design and optimization of a monoaxial tracking system for

Hindawi Publishing CorporationJournal of Solar EnergyVolume 2013 Article ID 586302 6 pageshttpdxdoiorg1011552013586302

Research ArticleDesign and Optimization of a Monoaxial Tracking System forPhotovoltaic Modules

Cstslin Alexandru

Transilvania University of Brasov 29 Eroilor Boulevard 500036 Brasov Romania

Correspondence should be addressed to Catalin Alexandru calexunitbvro

Received 28 January 2013 Revised 12 June 2013 Accepted 2 July 2013

Academic Editor Koray Ulgen

Copyright copy 2013 Catalin Alexandru This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents researches on increasing the energetic efficiency of a photovoltaic (PV) string by designing and optimizing atrackingmechanism that simultaneously changes the daily position of the modules using a single driving source (there are moduleswith individual supports) The motion is transmitted from the driving source which is a linear actuator with a parallelogrammechanism The main task in optimizing the tracking system is to maximize the energetic gain by increasing the solar input andminimizing the energy demand for tracking The study is performed by developing the virtual prototype of the tracking systemwhich integrates the mechanical device and the control system in mechatronic concept Virtual prototyping software solutions(ADAMS EASY5 and MAT) are used in this study

1 Introduction

The realization of the PV strings (system of PV modules thatfunction as a single electricity-producing unit) appeared as anecessity for the development of large systems for producingelectricity The energetic efficiency of the PV strings dependson the degree of use of the solar radiation [1] which can bemaximized by use of tracking systemsThese aremechatronicdevices which ensure the optimal positioning of the stringrelative to the Sunrsquos position

Depending on the degree of mobility there are two basictypes of tracking systems monoaxis and dual-axis systemsThemonoaxis trackers perform only the daily motion the tiltangle of the motion axis corresponding to the latitude angleof the location [2] while the dual-axis trackers perform bothmotions (daily and seasonalelevation) so that they are ableto follow very precisely the Sun path throughout the yearThe dual-axis tracking systems can increase the energeticefficiency up to 40ndash45 against the equivalent fixed systemswhile the energy gain for the mono-axis systems is lower (upto 30ndash35) [3ndash6]

From energetic point of view the PV string with trackingis efficient if the energy that it produces (119864

119879) is substantially

greater than the sumof the energy produced by the equivalent

string without trackingfixed (119864119865) and the energy demand for

orientation (119864119862)

119864119879≫ 119864119865+ 119864119862 (1)

The optimal design of the tracking system aiming to max-imize the energetic efficiency has become an importantchallenge in the modern research and technology

In practice the orientation of the PV strings can berealized in two ways independent orientation for eachmodule of the string (module with its own tracking systemmotor source) simultaneous orientation of themodules fromthe same motor source with the help of motion transmit-ting mechanisms The simultaneous orientation with thepredicted advantages (coming mainly from minimizing thenumber of motor sources) and the characteristic problemsopens a research area insufficiently explored since now

In the literature there is no unitary modeling for thetracking mechanisms of the PV strings referring to thestructural kinematical and dynamical issues At the sametime there is no general approach for conceptual designand structural synthesis of these mechanisms Thereby thenecessity of amethod for the unitarymodeling of the trackingmechanisms become obvious and according to the strategyproposed by the paper this method is based on the MBS

2 Journal of Solar Energy

(Multibody Systems) theory [7 8] which facilitates the self-formulating algorithms

There are several works that approach control issuesmostly for the tracking systems of the individual modulesusing different techniques (closed loop systems with photosensors open loop systems based on astronomical com-puterized systems or hybrid combinations) and controllers(PID FNC and FNLC) [9ndash12] The research is focusedmostly on the evaluationprediction of the energy achievedby tracking and less on the energy demand for performingthe orientation

There are different models for the evaluation of theradiation potential as input data in the tracking systemsdesign The solar radiation can be measured using tradi-tional instruments or can be digitally recorded with a dataacquisition system At the same time there were developedlarge meteorological databases such as Meteonorm Thetraditional Angstromrsquos linear approach is based on measure-ments of sunshine duration while relatively new methodsare based on artificial neural networksmdashANN [13] Severalmodels for estimating the monthly mean solar radiation(linear Angstrom-Prescott variation quadratic equation log-arithmic variation and exponential function) were studied in[14] the root mean square error being the main element ofthe comparative analysisThemathematicalmodel developedin [15] is used for estimating the hourly and daily radiationincident on three-step tracking planes

