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High Level Virtual Prototyping with Hardware in the Loop

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International Workshop on <strong>Virtual</strong> and Intelligent Measurement Systems29-30 April 2000, Annapolis, MD, USA<strong>High</strong> <strong>Level</strong> <strong>Virtual</strong> <strong>Prototyp<strong>in</strong>g</strong> <strong>with</strong> <strong>Hardware</strong> <strong>in</strong> <strong>the</strong> <strong>Loop</strong>A. Monti ( + ), R. Dougal ( ++ ), B. Pettus ( ++ ), E. Santi ( ++ )( + ) Dip. di Elettrotecnica, Politecnico di Milano, Milano, Italy( ++ ) Dep. of Electrical Eng<strong>in</strong>eer<strong>in</strong>g, University of South Carol<strong>in</strong>a, Columbia (SC), USAAbstract<strong>Virtual</strong> prototyp<strong>in</strong>g of complex systems presents <strong>in</strong>terest<strong>in</strong>gchallenges, especially <strong>with</strong> regard to systems <strong>in</strong> whichsome components are represented by software models ando<strong>the</strong>rs are present as real hardware. We describe here oneapproach to solv<strong>in</strong>g such a problem. In this <strong>in</strong>stance, twomotors were controlled by a dSpace general-purposecontroller board that was coupled to <strong>the</strong> <strong>Virtual</strong> Test Bedsoftware environment for system simulation.I. IntroductionSimulation of complex systems where manycomponents <strong>in</strong>teract presents peculiar challenges. Considerthat a particular system might be analyzed differently bydifferent users, each one of <strong>the</strong>m focus<strong>in</strong>g on a differentaspect of <strong>the</strong> system performance and each one hav<strong>in</strong>g adifferent metric for what is important. Consider that <strong>the</strong>complexity of <strong>the</strong> system may bridge several areas oftechnical expertise, and that users <strong>in</strong> each of thosetechnical areas traditionally work <strong>with</strong> <strong>the</strong>ir own set ofdesign and simulation tools. Consider also that some partsof <strong>the</strong> system may be already available while o<strong>the</strong>r partsare still be<strong>in</strong>g designed. To <strong>the</strong> extent possible, one maywish to substitute real components for <strong>the</strong>ir models everytime that a new component becomes available. Such anapproach keeps <strong>the</strong> design/simulation "alive", promotesiteration, allows an opportunity to validate models, and<strong>in</strong>troduces at <strong>the</strong> earliest possible time potentiallycomplicat<strong>in</strong>g nuances that were not orig<strong>in</strong>ally accountedfor <strong>in</strong> <strong>the</strong> component models. The cost of this approach isthat it requires a sophisticated capability for work<strong>in</strong>g <strong>with</strong><strong>Hardware</strong> In <strong>the</strong> <strong>Loop</strong> (HIL) [1-2]. All of <strong>the</strong>seconsiderations suggest <strong>the</strong> desirability of a new high-level<strong>in</strong>terface that allows many types of users to be comfortable<strong>with</strong> <strong>the</strong> virtual prototyp<strong>in</strong>g tool. An attempt to developsuch a tool has been underway at <strong>the</strong> University of SouthCarol<strong>in</strong>a for several years now under <strong>the</strong> program name<strong>Virtual</strong> Test Bed. We have just recently begun <strong>the</strong> processof <strong>in</strong>corporat<strong>in</strong>g hardware <strong>in</strong> <strong>the</strong> loop.II.The VTB ProjectThe <strong>Virtual</strong> Test Bed (VTB) is software for virtualprototyp<strong>in</strong>g of multi-technical dynamic systems. With<strong>in</strong><strong>the</strong> context of "virtual prototyp<strong>in</strong>g" we <strong>in</strong>clude not onlysimulation of system dynamics, but also solid model<strong>in</strong>g of<strong>the</strong> system, and visualization of <strong>the</strong> system dynamics. Oneof <strong>the</strong> project goals is to extend <strong>the</strong> context of virtualprototyp<strong>in</strong>g to <strong>in</strong>clude operation of hybrid systems --where some of <strong>the</strong> parts exist as real hardware and o<strong>the</strong>rparts exist as simulation models. The work reported <strong>in</strong> thispaper focuses on our approach to achiev<strong>in</strong>g that goal. Tobetter understand <strong>the</strong> context