Optimal observers and optimal control : improving car efficiency with Kalman et Pontryagin Kenneth Sebesta To cite this version: Kenneth Sebesta. Optimal observers and optimal control : improving car efficiency with Kalman et Pontryagin. General Mathematics [math.GM]. Université de Bourgogne, 2010. English. NNT : 2010DIJOS097. tel-00935177 HAL Id: tel-00935177 https://tel.archives-ouvertes.fr/tel-00935177 Submitted on 23 Jan 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Optimal Observers and Optimal Control: Improving Car Efficiency with Kalman and Pontryagin by Kenneth D. Sebesta Dissertation submitted to the Faculty of the Graduate School of the University of Luxembourg in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2010 Jury: Professor Juergen Sachau, Co-Advisor Professor Eric Busvelle, Co-Advisor Professor Ugo Boscain, Chair Professor Jean-Regis Hadji-Minaglou Professor Hassan Hammouri Professor Thierry-Marie Guerra c Copyright by Kenneth D. Sebesta 2010 Preface The information age has radically shifted every aspect of our lives, perhaps first and foremost our scientific ones. Before the information age, 99% of humanity’s interaction with technology was limited to a car, airplane, telephone, or television. While technology had had a dramatic impact on life— from medicine to cheap manufacturing— for the populace at large direct everyday interaction with technology was rare. Internet has changed all that. It has brought high technology into everyday lives, to the point that it is unimaginable to do without. Science is no longer the exclusive domain of the scientist. Now we enter into the age of the makers . Makers don’t invent from whole cloth, they assemble. They take bits bits and pieces gathered from the far-flung corners of the world and combine them to do something new, something different. Oftentimes, something scientific . —————————————— Who is a scientist? Historically, science was largely performed by the nobles and well-to- do. In the 19 th century the natural sciences— geology, astronomy, etc...— were regarded as social activities. Discovering a new plant, or planet for that matter, was as much a way to impress ones friends as it was to push back the frontiers of science. It wasn’t until the early-to-mid 20 th century that science become a career instead of a hobby. WWI and especially WWII were times of tremendous scientific progress, pushed by the various governments’ fervent desires to discover and invent the secret weapons that would win the war. With the governments’ desire came funding, stability, and jobs. Now in the early 21 st Century, science is undergoing another transformation. Scientific principles are no longer hidden in an ivory tower, papers are no longer locked behind closed doors. Individuals are now able to quickly and efficiently access the scientific world. In a way, science has gone full loop. In past times, only the rich had the time to indulge in idle fantasies. Now, we are perhaps all rich enough for such explorations. Now, we are becoming makers . —————————————— Most hard science will still be done by professional scientists, just like most hard journal- ism is done by professional journalists. But just as the journalistic world is supplemented by the bloggers, so is the scientific world supplemented by the makers. We must not forget this burgeoning world of the amateur scientist. To this end, our scientific output must not be hidden. It must be obvious, available, and accessible. In this spirit, this dissertation is an experiment, much the same that a PhD is an experiment. This dissertation is designed such that the results and application are easy to understand for those with a less-than-formal background. i Dedication To Laura. The best moments of my life have been spent with you. ii Acknowledgments It is difficult to express in words the journey of science. It is an open-ended trip where the consequences of decisions are years in the making. An uphill trip littered with the refuse of cast-off ideas and rejected works. A sublime trip that is filled with the joy of accomplishment, of exploration, and of knowledge. It is said that research is “spending six months of work in order to find out which two weeks made it all worthwhile”. My thanks go to all those who helped me recognize my two weeks. First and foremost, I’d like to thank my advisor, Professor Juergen Sachau for giving me an invaluable opportunity to work on challenging and extremely interesting projects over the past four years. He has always made himself