In these terms the present paper approaches the improve-ment of the energetic efficiency of a PV string by designingand optimizing a mono-axis Sun tracker that simultaneouslychanges the daily position of the PV modules with a singledriving source The main task in optimizing the mechanismis to maximize the energetic gain by increasing the solarradiation input and minimizing the energy demand fortrackingThe incident radiation is estimated by using amath-ematic algorithm based on the direct terrestrial radiation andthe angle of incidence The paper proposes the integrationof the mechanical and electronic (control) components atthe virtual prototype level (ie modeling in mechatronicconcept) which allows performing the energy balance of thePV system

2 Designing the Tracking System

The system approached in this paper corresponds to a mono-axis trackingmechanism (Figure 1) at which the dailymotionis transmitted from the motor source which is a linearactuator with a multiparallelogram mechanism the revoluteaxes of the PV modules (in this case three modules) beingparallel with the polar axis The design is made for aninline string configuration but it can be adapted for otherconfigurations or for a higher number of modules Thedriving actuator is disposed on a fixed frame and this haspositive effect on the mass and inertia loading in the trackingmechanism

The structural model of the tracking system is shownin Figure 2 the representation being made in the motionplan (Π) which is normal to the polar axis The geometric

Figure 1 The virtual prototype of the PV string with monoaxistracking system

Motor source

5 643

2 1

H

G

F

E

D

CB

Module 1

Support 1

Module 2

Support 2

Module 3

Support 3

A2998400

Πperp polar axis

Figure 2 The structural model of the tracking mechanism

constraints from A and B are translational joints while theothers (C H) are revolute joints The intermediary ele-ment 21015840 whichmoves rod 3 of the parallelogrammechanismis rigidly connected to the actuator piston 2 Each modulerotates around its own support which is fixed on the ground

For simulating the dynamic behavior of the trackingsystem the virtual prototype was developed in mechatronicconcept by using a digital software platform which integratesthe following components CADmdashComputer Aided Design(CATIA)mdashto create the solid model MBSmdashMultiBody Sys-tems (ADAMS)mdashfor analyzing and optimizing the mechan-ical device and DFCmdashDesign for Control (EASY5 andADAMSControls)mdashfor the control system design

For connecting the mechanical model and the electroniccontrol system the input and output plants have beendefined The control force generated by the linear actuatorrepresents the input parameter in the mechanical modelTheoutput transmitted to the controller is the position angle ofthemodules (ie the daily angle)The input and output plantsare saved in a specific file for EASY5 (lowastinf) which is used tocreate the control system diagram (Figure 3) In the controlsystem model the TI block (tabular function of time) is thedatabase of the imposed daily angle while the MSCADAMSblock includes the mechanical device plant

From the controller point of view for obtaining reducedtransitory period and small errors a generic control loopfeedback mechanism (PID controller) was used The con-troller tuning (aiming to obtain the proportional P Integral Iand derivative D terms) was performed in an optimal designprocess with Matrix Algebra Tool (MAT) the model being

Journal of Solar Energy 3

Figure 3 The control system block diagram

transferred toMAT by using the EMX file formatThe designobjective refers to the minimization of the tracking error (thedifference between the imposed and current daily angle seeFigure 3)

In MAT the optimization was performed by using theldquominimize Vrdquo function

[119909 119891] = minimize V (function name 1199090 1198670 tol delx)

(2)

where 1199090is the initial guess for minimizer 119867

0the initial

guess for Hessian tol the relative tolerance for 119909 delx therelative step size for computing gradients by differencing xtheminimizer of the function and119891 the value of the functionat 119909

The next step was to create the MAT minimizer functionthat performs the optimization The study is performedby calling the ldquominimize Vrdquo function with the minimizerfunction as the first argument MAT will repeatedly call thefunction as it performs the minimization procedure Thefunction will set the tracking error appropriately and returnthe error in the simulation defined as the sum of the squaresof the differences between the simulation and desired valuesThe values of the proportional integral and derivative termswill result in a simulation that meets the design requirementsas follows P = 2150 I = 1503 and D = 1405