of our work, we present firstan overview of <strong>the</strong> <strong>Virtual</strong> Test Bed projectThe <strong>Virtual</strong> Test Bed project is dedicated to develop<strong>in</strong>g anew environment for simulation and virtual prototyp<strong>in</strong>g ofpower electronic systems [3-4]. One of its challenges is tofully accommodate <strong>the</strong> breadth of discipl<strong>in</strong>es that powerelectronics encompasses, <strong>in</strong>clud<strong>in</strong>g analog electronics,digital electronics, power systems, controls, electromechanics,and mechanical systems. We have addressed<strong>the</strong>se challenges by choos<strong>in</strong>g to support:Multiformalism: Different languages can be use to buildmodels of <strong>the</strong> different components that make up a system.This allows an <strong>in</strong>dividual to build models us<strong>in</strong>g <strong>the</strong>language preferred <strong>with</strong><strong>in</strong> his or her discipl<strong>in</strong>e. Inparticular <strong>the</strong> system now <strong>in</strong>tegrates dynamic modelsdef<strong>in</strong>ed by such widely used tools such asMatlab/Simul<strong>in</strong>k, SPICE, and ACSL [5-7-8].<strong>High</strong>ly <strong>in</strong>teractive environment: Users can change <strong>the</strong>system topology or parameters while a simulationexecutes. This allows <strong>the</strong> user to rapidly <strong>in</strong>vestigate<strong>in</strong>teractions between components or to explore <strong>the</strong><strong>in</strong>fluence of design parameters on system performance.<strong>High</strong>-level visualization: Visualization models of <strong>the</strong>system can be easily created and l<strong>in</strong>ked to live simulation


data. Visualization aids <strong>the</strong> user to rapidly comprehend <strong>the</strong>system performance. Visual outputs <strong>in</strong>clude data-drivenanimation of <strong>the</strong> motion of solid objects, imposition on topof <strong>the</strong> solid objects of novel representations of abstractsimulation data, or simply oscilloscope-like graphs.Distributed computation: Large or complicated systemsrequire that computational load be distributed across anetwork <strong>in</strong> order to achieve speeds suitable for <strong>in</strong>teractiveexplorations. This naturally supports hardware-<strong>in</strong>-<strong>the</strong>-loopoperations.The structure here <strong>in</strong>troduced is well summarized <strong>in</strong> Figure1. Let us now go <strong>in</strong>to details about <strong>the</strong> component structureto better appreciate <strong>the</strong> system design.PC1VTBSocketPC2DOSMatlab Eng<strong>in</strong>eThe VTB has o<strong>the</strong>r significant strengths, <strong>in</strong>clud<strong>in</strong>gautomatic enforcement of physical constra<strong>in</strong>ts (such asensur<strong>in</strong>g that <strong>the</strong> sum of currents at a node is zero).MatlabPC busDspaceBoardIII.Demonstration SystemOur HIL capability was developed <strong>with</strong> reference to aspecific laboratory setup so as to focus our effort and toallow immediate test<strong>in</strong>g of <strong>the</strong> system. The hardwaresystem amounted to a two-axis DC motor drive. Our<strong>in</strong>terest was <strong>in</strong> design<strong>in</strong>g <strong>the</strong> higher-level logic to control<strong>the</strong> motors <strong>in</strong> coord<strong>in</strong>ation <strong>with</strong> software models of o<strong>the</strong>rcomponents of <strong>the</strong> system. Work<strong>in</strong>g <strong>in</strong> this way, we wereable to directly verify <strong>the</strong> consequences of <strong>the</strong> commandsignals sent to <strong>the</strong> drive and to use a real oscilloscope toobserve <strong>the</strong> system operation. At <strong>the</strong> same time, <strong>the</strong>advanced visualization capabilities of <strong>the</strong> <strong>Virtual</strong> Test Bedshowed on a PC screen <strong>the</strong> operation of <strong>the</strong> entire system.The motor control system was based on a dSpace board[9], which could be easily programmed us<strong>in</strong>gMatlab/Simul<strong>in</strong>k. The authors added a custom <strong>in</strong>terface toMatlab to exchange data <strong>with</strong> <strong>the</strong> control board work<strong>in</strong>g <strong>in</strong>real time. The system is based on <strong>the</strong> Matlab Eng<strong>in</strong>e [6]<strong>in</strong>terface and allows one to send data to and receive datafrom <strong>the</strong> Matlab workspace. A set of custom Matlabcommands (developed by <strong>the</strong> authors) allowscommunication <strong>with</strong> <strong>the</strong> real time dSpace board. The dataexchange <strong>with</strong> VTB was implemented via a socketcommunication channel. This arrangement allows hav<strong>in</strong>gVTB and <strong>the</strong> dSpace board runn<strong>in</strong>g on differentcomputers, if so desired. This feature adds flexibility to <strong>the</strong>virtual simulation environment.From <strong>the</strong> VTB po<strong>in</strong>t of view, <strong>the</strong> external system is adevice that receives virtual data from <strong>the</strong> simulationenvironment and that sends back real data from <strong>the</strong>hardware environment. This is reasonably transparent to<strong>the</strong> user, who has only to def<strong>in</strong>e <strong>the</strong> parameters for <strong>the</strong>socket communication (<strong>the</strong> name of <strong>the</strong> PC hav<strong>in</strong>g <strong>the</strong>DSP board) and <strong>the</strong> number of <strong>the</strong> <strong>in</strong>put/output channel. In<strong>the</strong> demonstration case two data are sent from <strong>the</strong>simulation environment to <strong>the</strong> hardware (<strong>the</strong> two axisposition references) and two are sent back from <strong>the</strong>hardware to <strong>the</strong> simulation environment (<strong>the</strong> real positionof <strong>the</strong> two motors).Digital and Analog I/OControlledFigure 1: Diagram of <strong>the</strong> HIL system, <strong>in</strong>clud<strong>in</strong>gtwo motor drives, <strong>the</strong> <strong>in</strong>terfaces, <strong>the</strong> PC and <strong>the</strong>DSPACE boardIV.The Matlab-dSPACE InterfaceThe heart of <strong>the</strong> communication protocol <strong>with</strong> <strong>the</strong>dSPACE board is <strong>the</strong> Matlab eng<strong>in</strong>e. The Matlab eng<strong>in</strong>eallows data exchange between Matlab and C customsoftware.The ma<strong>in</strong> program is a DOS application runn<strong>in</strong>g on <strong>the</strong>PC connected to <strong>the</strong> dSPACE system. The structure of <strong>the</strong>application is well summarized <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g:• wait for VTB startup• start Matlab Eng<strong>in</strong>e• set up <strong>the</strong> communication <strong>with</strong> Matlab def<strong>in</strong><strong>in</strong>g <strong>the</strong> setof shared data• select <strong>the</strong> dSpace board to be used <strong>in</strong> <strong>the</strong> experiment• wait for VTB dataAt every cycle <strong>the</strong> follow<strong>in</strong>g set of operations isperformed:• send <strong>the</strong> data from VTB to dSpace system us<strong>in</strong>g <strong>the</strong>Matlab eng<strong>in</strong>e• acquire from dSPACE <strong>the</strong> feedback data• send <strong>the</strong> feedback data through <strong>the</strong> socketcommunication channel to VTBThis set of data exchange is guaranteed thanks to a set ofuser def<strong>in</strong>ed new Matlab commands that run through <strong>the</strong>Matlab eng<strong>in</strong>e:HW


• [xf, yf] = placexy(x,y): it sends <strong>the</strong> new reference xand y to <strong>the</strong> motor controllers and receives back <strong>the</strong>real xf and yf position• enable_motor(num): it enables <strong>the</strong> position and speedcontrol of <strong>the</strong> motor num• disable_motor(num):it disables <strong>the</strong> position and speedcontrol of <strong>the</strong> motor numThe gun visualization is shown <strong>in</strong> Figure 2. The gunangular position and pitch are given by <strong>the</strong> actual angularposition of <strong>the</strong> two motors. VTB receives <strong>the</strong> actual motorposition from <strong>the</strong> dSpace board and animates <strong>the</strong> gun. Thegun itself is placed aboard <strong>the</strong> ship shown <strong>in</strong> Figure 3. Thereference angle for <strong>the</strong> two motors could come from <strong>the</strong>position of an “enemy” airplane, which could also be partof <strong>the</strong> VTB visualization.V. The VTB Interface and VisualizationCapabilityVTB allows advanced data visualization. The purpose is tohelp <strong>the</strong> user understand <strong>the</strong> simulation results and to put<strong>the</strong>m <strong>in</strong> a visual form that may be more familiar andmean<strong>in</strong>gful to <strong>the</strong> user. In particular VTB allows datadrivenanimations. In <strong>the</strong> case of <strong>the</strong> two-axis motorcontrol presented here, an animation has been implementedshow<strong>in</strong>g a possible application of <strong>the</strong> two-axis motorcontroller. The application is <strong>the</strong> two-axis position controlof a gun <strong>in</strong> a ship.Figure 2: VTB visualization of a gun whoseposition is controlled by <strong>the</strong> two-axis motorsystem. The gun is aboard a ship.