Mass USA 1989

[3] Y Zhang and J Jiang ldquoBibliographical review on reconfigurablefault-tolerant control systemsrdquo Annual Reviews in Control vol32 no 2 pp 229ndash252 2008

[4] H E Rauch ldquoIntelligent fault diagnosis and control reconfigu-rationrdquo IEEE Control Systems vol 14 no 3 pp 6ndash12 1994

[5] M Bruccoleri M Amico and G Perrone ldquoDistributed intel-ligent control of exceptions in reconfigurable manufacturingsystemsrdquo International Journal of Production Research vol 41no 7 pp 1393ndash1412 2003

[6] M G Mehrabi A G Ulsoy Y Koren and P Heytler ldquoTrendsand perspectives in flexible and reconfigurable manufacturingsystemsrdquo Journal of Intelligent Manufacturing vol 13 no 2 pp135ndash146 2002

[7] ldquoINLmdashIdaho National Laboratoryrdquo httpsinlportalinlgovportalserverptcommunityinstrumentation control and in-telligent systems315dcnf

[8] M Boroushakia M B Ghofrania C Lucasb and M J Yaz-danpanahb ldquoAn intelligent nuclear reactor core controller forload following operations using recurrent neural networks andfuzzy systemsrdquo Annals of Nuclear Energy vol 30 no 1 pp 63ndash80 2003

[9] M Boroushakia M B Ghofrania C Lucasb M J Yazdan-panahb and N Sadatic ldquoAxial offset control of PWR nuclearreactor core using intelligent techniquesrdquo Nuclear Engineeringand Design vol 227 no 3 pp 285ndash300 2004

[10] S S Khorramabadi M Boroushaki and C Lucas ldquoEmotionallearning based intelligent controller for a PWR nuclear reactorcore during load following operationrdquoAnnals of Nuclear Energyvol 35 no 11 pp 2051ndash2058 2008

[11] M Boroushaki M B Ghofrani C Lucas and M J Yazdan-panah ldquoIdentification and control of a nuclear reactor core(VVER) using recurrent neural networks and fuzzy systemsrdquoIEEE Transactions on Nuclear Science vol 50 no 2 pp 159ndash1742003

[12] D Ruan ldquoIntelligent systems in nuclear applicationsrdquo Interna-tional Journal of Intelligent Systems vol 13 pp 115ndash125 1998

[13] R S Gilbert ldquoControl and safety computers in CANDU powerstationsrdquo inNuclear Power and Electronics IAEA Bulletin 1985httpwwwiaeaorgPublicationsMagazinesBulletinBull27327302390712pdf

[14] httpwwwmathworkscom[15] httpenwikipediaorgwikiModel predictive control[16] S J Qina and T A Badgwell ldquoSurvey of industrial model

predictive control technologyrdquoControl Engineering Practice vol11 pp 733ndash764 2003 httpwwwelseviercom

[17] K Hu and J Yuan ldquoMulti-model predictive control methodfor nuclear steam generator water levelrdquo Energy Conversion andManagement vol 49 no 5 pp 1167ndash1174 2008 httpwwwsciencedirectcom

[18] M G Na ldquoAuto-tuned PID controller using a model predictivecontrol method for the steam generator water levelrdquo IEEETransactions on Nuclear Science vol 48 no 5 pp 1664ndash116712001

[19] G Xia J Su and W Zhang ldquoMultivariable integrated modelpredictive control of nuclear power plantrdquo in Proceedings of the2nd International Conference on FutureGenerationCommunica-tion andNetworking Symposia (FGCNS rsquo08) pp 8ndash11 December2008

[20] M G Na and I J Hwang ldquoDesign of a PWR power controllerusing model predictive control optimized by a genetic algo-rithmrdquoNuclear Engineering and Technology vol 38 no 1 2006httpwwwknsorgjknsfilev38JK0380081pdf

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



been a significant effort made in the area of automatic andfault-tolerant control research and development that can beapplied for operating power plants