Finally in the cosimulation process ADAMS accepts thecontrol force from EASY5 and integrates the mechanicalmodel in response to this At the same timeADAMSprovidesthe current daily angle for EASY5 to integrate the controlsystem model

3 Designing the Tracking Law

The PV modules can be rotated without brakes duringthe daylight or can be discontinuously driven (step-by-stepmotion) The key idea for optimizing the motion law is

to maximize the energy gained through the step-by-steporientation for absorbing a quantity of solar energy closedby the ideal case (continuous orientation) and to minimizethe energy demand for performing the tracking

The energy produced by the PV string depends on thequantity of incident radiation the module efficiency and thenumber of modules The incident radiation depends on thedirect terrestrial radiation and the angle of incidence Thedirect radiation is established using the Meliszligrsquos empiricalmodel [16] depending on the extraterrestrial radiation themedium solar constant the day number during a yearthe atmosphere clarity the solar altitude angle the solardeclination the latitude angle the solar hour angle and thesolar time

The incidence angle is determined from the scalar prod-uct of the sunray vector and the normal vector on moduledepending on the diurnal and seasonal angles of the sunraysthe daily and elevation angles of the module and theazimuthal angle [3] In this way the incident solar radiationcan be estimated in every day during a year for differentlocations and tracking strategies

The paper presents the exemplification for the summersolstice day the numeric simulations being performed for theBrasov geographic area with the following input data thelocation latitude 120593 = 455∘ the solar declination 120575 = 2345∘the day number during the year 119899 = 172 (June 21) the localtime (from sunrise to sunset) 119879 isin (5 35 21 04)

For identifying the optimal motion field there wasconsidered the correlation between the motion amplitudeand the local time for obtaining symmetric revolute motionsrelative to the solar noon position (120573lowast = 0 119879 = 13 19)The analysis has been performed for the following cases (a)120573lowastisin [+90

∘ minus90∘] 119879 isin [5 35 21 04] the maximum

motion field (b) 120573lowast isin [+75∘ minus75∘] 119879 isin [6 52 19 46] (c)120573lowastisin [+60

∘ minus60∘] 119879 isin [810 1829] (d) 120573lowast isin [+45∘ minus45∘]

119879 isin [9 27 17 11] (e) 120573lowast isin [+30∘ minus30∘] 119879 isin [10 44 15 53](f) 120573lowast isin [+15∘ minus15∘] 119879 isin [12 02 14 36] In addition forthe fixed (nontracked) string 120573lowast = 0 throughout the daylight(119879 isin [5 35 21 04]) In this study the PVmodules are rotatedwithout brakes (continuousmotion) After sunset (2104) thetracking system returns to the initial position for the next day(facing East) on the same route with continuous motion

In this way the incident radiation curves have beenobtained (Figure 4) Integrating these curves and taking intoaccount the number ofmodules in the string (3modules) theactive surface of each module (126m2) and the PV moduleefficiency (ie the solar radiation conversion rate) (15) theenergy produced by the PV string (with andwithout tracking)has been obtained

Afterwards the energy demand for realizing the motionlaws was determined by using the virtual prototype of thetracking system The return of the tracking system in theinitial position is also considered In this way the energybalance was performed the results being systematized inTable 1 The energy gain (120576) is computed relative to the fixedstring

120576 = [119864119879minus (119864119865+ 119864119862)] sdot100

119864119865

(3)


500 915 1330 1745 2200Local time (h)

0

225

450

675

900

Inci

dent

radi

atio

n (W

m2)

(a)(b)(c)(d)

(e)(f)Fixed

Figure 4The incident radiation curves for the continuous trackingcases

Table 1 The energy balance for the continuous tracking cases

Trackingcase 119864

119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 []

(a) 522263

369218

5290 4002(b) 521821 3997 4025(c) 517933 2435 3962(d) 505686 1532 3655(e) 479672 701 2973(f) 434882 178 1774

