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Control of an Automotive Electromagnetic Suspension System

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Control of an Automotive Electromagnetic Suspension System Control of an automotive electromagnetic suspension system T.P.J. van der Sande D&C 2011.016 Master’s thesis Coach(es): ir. B.L.J. Gysen dr.ir. I.J.M. Besselink Supervisor: prof.dr. H. Nijmeijer Committee: prof.dr. H. Nijmeijer dr.ir. I.J.M. Besselink dr.ir. J.J.H. Paulides Eindhoven University of Technology Department of Mechanical Engineering Master Automotive Technology Dynamics & Control Eindhoven, March, 2011 Acknowledgements First and foremost, my gratitude goes out to ir. Bart Gysen, my direct supervisor for this project. His ever present support greatly helped me in performing this research. Second, my thanks go out to prof. Henk Nijmeijer, dr. Igo Besselink, dr. Johan Paulides and prof. Elena Lomonova. Their guidance, valuable tips and critical questions often helped me in the right direction. Thirdly, I would like to thank the EPE group for offering me this interesting and challenging research topic in which I could further enhance not only my theoretical but also my practical skills. A special note goes to my roommates, for the interesting discussions. Finally, I would like to thank my family, girlfriend and other friends for their support and encouragement. This made my graduation project much more enjoyable. i Abstract The main research goal of this thesis is to determine what performance gains can be achieved with a high bandwidth electromagnetic active suspension. As a baseline vehicle a BMW 530i is used, for which a retrofit electromagnetic suspension consisting of a spring and tubular perma- nent magnet actuator (TPMA) is designed. To design a control system for this actuator, a model of the BMW has been created, which consists of a quarter car model with variable sprung mass, damping coefficient and tire stiffness. As input to this model a road disturbance is used, that was modeled as a white noise source filtered by a first order low-pass filter. To test the performance of the actuator and controllers a full size quarter car test setup is used. As control objectives minimization of the sprung acceleration and dynamic tire compression are used with constraints on the suspension travel and RMS actuator force. The sprung accel- eration is used as an indication for ride comfort and the dynamic tire compression is used as an indication for handling quality. To account for human sensitivity to vibrations, the ISO2631-1 standard is used to filter the sprung acceleration. The suspension travel of the controlled system is limited to the maximum value that the BMW achieved with its spring and damper settings over a given road. Furthermore, the maximum RMS actuator force of 1000 N results from thermal limits. Two control approaches are considered, linear quadratic optimal control and robust control. For the former, a controller is found using a linearized quarter car model. By choosing three weighting factors either comfort or handling can be emphasized. Variations of the plant are accounted for by using robust control. Using frequency dependent weighting, certain frequencies can be emphasized. For instance, human sensitivity to vertical vibrations is incorporated using an approximation of ISO2631-1. By varying this weighting together with the other weighting filters either comfort or handling can emphasized, similar to the linear quadratic control. Measurements on the quarter car setup show that an improvement in comfort of 35 % can be achieved with linear quadratic control. This differs 55 % from the value predicted by simulations. However, this deviation can be explained by friction in the test setup and actuator as well as by uncertainties that were not modeled when designing the LQ controller. In case of the handling controller, measurements do match the simulations better on the smooth road. Dynamic tire compression is stability issues of the controller. With robust control an improvement of 48 % in comfort can be achieved on the setup at the cost of an increase of 99.3 % in dynamic tire compression. In terms of handling, an improve- ment of 17.7 % is achieved, worsening comfort by 10.7 %. Frequency weighting clearly has a desirable effect, as comfort decreases by 6 % for the handling controller on rough road whereas sprung acceleration worsens by 75 %. This means that all vibrations occur outside of the human sensitivity range. Deviations of the measurements from the simulations can be explained by stick slip friction in the suspension actuator as well as vibrations passing through the test setup. ii Samenvatting De belangrijkste onderzoeksvraag van deze thesis is wat voor prestatie winst er kan worden be- haald met een hoge bandbreedte electromagnetische actieve ophanging. Als basis voertuig wordt een BMW 530i gebruikt, waarvoor een retrofit tubulaire permanent magneet actuator, bestaande uit een veer en actuator, ontworpen is. Om het regelsysteem van deze actuator te ontwerpen is er een model van de BMW gemaakt dat bestaat