åFigure 3: VTB visualization of <strong>the</strong> ship carry<strong>in</strong>g<strong>the</strong> gun. The arrow shows <strong>the</strong> position of <strong>the</strong> gun.VI. The Distributed Environment andNetwork SupportCommunication at <strong>the</strong> computer-to-computer level (PC1 toPC2 <strong>in</strong> figure 1) is handled by use of W<strong>in</strong>dows/NTsockets. This is a generic technique and functionalequivalents exist for o<strong>the</strong>r environments. The connectionto <strong>the</strong> <strong>in</strong>dividual PC’s is a 10 Mbit E<strong>the</strong>rnet, creat<strong>in</strong>g apotential bottleneck although <strong>the</strong> highest communicationbandwidth achieved <strong>in</strong> our system is currently only onethird of <strong>the</strong> available network bandwidth (<strong>in</strong> <strong>the</strong> best caseof unidirectional communication from VTB to <strong>the</strong> dSpaceboard). However, <strong>the</strong> variable latency times are potentiallymore troublesome than <strong>the</strong> bandwidth. A next -generationversion of <strong>the</strong> system will have a dedicated connection,result<strong>in</strong>g <strong>in</strong> predictable performance.It is possible to compensate for some of <strong>the</strong> effects of(variable) delays <strong>in</strong> <strong>the</strong> network. For <strong>in</strong>stance, <strong>the</strong>re are anumber of distributed clock algorithms that can keep localclocks synchronized <strong>in</strong> <strong>the</strong> presence of significant networkdelays. Reference [10] has a good discussion of <strong>the</strong>sealgorithms. Current network response times are sufficientfor distributed large subsystems hav<strong>in</strong>g slow responsetimes but improvements may be needed for device-levelconnections hav<strong>in</strong>g faster response times.VII.ResultsThe data protocol has been implemented and tested.Figure 4 shows an <strong>in</strong>terest<strong>in</strong>g result. The position of onemotor is fed to <strong>the</strong> horizontal <strong>in</strong>put of <strong>the</strong> oscilloscope,while <strong>the</strong> position of <strong>the</strong> o<strong>the</strong>r motor is fed to <strong>the</strong> vertical<strong>in</strong>put. A VTB model runn<strong>in</strong>g on ano<strong>the</strong>r computergenerates <strong>the</strong> reference signals for <strong>the</strong>se movements.Figure 5 shows <strong>the</strong> commanded position and actualposition of one motor. The delay is two VTB time steps.This can be seen from <strong>the</strong> figure: <strong>the</strong> commanded positionat time step #171 has a numerical value of 106.393 and <strong>the</strong>actual position reaches a value close to it (106.535) at timestep #173.The delay is mostly due to network delay. This can beseen from Figure 6, which shows <strong>the</strong> actual motor positionand <strong>the</strong> commanded motor position measured at <strong>the</strong> DSPboard. This allows look<strong>in</strong>g at <strong>the</strong> motor controller response


time separately from <strong>the</strong> network delay: <strong>the</strong> dSpace boardreceives <strong>the</strong> new commanded position and <strong>the</strong> controlleradjusts <strong>the</strong> actual motor position to follow it. The twowaveforms are substantially <strong>in</strong> phase, which <strong>in</strong>dicates that<strong>the</strong> delay measured by VTB (Figure 5) is due to <strong>the</strong>network connection. The response time to a step referencechange of <strong>the</strong> dSpace position controller is approximately120ms.The communication bandwidth is approximately threedata po<strong>in</strong>ts per second <strong>in</strong> <strong>the</strong> case of bi-directionalcommunication between VTB and <strong>the</strong> dSpace