Because the energy intake brought by the tracking cases(a) and (b) is very small comparative with (c) the case (c) hasbeen chosen as optimal in other words the optimal field forthe daily angle of the PV string is 120573lowast isin [+60∘ minus60∘] In thesame idea as can be seen in Figure 4 the solar radiation hassmall values in the limit positions close to the sunrise andsunset and for this reason it is not efficient to track the Sunin these areas

The continuous orientation (without brakes) was usedonly for establishing the optimal angular field of the dailymotion In the next stage the step-by-step tracking is imple-mented to avoid the continuous orientation disadvantagessuch as the high operating time of the system which hasnegative influence on the reliability the need to achievelarge transmission ratios which can cause constructive issuesthe behavior of the system under the action of externalperturbations (eg wind) whose effect can be amplified if thesystem is moving

Under these circumstances several step-by-step trackingstrategies have been evaluated depending on the numberof steps (in consequence the step dimension Δ120573lowast) forrealizing the optimal angular field of the daily motion 120573lowast isin[+60∘ minus60∘] 12 steps (Δ120573lowast = 10∘) 10 steps (Δ120573lowast = 12∘) 8

steps (Δ120573lowast = 15∘) 6 steps (Δ120573lowast = 20∘) 4 steps (Δ120573lowast = 30∘)or 2 steps (Δ120573lowast = 60∘)

One of the most important problems in the step-by-step tracking is to identify the optimal actuating time

0 6 12 18 24Local time (h)

minus60

minus30

0

30

60

Dai

ly an

gle (

deg)

Figure 5 The 8-step tracking law

Table 2 The energy balance for the step-by-step tracking cases

Number ofsteps 119864

119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 [] 120576

119905[]

12 516140

369218

2868 3902 984810 515917 27588 3899 98408 515506 26874 3889 98176 514618 26214 3867 97604 512075 25158 3801 95942 501290 2436 3511 8862

The solution is obtained by developing an algorithm based onthe following phases the optimal angular field is segmentedinto the intermediary positions depending on the step dimen-sion for each case (eg for 8 steps there are the followingpositions 120573lowast = plusmn60∘ plusmn45∘ plusmn30∘ plusmn15∘ 0∘) and the incidentradiation curves are consecutively obtained considering themodule fixed in these positions during the daylight analyzingthese curves the moment in which the value of the incidentradiation for a certain position ldquokrdquo becomes smaller than thevalue in the next position ldquok + 1rdquo is identified the analysiscontinues with the next pair of positions ldquok + 1rdquo and ldquok + 2rdquoand so on For example Figure 5 shows the 8-step trackinglaw which has been obtained in accordance with the previousdescribed algorithm

For the considered step-by-step tracking cases the resultsof the energy balance are systematized in Table 2 The energygain (120576) is computed relative to the fixed string case (see (3))while the step-by-step tracking efficiency (120576

119905) is determined

as relative value to the energy gain of the optimal continuoustracking case with the corresponding value fromTable 1 caseldquocrdquo (120576(119888) = 3962 Whday) being as follows

120576119905= 120576 sdot100

120576(119888) (4)

The energy demand for realizing the step-by-step motionlaws is a little bit greater than the energy demand for thecontinuous motion and this is because of the overshootingsthat appear when the actuator is started (each step meaningan actuator starter) However the differences in energydemand are relatively small there being the same lineartravel of the actuator (ie the same angular travel of the PV


0 6 12 18 24Local time (h)

0

75

15

225

30

Ener

gy d

eman

d (W

hda

y)

Figure 6 The energy demand for the 8-step tracking law

modules) For instance the energy demand for the 8-steptracking case is shown in Figure 6

Therefore by using the proposed algorithm for configur-ing the step-by-step tracking obtained values (in terms ofenergy gain) are close to those of the continuous tracking(which is not viable for physical implementation due to theaforementioned disadvantages) and this demonstrates theviability of the adopted optimization strategy Concerning theoptimal number of tracking steps it was demonstrated thatthe amount of energy gain per step decreases when the ordernumber of the step increases [17 18] The energy brought bythe final step has to be greater than the energy demand forrealizing this step

