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Controversy around the CRONE suspension. And the war that followed CSOIS AFC Group Meeting, 10/08/2009 Christophe Tricaud. Outline. A little insight about research in France What is the CRONE suspension? What is wrong with it? What is in fact not wrong with it? And the fight goes on…..
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Controversy around the CRONE suspension And the war that followed CSOIS AFC Group Meeting, 10/08/2009 Christophe Tricaud
Outline • A little insight about research in France • What is the CRONE suspension? • What is wrong with it? • What is in fact not wrong with it? • And the fight goes on….. • Appendix: the French education system
Car Suspension u(t) : force developed by the suspension f0(t) : dynamic solicitation
Problems of the CRONE Suspension • In the laplace domain, the car’s vertical displacement is given by: • The general suspension has a general transfer function of the form • Which makes it a PD controller • The theoretical CRONE suspension is of the form • We can notice that C(0)=0, which makes it unable to hold the car’s own weight
Problems of the CRONE Suspension • Simple maths prove that the optimal static solution for the suspension is • Which is not of fractional order. The response of a fractional order control would induce an overshoot which is not the optimal solution.
Problems of the CRONE Suspension • Consider the uncertain system • And the following controller • The closed loop transfer function of such a system is • Such a transfer function is stable but for a second order system (like a car suspension system) the system becomes internally unstable to a white noise.
Other Problems • Based on the technological values given in the papers, the CRONE suspension’s static stiffness of 215 N/m is too low to work on an actual vehicle. • The hydropneumatic spheres used for the suspension can only be adjusted up to 20% which makes it impossible to realize a CRONE suspension as specified. • A spring’s stiffness necessarily varies when the load changes. In the CRONE suspension, the spring’s stiffness is assumed to be independent of the load, which makes it technologically impossible.
Don’t worry, there is no problem • The CRONE suspension DOES take into account the weight of the vehicle via a static precompensator. It makes sure the vehicle is at a constant height under static conditions. • The integer order “optimal” LQG controller sure has no overshoot, but has very poor isolation properties. A suspension’s primary objective is to give passengers a smooth drive. • A road profile is under no circumstance a “white” noise, therefore the CRONE suspension is not unstable within it’s working bandwidth.
Numbers Talk Step response of car body for three different masses (150 kg, 250 kg, 400 kg) and for a vehicle equipped with a Hydractive suspension in soft mode (a) and with a Hydractive CRONE suspension in comfort mode (b).
Latest Developments • Résultats de simulations de suspensions hydro-pneumatiques, Benoît Bergeon • Commentaires sur l’article R 7 422 des Techniques de l’Ingénieur, Benoît Bergeon & Gérard Montseny • Some traditional suspensions perform better than the CRONE suspension.
Appendix French Education System
CPGE • The preparatory classes, either in literature, sciences or management (generally two or three years) is the traditional way to enter the most prestigious grandes écoles. Most of them are in state high schools; there are a few private preparatory classes but they are expensive. Admission in preparatory classes are based on an academic report. Many students register in more than one class to maximize their chance of admission. Some of these classes are very selective and successful at placing students into the top schools. • The workload is generally very high and in-class competition between students is encouraged in some schools. Some classes may be psychologically stressful (depending on the students and the teachers' behaviour), and some students give up before the completion of their studies. The goal of preparatory classes is to prepare the student to match the academic level expected to pass the competitive recruitment examination of the main grandes écoles.
CPGE • In addition to class time and homework, students spend several hours each week completing exams and 'colles' (very often written 'khôlles' to look like a Greek word, this way of writing being initially a khâgneux joke). The so called 'colles' are unique to French academic education in CPGEs. They consist of oral examinations twice a week, in maths, physics, French and the foreign languages, usually English and Spanish. Students, usually in groups of three, spend an hour facing a professor alone in a room, answering questions and solving problems. • 'Colles' are regarded as extremely stressful, particularly due to the high standards expected by the teachers, and the subsequent harshness that may be directed at students who do not perform adequately, but they are important in as much as they prepare the students, from the very first year, to the oral part of the competitive examination, reserved to the happy few who successfully pass the written part.