board. In <strong>the</strong>case of unidirectional communication (no real position sentback to VTB) <strong>the</strong> speed was approximately twenty timeshigher. At this po<strong>in</strong>t <strong>the</strong> reason for this deterioration ofcommunication speed <strong>in</strong> <strong>the</strong> case of bi-directionalcommunication is not clear.Figure 6: Oscilloscope measurement show<strong>in</strong>gactual motor position <strong>in</strong> <strong>the</strong> upper trace andcommanded position <strong>in</strong> <strong>the</strong> lower trace (timescale 2s/div).Attempts to speed up communication are under way. Apromis<strong>in</strong>g approach is open<strong>in</strong>g a direct communicationchannel between VTB and <strong>the</strong> dSpace board bypass<strong>in</strong>gMatlab (see Figure 1).Figure 4: The real position of <strong>the</strong> motor as shown<strong>in</strong> x-y mode <strong>in</strong> <strong>the</strong> scope (<strong>the</strong> position referencecame from <strong>the</strong> VTB model)Figure 5: Commanded position and actualposition of one of <strong>the</strong> motors as visualized byVTB. The actual position is delayed <strong>with</strong> respectto <strong>the</strong> commanded position by two time steps.VIII. ApplicationsThe HIL experience here described is a start<strong>in</strong>g po<strong>in</strong>tfor a wider experience <strong>in</strong> VTB project. New features willbe added to automate <strong>the</strong> <strong>in</strong>terface between any plant partand <strong>the</strong> simulator.The pr<strong>in</strong>ciple of <strong>the</strong> VTB design approach, <strong>with</strong>reference to HIL, could be summarized as follows:• at <strong>the</strong> beg<strong>in</strong>n<strong>in</strong>g of <strong>the</strong> project noth<strong>in</strong>g is availableso that a complete virtual model is compulsory• dur<strong>in</strong>g <strong>the</strong> project, as soon as a part is available,def<strong>in</strong>e <strong>the</strong> <strong>in</strong>terface, and substitute <strong>the</strong> virtualmodel <strong>with</strong> <strong>the</strong> real plantThis should guarantee that any subsystem of a complexpart is developed <strong>with</strong> an appropriate <strong>in</strong>terface <strong>with</strong> <strong>the</strong>rest of <strong>the</strong> system.Fur<strong>the</strong>rmore, <strong>the</strong> realized system is also extremely<strong>in</strong>terest<strong>in</strong>g from <strong>the</strong> didactic po<strong>in</strong>t of view. In effect, itallows a group of students to share among <strong>the</strong>mselves as<strong>in</strong>gle remote real platform. Students can design anddevelop a system us<strong>in</strong>g only virtual prototypes, <strong>the</strong>n, when<strong>the</strong> simulation is completely work<strong>in</strong>g, <strong>the</strong>y can substitute<strong>the</strong> virtual prototypes <strong>with</strong> real hardware accessed througha network connection.An <strong>in</strong>terest<strong>in</strong>g example has been already developed<strong>with</strong> reference to <strong>the</strong> current application.


As discussed above, <strong>the</strong> system implemented <strong>in</strong>cludestwo DC motors <strong>with</strong> position control. The complete systemhas been modeled <strong>with</strong> Simul<strong>in</strong>k before <strong>the</strong>implementation. Only <strong>the</strong> speed and position control hasbeen at <strong>the</strong> end downloaded on <strong>the</strong> dSPACE board.This procedure suggests a set of exercises for studentthat will be applied <strong>in</strong> <strong>the</strong> Electrical Drive course atPolitecnico di Milano:• development of a suitable model start<strong>in</strong>g from plantspecification• tun<strong>in</strong>g of <strong>the</strong> speed control• design of <strong>the</strong> position control us<strong>in</strong>g pole placementapproach• design of coord<strong>in</strong>ated trajectories on a two axis controlLet us focus, e.g., on <strong>the</strong> third example that has beenalready def<strong>in</strong>ed <strong>in</strong> details.Start<strong>in</strong>g from <strong>the</strong> project specification a detailed modelof <strong>the</strong> control can be def<strong>in</strong>ed <strong>in</strong> terms of transfer function.Apply<strong>in</strong>g <strong>the</strong> control <strong>the</strong>ory <strong>the</strong> controller transfer