4 Conclusions

The application is a relevant example regarding the imple-mentation of the virtual prototyping tools in the designprocess of the tracking systems One of the most importantadvantages of this kind of simulation is the possibility toperform virtual measurements in any area and for anyparameter (motion force energy) At the same time byintegrating the electronic control system and the mechanicaldevice of the tracking mechanism at the virtual prototypelevel the physical testing process is greatly simplified andthe risk of the control law being poorly matched to the realphotovoltaic tracking system is minimized

The optimization strategy based on the minimization ofthe angular field for the daily motion and the determinationof the optimal actuating time to perform the motion stepsleads to an efficient PV system without developing expensivehardware prototypes In this way the behavioral performancepredictions are obtained much earlier in the design cyclethereby allowing more effective and cost efficient designchanges

Considering the algorithm of the product design devel-opment the virtual prototype precedes the manufacturingand implementation stage Based on the simulation andoptimization results (some of them being presented in thispaper) the embodiment design has been recently finishedand the technical documentation formanufacturing has beenelaborated The physical prototype of the tracking systemis about to be developed and it will be implemented in

the Green Energy Independent University Campus This willallow a relevant comparison between the virtual prototypeanalysis and the data achieved by measurements

References

[1] G N Tiwari Solar Energy Alpha Science Int Ltd PangbourneUK 2002

[2] E Calabro ldquoAn algorithm to determine the optimum tilt angleof a solar panel from global horizontal solar radiationrdquo Journalof Renewable Energy vol 2013 Article ID 307547 12 pages 2013

[3] C Alexandru and C Pozna ldquoSimulation of a dual-axis solartracker for improving the performance of a photovoltaic panelrdquoProceedings of the Institution ofMechanical Engineers A vol 224no 6 pp 797ndash811 2010

[4] C Alexandru and I N Tatu ldquoOptimal design of the solartracker used for a photovoltaic stringrdquo Journal of Renewable andSustainable Energy vol 5 no 2 Article ID 023133 pp 1ndash16 2013

[5] S Seme and G Stumberger ldquoA novel prediction algorithm forsolar angles using solar radiation and Differential Evolution fordual-axis sun tracking purposesrdquo Solar Energy vol 85 no 11pp 2757ndash2770 2011

[6] G K Singh ldquoSolar power generation by PV (photovoltaic)technology a reviewrdquo Energy vol 53 pp 1ndash13 2013

[7] M Ceccarelli ldquoChallenges for mechanism designrdquo in Proceed-ings of the 10th IFToMM International Symposium on Science ofMechanisms and Machines pp 1ndash13 2009

[8] W Schiehlen ldquoMultibody systems roots and perspectivesrdquoMultibody System Dynamics vol 1 no 2 pp 149ndash188 1997

[9] K S Karimov M A Saqib P Akhter M M Ahmed J AChattha and S A Yousafzai ldquoA simple photo-voltaic trackingsystemrdquo Solar Energy Materials and Solar Cells vol 87 no 1ndash4pp 49ndash59 2005

[10] F R Rubio M G Ortega F Gordillo and M Lopez-MartınezldquoApplication of new control strategy for sun trackingrdquo EnergyConversion andManagement vol 48 no 7 pp 2174ndash2184 2007

[11] S Abdallah and S Nijmeh ldquoTwo axes sun tracking system withPLC controlrdquo Energy Conversion and Management vol 45 no11-12 pp 1931ndash1939 2004

[12] M Alata M A Al-Nimr and Y Qaroush ldquoDeveloping amultipurpose sun tracking system using fuzzy controlrdquo EnergyConversion and Management vol 46 no 7-8 pp 1229ndash12452005

[13] F S Tymvios C P Jacovides S C Michaelides and CScouteli ldquoComparative study of Angstromrsquos and artificial neuralnetworksrsquo methodologies in estimating global solar radiationrdquoSolar Energy vol 78 no 6 pp 752ndash762 2005

[14] R Sorichetti and O Perpinan ldquoPV solar tracking systemsanalysisrdquo in Proceedings of the 22nd European Photovoltaic SolarEnergy Conference (EUPVSEC rsquo07) pp 246ndash252 2007

[15] B Ai H Shen Q Ban B Ji and X Liao ldquoCalculation ofthe hourly and daily radiation incident on three step trackingplanesrdquo Energy Conversion andManagement vol 44 no 12 pp1999ndash2011 2003