available for help and advice and there has never been an occasion when I’ve knocked on his door and he hasn’t given me time. I would also like to thank my co-advisor, Professor Eric Busvelle. Without his extraor- dinary theoretical ideas and computational expertise, this thesis would have been a distant dream. Seldom have I encountered anyone with such clarity of vision. Thanks are due to Professors Ugo Boscain and Jean-Regis Hadji-Minaglou for agreeing to serve on my thesis committee, and to Professors Thierry-Marie Guerra and Hassan Hammouri for taking the time to review the manuscript as my reviewers. Special thanks to Professor Jean-Paul Gauthier, for whom nothing is impossible; and to Dr. Nicolas Boizot, who walked side by side with me on our common path, in Burgundy and Luxembourg alike. iii iv Contents List of Figures xii List of Tables xiii List of Abbreviations xv List of Abbreviations xv Introduction 1 Notation conventions 3 1 State of the (Theoretical) Art 5 1.1 Statemodels .................................... 6 1.2 Observermodel................................... 6 1.2.1 Modeling .................................. 6 1.2.1.1 Model variables . 6 1.2.1.2 Referenceframes. 8 1.2.1.3 Kinematics ............................ 8 1.2.1.4 Energy analysis . 10 1.2.2 Completeobservermodel . 11 1.2.3 Observability normal form . 12 1.3 Controllermodel .................................. 16 1.3.1 Modeling .................................. 16 1.3.1.1 Model variables . 16 1.3.1.2 Cost................................ 17 1.3.1.3 Kinematics ............................ 17 1.3.2 Completecontrollermodel. 17 1.4 Discussion...................................... 18 2 State of the (Practical) Art 19 2.1 Microprocessors................................... 21 2.2 Microcontrollers .................................. 21 2.3 Sensorpackage ................................... 21 v 2.3.1 GPS..................................... 22 2.3.2 Accelerometer................................ 22 2.3.3 Odometer.................................. 24 2.3.4 Fuelinjectortimer ............................. 24 2.3.4.1 Engine angular distance/velocity . 25 2.3.4.2 Fuelflowmeter.......................... 26 2.4 Othersensors .................................... 27 2.4.1 Gyroscope.................................. 27 2.4.2 Compass .................................. 28 2.5 Additionalequipment ............................... 28 2.5.1 Data storage . 28 2.5.2 Digital Elevation Map . 29 3 Efficiency mapping 31 3.1 Model ........................................ 33 3.1.1 Valuesused................................. 34 3.1.2 Carmodelobserver............................. 34 3.1.2.1 Car model observability . 34 3.1.2.2 Choice of observer . 35 3.1.2.3 Jacobian . 37 3.1.3 Observerpseudo-code . 38 3.1.4 Tuning.................................... 39 3.1.4.1 Tuning state model covariances . 39 3.1.4.2 Tuning measurement model covariances . 41 3.1.4.3 Valuesused............................ 42 3.1.4.4 Normalization . 42 3.2 Datagathering ................................... 43 3.3 Results........................................ 44 3.3.1 Highway................................... 44 3.3.2 In-town ................................... 45 3.3.3 Maximum acceleration . 45 3.3.4 Efficiencymap ............................... 45 3.3.5 Discussion.................................. 46 3.4 Curvefitting .................................... 48 3.4.1 Efficiencyfitting .............................. 48 3.4.1.1 Polynomials of highest degree 2 . 49 3.4.1.2 Polynomials of highest degree 3 . 50 3.4.1.3 Polynomials of highest degree 4 . 50 3.4.1.4 Conclusion . 51 3.4.2 Specificfuelconsumptionfitting . 51 3.4.2.1 Polynomials of highest degree 2 . 52 3.4.2.2 Polynomials of highest degree 3 . 52 3.4.2.3 Polynomials of highest degree 4 . 53 3.4.2.4 Conclusion . 53 3.4.3 Pin fitting.................................. 54 3.4.3.1 Polynomials of highest degree 2 . 54 vi 3.4.3.2 Polynomials of highest degree 3 . 54 3.4.3.3 Polynomials of highest degree 4 . 54 3.4.3.4 Conclusions . 54 3.5 Validation...................................... 54 3.6 Additionalresults.................................. 55 4 Applying Pontryagin’s Maximum Principle 59 4.1 Definingoptimality................................. 60 4.2 Fixed time versus non-fixed time optimization . 61 4.3 Global vs. local optimization . 61 4.4 One dimension: acceleration on the straight and level . 62 4.4.1 CVTcase.................................. 63 4.4.1.1 T, non-fixed horizon . 64 4.4.2 Multi-speedtransmissioncase. 66