functioncan be calculated.The <strong>the</strong>ory can <strong>the</strong>n experimentally verified:• program VTB to def<strong>in</strong>e a reference trajectory• download <strong>the</strong> new control us<strong>in</strong>g <strong>the</strong> obta<strong>in</strong>ed transferfunction• start VTB and dSPACE system analyz<strong>in</strong>g <strong>the</strong> positionevolution both graphically and visuallyThis could be considered a first test: <strong>the</strong>n <strong>the</strong> studentcould check <strong>the</strong> control parameter sensitivity syn<strong>the</strong>siz<strong>in</strong>gdifferent controllers start<strong>in</strong>g form wrong plant parameterspecification. The procedure is really simple andcompletely automated and allows <strong>the</strong> student to set-up asequence of experiments <strong>in</strong> a very short time.Thanks to <strong>the</strong> network distributed characteristics of <strong>the</strong>application, <strong>in</strong> a short time <strong>the</strong> experiment will be <strong>in</strong>cluded<strong>in</strong> a <strong>Virtual</strong> Laboratory structure so that students wouldaccess <strong>the</strong> laboratory at any time from <strong>the</strong> universitynetwork for <strong>the</strong> practical tests.IX.Fur<strong>the</strong>r DevelopmentsTwo fur<strong>the</strong>r developments are under consideration at<strong>the</strong> moment:• <strong>the</strong> DSPACE board can be used not only as an<strong>in</strong>terface to control systems but also as a generalpurpose data acquisition board. For this reason <strong>the</strong>authors are work<strong>in</strong>g to def<strong>in</strong>e advanced Matlabcommands to make communication easier and moreflexible• at <strong>the</strong> moment Matlab acts as a bottleneck on <strong>the</strong>communication protocol. The authors are work<strong>in</strong>g on<strong>the</strong> possibility to directly communicate <strong>with</strong> <strong>the</strong>dSPACE board at low level. This should improve <strong>the</strong>total throughput and <strong>the</strong> simulation performance.X. ACKNOWLEDGMENTThis work was supported <strong>in</strong> part by <strong>the</strong> Office of NavalResearch under Grant N00014-96-1-0926. The activity of<strong>the</strong> first author has been partially supported by C.N.R. (<strong>the</strong>Italian Council for Research) <strong>in</strong>side <strong>the</strong> <strong>in</strong>itiative ShortTerm Mobility for Researchers. The help of Teems Lovettand Bill Mckay from <strong>the</strong> University of South Carol<strong>in</strong>a <strong>in</strong><strong>the</strong> implementation of <strong>the</strong> network communicationsoftware is gratefully acknowledged. The help ofFerd<strong>in</strong>anda Ponci <strong>in</strong> <strong>the</strong> hardware realization is alsogratefully acknowledged.REFERENCE[1] Carmeli, S., Castelli Dezza, F., Monti, A., “A new platformfor real time test<strong>in</strong>g of electrical drive digital control”, IEEECOMPEL 98, 19-22 July 1998, Como (Italy)[2] De Paola, E., Mar<strong>in</strong>a, G., Monti, A., Tramalloni, L., "Afrequency analysis method for real-time simulation", EPE99,Lausanne (CH), September 1999[3] Beker, B.; Hudg<strong>in</strong>s, J.L.; Coronati, J.; Gillett, B.; Shekhawat,S., Extraction of parasitic circuit elements <strong>in</strong> a PEBB forapplication <strong>in</strong> <strong>the</strong> virtual test bed, Industry ApplicationsConference, 1997. Thirty-Second IAS Annual Meet<strong>in</strong>g, IAS'97., Conference Record of <strong>the</strong> 1997 IEEE Volume: 2 ,Page(s): 1217 -1221 vol.2[4] Gokdere, L.U.; Brice, C.W.; Dougal, R.A., Graphical andvisual simulation of electric drive systems , Electric Mach<strong>in</strong>esand Drives, 1999. International Conference IEMD '99,Page(s): 685 -687[5] MGA Software, "ACSL Model, ACSL reference manual",1995 (for more details see http://www.acslsim.com/)[6] The Mathworks, "Matlab: Application Program InterfaceGuide", 1996 (for more details seehttp://www.mathworks.com/)[7] The Mathworks, "Simul<strong>in</strong>k: User Guide", 1998[8] Microsim, "PSPICE A/D Simulator User Guide", 1997 (formore details see http://pcb.cadence.com/)[9] dSpace, "Matlab Interface and Trace Library", 1999 (for moredetails see http://www.dspace<strong>in</strong>c.com/)[10] Shem-Tov Agrawala, Ashok K., Levi “Real-Time SystemDesign”, McGraw-Hill, 1990.

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