uit een kwart voertuig model met variable geveerde massa, dempings coefficient en band stijfheid. Als ingang voor het model wordt een wegverstor- ing gebruikt, bestaande uit witte ruis gefilterd met een eerste orde laag doorlaat filter. Om de prestaties van de actuator en regelaars te bepalen is er een kwart voertuig opstelling gebruikt op ware grootte. Het regeldoel is het minimaliseren van de geveerde acceleratie of de dynamische band in- drukking met als randvoorwaarden de veerweg en RMS actuator kracht. De afgeveerde ver- snelling wordt gebruikt om de mate van comfort te bepalen. De dynamische band indrukking geeft een idee van de kwaliteit van de wegligging. Om rekening te houden met de menselijke gevoeligheid voor verticale vibraties wordt het ISO2631-1 criterium gebruikt. De limiet op de veerweg wordt bepaald door de veerweg van de BMW over dezelfde weg, terwijl de 1000 N actu- ator kracht limiet bepaald wordt door de thermische eigenschappen van deze. Twee controle topologien worden beschouwd, een linear kwadratisch en robuuste regelaar. Voor de eerste geldt dat er een optimale regelaar ontworpen wordt aan de hand van een gelin- earizeerde versie van het kwart voertuig model. Door het kiezen van drie weegfactoren kunnen comfort of wegligging benadrukt worden. Om zeker te zijn dat de regelaar stabiel is met de vari- aties die op kunnen treden in het system wordt een robuuste regeling gebruikt. Deze methode maakt het mogelijk om frequentie afhankelijke weegfilters te gebruiken. Een voorbeeld hiervan is het ISO2631-1 criterium, waarvan een benadering van wordt gebruikt om menselijke gevoeligheid voor verticale vibraties extra te benadrukken. Door dit weegfilter te gebruiken in combinatie met andere weegfilters kan comfort of wegligging benadrukt worden. Metingen op de kwart voertuig opstelling laten zien dat comfort met 35 % verbeterd kan worden met een linear kwadratische regelaar. Dit wijkt 55 % af van de verbetering voorspeld door simulaties. Dit kan echter verklaard worden door wrijving in de opstelling en actuator alsmede door onzekerheden die niet meegenomen zijn in het ontwerpen van de LQ regelaar. De resultaten van de regelaar die ontworpen is voor wegligging komen beter overeen met de simulaties. Een verbetering van 48.5 % kan worden behaald. Dit kon echter niet worden geverifieerd op de ruwe weg door instabiliteit van regelaar. Met de robuuste regelaar kan een verbetering van 48 % worden gehaald in comfort op de test opstelling ten koste van een verslechtering in dynamische band indrukking van 99.3 %. Voor wegligging kan er een verbetering van 17.7 % behaald worden waarbij comfort met 10.7 % verslechterd wordt. De toepassing van frequentie afhankelijke filters heeft een gewenst effect aangezien comfort met maar 6 % wordt verslechterd terwijl de verticale acceleratie met 75 % iii verslechtert. Dit betekent dat alle vibraties optreden buiten het gebied waar mensen het meest gevoelig zijn. Verschillen tussen de metingen en simulaties kunnen verklaard worden door ’slick- slip’ wrijving in de actuator en in de test opstelling. Verder spelen vibraties die via het frame van de test opstelling naar de sensoren komen een rol. iv Used Symbols and Abbreviations Abbreviations Name Meaning ABC Active body control DOF Degrees of freedom LQ Linear quadratic LQG Linear quadratic gaussian LQOF Linear quadratic output feedback LQR Linear quadratic regulator NS Nominal stability RC Robust control RS Robust stability RP Robust performance RMS Root mean square TPMA Tubular permanent magnet actuator VAG Volkswagen Audi group v Symbols Symbol Meaning ν Cut off frequency of road signal α Side slip angle dr Lateral tire damping ds Sprung damping Croad Road actuator controller 1 Uncertainty matrix Ei Actuator phase back EMF Fact Suspension actuator force Fra Road actuator force Fy Lateral tire force iO Current amplitude J LQ control objective kEi Actuator EMF constant kr Lateral tire stiffness kra Road actuator spring stiffness ks Sprung stiffness kt Tire stiffness Li Actuator phase inductance mc Contact patch mass ms Sprung mass mra Road actuator mass mu Unsprung mass µ Structured singular value ns Spatial frequency Q Weighting matrix for LQ control R Controllability matrix Ri Actuator phase resistance Gain that defines road amplitude τp Pole pitch ts Sampletime v Suspension speed Vi Supply voltage Vx Forward velocity w White noise Wi Weighting filter i yc Controlled output yr Lateral tire deflection vi Symbol Meaning z Suspension travel zr Road displacement zs Displacement of sprung mass zt Tire compression zu Displacement of unsprung mass φ Speed dependent commutation angle Conventions dz .t/ DPz .t/ (1) dt d2z .t/ DRz .t/ (2) dt 2 vii Contents 1 Introduction 1 1.1 Problem statement and objectives . 5 1.2 Literature review . 5 1.3 Outline . 8 2 Actuator and car model 9 2.1 BMW 530i . 9 2.2 Active suspension system . 11 2.2.1 Actuator . 11 2.2.2 Sensors . 16 2.3 Simplified car model . 17 2.3.1 Quarter car model . 17 2.3.2 Road input . 18 2.4 Summary . 21 3 Control of the active suspension 22 3.1 Control objectives .
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