Intelligent control systems with fault diagnostic capabili-ties have been deployed in other safety-critical industries andapplications such as aerospace chemical process and med-ical industries for quite some time now Novel approachesfor fault diagnosis and control reconfiguration for complexsystems as well as trends and perspectives of intelligentcontrol in manufacturing systems are widely discussed [4ndash6] The use of fuzzy logic and neural network approachto intelligent reactor controller design appears to be theoverall trend in the industry today regardless of the typeof the reactor design or country of origin The 2003 OakRidge National Laboratory report for the US Departmentof Energy [7] states that the main focus in the controlcommunity is to integrate functions of intelligent systemssuch as fuzzy logic neural networks genetic algorithmsand knowledge-based systems with the conventional controlsystems to perform complex tasks more easily Other studiesidentify a WWPR-type (Water-Water Power Reactor) reactorcore using a multi-nonlinear autoregressive with exogenousinputs (NARX) structure that makes use of neural networkswith different time steps and a heuristic compound learningmethod with off- and online batch learning [8ndash11] Resultsof these studies show that the proposed controller is verywell able to control the reactor core during load followingoperations using optimum control rod group manoeuvreand variable overlapping strategy Power control stability ofthe Belgian Reactor 1 (BR1) at the Research Centre for theApplications of Nuclear Energy (SCK-CEN) was improvedby using a fuzzy logic control scheme [12] and showed goodpotential compared with human control room operators ForGeneration-3 CANDU-based plants requirements for useof control computers in shutdown and other safety systemswere identified as early as 1980s [13] but in most operatingunits only minimal changes have been implemented todate

2 Liquid Zone Control (LZC) System

21 Project Methodology This paper describes efforts of apreliminary study where a specific case of a known LiquidZone Control Valve problem was looked at First historicalplant data and troubleshooting results were obtained andanalysed to define the problemanddevelop a projectmethod-ology It is important to point out that although this conditionhas been experienced at several reactor units at some timeengineering analysis and troubleshooting activities have notproduced conclusive findings identifying the root causes ofthis phenomenon Furthermore since this condition appearsintermittent in nature and affects different units at varioustimes no comprehensive in-depth study has been conductedto review this issue from multidiscipline point of view Thisproject set out to conduct some preliminary analysis and setup a framework for a detailed research study that may bebeneficial for this case In order to comply with allocatedtime and scope constraints it was necessary to make somesimplification and use assumptions for unknown parameters

Powersetpoint

Bulkpower

Powermeasurement

Bulk powererror

LZC control

LZC system

routine

Figure 1 Simplified reactor control scheme in CANDU whereLiquid Zone Control system is shown as a means for fine reactivitycontrol and reduction of power error

First the existing LZ control system design was analysedand a simplified model was set up in MatLab Simulink 77R2008 [14]

Next step response simulation was conducted to deter-mine whether the modeled system response matches historicplant data This step was important to ensure that simplifica-tions and assumptions made during initiation of the projectare acceptable and do not have a significant impact on themodel accuracy

Next an attempt was made to look at how the modelperformance can be improved with minimal changes tothe existing components and using only conventional PIcontroller technology that is already available at the plant inquestion

Lastly other available technologies and methods basedon modern intelligent control techniques were looked at toevaluate their potential for the selected case study for exam-ple fuzzy logic and neural network-based control schemesThemain emphasis wasmade on evaluatingModel PredictiveControl-based (MPC) controller integrationwith the originalsystem model Although further and more detailed studiesare required to produce comprehensive results some prelim-inary tests were done to check the proposed modified systemresponse with the same step input disturbance

Finally project conclusions feasibility of the proposedchanges and proposals for future work are shown in the lastsection of this paper These steps are shown in Figure 2 as aproject task breakdown structure diagram

22 Liquid Zone Control System Description In a typicalCANDU reactor Liquid Zone system is comprised of 14light-water filled compartments distributed throughout thereactor core Light water in the LZ compartments acts as aneutron absorber and thus Reactor Regulating System (RRS)automatically modulates zone levels by adjusting inflowsfor bulk and spatial neutron flux control Individual zonepower is measured using both neutronic and thermal powermeasurements and compared to the setpoint A simplifiedreactor control scheme inCANDU is shown in Figure 1 Zone