[16] M Meliszlig Regenerative Energiequellen Praktikum SpringerBerlin Germany 1997

[17] B Burduhos D Diaconescu I Visa and A Duta ldquoElectricalresponse of an optimized oriented photovoltaic systemrdquo inProceedings of the 12th International Conference onOptimization


of Electrical and Electronic Equipment (OPTIM rsquo10) pp 1138ndash1145 May 2010

[18] I S Hermenean and I Visa ldquoStep-tracking program synthesisof an azimuth tracked concentrating photovoltaic (CPV) sys-temrdquo Environmental Engineering and Management Journal vol10 no 9 pp 1225ndash1234 2011

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Submit your manuscripts athttpwwwhindawicom


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EnergyJournal of


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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


(Multibody Systems) theory [7 8] which facilitates the self-formulating algorithms

There are several works that approach control issuesmostly for the tracking systems of the individual modulesusing different techniques (closed loop systems with photosensors open loop systems based on astronomical com-puterized systems or hybrid combinations) and controllers(PID FNC and FNLC) [9ndash12] The research is focusedmostly on the evaluationprediction of the energy achievedby tracking and less on the energy demand for performingthe orientation

There are different models for the evaluation of theradiation potential as input data in the tracking systemsdesign The solar radiation can be measured using tradi-tional instruments or can be digitally recorded with a dataacquisition system At the same time there were developedlarge meteorological databases such as Meteonorm Thetraditional Angstromrsquos linear approach is based on measure-ments of sunshine duration while relatively new methodsare based on artificial neural networksmdashANN [13] Severalmodels for estimating the monthly mean solar radiation(linear Angstrom-Prescott variation quadratic equation log-arithmic variation and exponential function) were studied in[14] the root mean square error being the main element ofthe comparative analysisThemathematicalmodel developedin [15] is used for estimating the hourly and daily radiationincident on three-step tracking planes

In these terms the present paper approaches the improve-ment of the energetic efficiency of a PV string by designingand optimizing a mono-axis Sun tracker that simultaneouslychanges the daily position of the PV modules with a singledriving source The main task in optimizing the mechanismis to maximize the energetic gain by increasing the solarradiation input and minimizing the energy demand fortrackingThe incident radiation is estimated by using amath-ematic algorithm based on the direct terrestrial radiation andthe angle of incidence The paper proposes the integrationof the mechanical and electronic (control) components atthe virtual prototype level (ie modeling in mechatronicconcept) which allows performing the energy balance of thePV system

2 Designing the Tracking System

The system approached in this paper corresponds to a mono-axis trackingmechanism (Figure 1) at which the dailymotionis transmitted from the motor source which is a linearactuator with a multiparallelogram mechanism the revoluteaxes of the PV modules (in this case three modules) beingparallel with the polar axis The design is made for aninline string configuration but it can be adapted for otherconfigurations or for a higher number of modules Thedriving actuator is disposed on a fixed frame and this haspositive effect on the mass and inertia loading in the trackingmechanism

The structural model of the tracking system is shownin Figure 2 the representation being made in the motionplan (Π) which is normal to the polar axis The geometric

Figure 1 The virtual prototype of the PV string with monoaxistracking system

Motor source

5 643

2 1

H

G

F

E

D

CB

Module 1

Support 1

Module 2

Support 2

Module 3

Support 3

A2998400

Πperp polar axis

Figure 2 The structural model of the tracking mechanism

constraints from A and B are translational joints while theothers (C H) are revolute joints The intermediary ele-ment 21015840 whichmoves rod 3 of the parallelogrammechanismis rigidly connected to the actuator piston 2 Each modulerotates around its own support which is fixed on the ground

For simulating the dynamic behavior of the trackingsystem the virtual prototype was developed in mechatronicconcept by using a digital software platform which integratesthe following components CADmdashComputer Aided Design(CATIA)mdashto create the solid model MBSmdashMultiBody Sys-tems (ADAMS)mdashfor analyzing and optimizing the mechan-ical device and DFCmdashDesign for Control (EASY5 andADAMSControls)mdashfor the control system design

For connecting the mechanical model and the electroniccontrol system the input and output plants have beendefined The control force generated by the linear actuatorrepresents the input parameter in the mechanical modelTheoutput transmitted to the controller is the position angle ofthemodules (ie the daily angle)The input and output plantsare saved in a specific file for EASY5 (lowastinf) which is used tocreate the control system diagram (Figure 3) In the controlsystem model the TI block (tabular function of time) is thedatabase of the imposed daily angle while the MSCADAMSblock includes the mechanical device plant

From the controller point of view for obtaining reducedtransitory period and small errors a generic control loopfeedback mechanism (PID controller) was used The con-troller tuning (aiming to obtain the proportional P Integral Iand derivative D terms) was performed in an optimal designprocess with Matrix Algebra Tool (MAT) the model being






(2)


0the initial

















120576 = [119864119879minus (119864119865+ 119864119862)] sdot100

119864119865

(3)


500 915 1330 1745 2200Local time (h)

0

225

450

675

900

Inci

dent

radi

atio

n (W

m2)

(a)(b)(c)(d)

(e)(f)Fixed



Trackingcase 119864

119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 []

(a) 522263

369218

5290 4002(b) 521821 3997 4025(c) 517933 2435 3962(d) 505686 1532 3655(e) 479672 701 2973(f) 434882 178 1774






0 6 12 18 24Local time (h)

minus60

minus30

0

30

60

Dai

ly an

gle (

deg)




119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 [] 120576

119905[]

12 516140

369218

2868 3902 984810 515917 27588 3899 98408 515506 26874 3889 98176 514618 26214 3867 97604 512075 25158 3801 95942 501290 2436 3511 8862





120576119905= 120576 sdot100

120576(119888) (4)



0 6 12 18 24Local time (h)

0

75

15

225

30

Ener

gy d

eman

d (W

hda

y)




4 Conclusions





References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of






















(2)


0the initial

















120576 = [119864119879minus (119864119865+ 119864119862)] sdot100

119864119865

(3)


500 915 1330 1745 2200Local time (h)

0

225

450

675

900

Inci

dent

radi

atio

n (W

m2)

(a)(b)(c)(d)

(e)(f)Fixed



Trackingcase 119864

119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 []

(a) 522263

369218

5290 4002(b) 521821 3997 4025(c) 517933 2435 3962(d) 505686 1532 3655(e) 479672 701 2973(f) 434882 178 1774






0 6 12 18 24Local time (h)

minus60

minus30

0

30

60

Dai

ly an

gle (

deg)




119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 [] 120576

119905[]

12 516140

369218

2868 3902 984810 515917 27588 3899 98408 515506 26874 3889 98176 514618 26214 3867 97604 512075 25158 3801 95942 501290 2436 3511 8862





120576119905= 120576 sdot100

120576(119888) (4)



0 6 12 18 24Local time (h)

0

75

15

225

30

Ener

gy d

eman

d (W

hda

y)




4 Conclusions





References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















500 915 1330 1745 2200Local time (h)

0

225

450

675

900

Inci

dent

radi

atio

n (W

m2)

(a)(b)(c)(d)

(e)(f)Fixed



Trackingcase 119864

119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 []

(a) 522263

369218

5290 4002(b) 521821 3997 4025(c) 517933 2435 3962(d) 505686 1532 3655(e) 479672 701 2973(f) 434882 178 1774






0 6 12 18 24Local time (h)

minus60

minus30

0

30

60

Dai

ly an

gle (

deg)




119879[Whday] 119864

119865[Whday] 119864

119862[Whday] 120576 [] 120576

119905[]

12 516140

369218

2868 3902 984810 515917 27588 3899 98408 515506 26874 3889 98176 514618 26214 3867 97604 512075 25158 3801 95942 501290 2436 3511 8862





120576119905= 120576 sdot100

120576(119888) (4)



0 6 12 18 24Local time (h)

0

75

15

225

30

Ener

gy d

eman

d (W

hda

y)




4 Conclusions





References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















0 6 12 18 24Local time (h)

0

75

15

225

30

Ener

gy d

eman

d (W

hda

y)




4 Conclusions





References

























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
























FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















design and optimization of a monoaxial tracking system for

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