System optimization






controller

MPC



Solution

current challenges

step input









Delay tank


He balance header

LZC inlet CV

LZC compartment

LZC pump










Ep = +KR (RI) = 05 (RI) (3)





BLIF = DLIF = 0







BLIF


119883998400 = 119860119909 + 119861119906119884 = 119862119909 + 119863119906


1119911 091 + minus

Linear valve


0455

(max 091 Ls)



for steady state

PID


Deadband005 s


091 max

0455


Scope 1+

minus

+

minus

11199042 + 2119904 + 1

119870minus
















PID

with optimization

Deadband005 s 1



0455


Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1







119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)



and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












System optimization






controller

MPC



Solution

current challenges

step input









Delay tank


He balance header

LZC inlet CV

LZC compartment

LZC pump










Ep = +KR (RI) = 05 (RI) (3)





BLIF = DLIF = 0







BLIF


119883998400 = 119860119909 + 119861119906119884 = 119862119909 + 119863119906


1119911 091 + minus

Linear valve


0455

(max 091 Ls)



for steady state

PID


Deadband005 s


091 max

0455


Scope 1+

minus

+

minus

11199042 + 2119904 + 1

119870minus
















PID

with optimization

Deadband005 s 1



0455


Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1







119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)



and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Delay tank


He balance header

LZC inlet CV

LZC compartment

LZC pump










Ep = +KR (RI) = 05 (RI) (3)





BLIF = DLIF = 0







BLIF


119883998400 = 119860119909 + 119861119906119884 = 119862119909 + 119863119906


1119911 091 + minus

Linear valve


0455

(max 091 Ls)



for steady state

PID


Deadband005 s


091 max

0455


Scope 1+

minus

+

minus

11199042 + 2119904 + 1

119870minus
















PID

with optimization

Deadband005 s 1



0455


Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1







119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)



and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










BLIF


119883998400 = 119860119909 + 119861119906119884 = 119862119909 + 119863119906


1119911 091 + minus

Linear valve


0455

(max 091 Ls)



for steady state

PID


Deadband005 s


091 max

0455


Scope 1+

minus

+

minus

11199042 + 2119904 + 1

119870minus
















PID

with optimization

Deadband005 s 1



0455


Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1







119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)



and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













PID

with optimization

Deadband005 s 1



0455


Scope 2+

minus

+

minus

119870minus1

1199042 + 2119904 + 1







119869 =

119873

sum

119894=1

119908119909119894(119903119894minus 119909119894)2+

119873

sum

119894=1

119908119906119894Δ1199062

119894 (6)



and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











and so forth



Setpoint 119903119894+

+

minus

minus

Optimization

119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894




Model

120576(119896)

119908119906119894 = for changes in 119906119894


119906(119896) 119906(119896 minus 1) 119906(119896 minus 119895)

119909(119896 + 1) 119910(119896 + Hp)



119894= ref-




119894





Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start


schemeEnd


No

No

Yes

Setpoint

Solve optimization

Setp

oint

s


Startcontroller

test


Calculate error

RP gt25

RD = 0(PLOG-PDLOG)

= 0

Yes

BLIF = DLIF = 0

LIFT = BIAS = 119903119894



119869 =119873sum119894=1

119908119909119894(119903119894 minus 119909119894)2 +

119873sum119894=1

119908119906119894Δ1199062119894

output 119909(119905) equal to 119909119894(119905)


119903119894 = 0455

120576(119896)












for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











for steady state 2

Deadband005 s 2

11199042 + 2119904 + 1

091 max 2

119870minusScope 3

0455

Constant

MPC

MPC controller

mv

mo

ref

md



+minus











0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16

18


Time (s)

(a)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14

16


Time (s)

(b)

0 1 2 3 4 5 6 7 8 9 100

02

04

06

08

1

12

14


Time (s)

(c)












5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















5 Conclusions







References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














References






















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article analysis of liquid zone control valve...

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