EMR coupled with Power-Oriented Graphs for automotive application

Transcription

1 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation EMR coupled with Power-Oriented Graphs for automotive application Dr. Federica GROSSI, Prof. Roberto ZANASI Università di Modena, Italy Dr.Walter LHOMME, Prof. Alain BOUSCAYROL L2EP, University Lille1, MEGEVH network,

2 Outline 2 1. Power-Oriented Graphs basic features 2. The studied system: simplified model of a vehicle with tire-soil interaction 3. Control structure 4. Simulations 5. Comparison with EMR 6. Conclusion

3 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 1. Power-Oriented Graphs basic features

4 Power-Oriented Graphs (POG) basic features 4 The Power-Oriented Graphs (POG) are ''block diagrams'' with a ''modular'' structure based on two blocks: Positive power flows Dashed line = power flowing through that section Product of conjugated variables = power Elaboration block Store and dissipate or generate energy Connection block Only transform the energy Direct correspondence between POG and state space equations

5 Dynamic modeling: electrical exemples 5 I R I I I R V c V c R VO C R Kirchhoff s current law C Kirchhoff s voltage law

6 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 2. The studied system: simplified model of a vehicle with tire-soil interaction

7 Simplified vehicle: the bicycle model 7 2D model with 3 rigid bodies motion possible in plane (xy) no suspensions interaction with the ground by means of tires Energetic model of the tire-soil interaction Degrees of freedom: 2 translational (wheels are solidly connected to chassis for translations) 3 rotational (wheels are independent from chassis for rotations)

8 Tire-road interaction: elastic dynamic model Main drawbacks of Pacejka s formulas: 1. The slip ratio can be used only when v x >0 ( or R>0) 8 2. They mix together the slip and skid phenomena. New definition for the slip ratio: elastic element SLIPPING SKIDDING Only when both the contact force in the x-direction and the angular velocity of the wheel in the y-direction are not zero. Only when the force vector exceeds the skidding threshold. The contact area changes its dimensions according to the adherence conditions.

9 POG scheme of the simplified vehicle 9 Contact point 2D mechanical dynamics of chassis and wheels Coordinate transformation Elastic element Both blocks have a force describing the tire as input and give a velocity as output

10 POG scheme: mathematical details Differential equations of the whole system: 10 Mass and inertia matrix Velocity vector Transformation matrices Stiffness and damping matrices

11 POG and EMR of the vehicle 11 Frx. x m. x m Fpx Env. x 2 tot tot Fry. y m MS2 2 m 1 tot r V. y m Fpy. X c Env. y Fc MS1 1 m Fr Fc Vcsl + Vcsk S+S

12 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 3. Control Structure

13 Maximum Control Structure 13 input torques 1-ref MS2 MS m 1 m coupling inertias coupling masses. Frx x m tot tot r tot Fry V Fr. y m. x m coupling Fpx. y m Fpy environment. X c Fc Env. x Env. y elastic element Fc Vcsl + Vcsk skidding and slipping S+S E M R Tuning chain Inversion 2-mes r1- meas fcx1-meas tot-ref 1-ref 1-ref Frx-ref. X c- ref fcx2-meas fcx1-ref M C S Maximum Control Structure Frx-ref. x m-ref

14 Model and control without the contact law 14 input torques coupling Equivalent wheel mas environment Frx Vrx Env. x Fpx 2 MS2 2 m tot tot Vrx E M Simplified MS1 1-ref 1 1 m R Model 2-mes tot-ref M C S Simplified Control Frx-ref Vrx-ref

15 Simplified control with the complete model 15 input torques coupling inertias coupling masses Frx environment Env. x Fpx 2 MS2 2 m 1 tot tot r tot Fry V Fpy Env. y elastic element Fc skidding and slipping E M R Complete Model MS1 1-ref 1 m Fr Fc S+S Vcsl + Vcsk 2-mes tot-ref P C S Simplified Control Frx-ref Vrx-ref

16 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 4. Simulation

17 Matlab-Simulink implementation 17 Global structure: EMR Inner structure: POG

18 Simulation results: complete model and control 18 reference real slip skid Electric vehicle with DC machine Control of velocity: structure based on inversion (MCS) The tire starts skidding

19 Simulation results: Model and control without the contact law 19 First order dynamic system No information on tires slipping

20 Simulation results: complete model and simplified control 20 slip skid Good control of the speed Bad behavior of tire skidding

21 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 5. Comparison POG - EMR

22 POG and EMR: comparison POG EMR Objective Analysis Control structure Energetic domains All known All known Power variables Scalar and vectorial Scalar and vectorial Analogy between energetic domains Firestone s Maxwell s Causality Integral and differential Integral Nr. Basic elements 2 4 main elements, several symbols Coupling Implicit Explicit Variable direction Explicit Explicit Power direction Implicit Not visible Mathematical model from the graphical scheme Directly obtainable Not directly obtainable Simulation Directly in Simulink Simulink library Graphical representation Linear Planar Control structure No methodology Methodology through inversion rules 22

23 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation 6. Conclusion

24 Conclusion 24 Power-Oriented Graphs (POG) and Energetic Macroscopic Representation (EMR) are energy-based techniques that can be used for modelling all types of physical systems involving power flows Cooperation of both POG and EMR is proposed A simplified vehicle model is given in POG and EMR formalisms An elastic dynamic model of the interaction between tires and ground has been used The MCS is given in order to control the longitudinal velocity of the vehicle A simplified control is also proposed Simulations in Matlab-Simulink

25 EMR 11 Lausanne July 2011 Joint Summer School EMR 11 Energetic Macroscopic Representation «BIOGRAPHIES AND REFERENCES»

26 - Authors - Dr. Federica GROSSI University of Modena, Italy PhD in Information and Telecommunication Tech. at University of Modena (2010) Research topics: graphical modelling techniques applied to electro-mechanical systems and hybrid automotive systems. Prof. Roberto ZANASI University of Modena, Italy PhD in System Engineering at University of Bologna (1992) Research topics: POG modelling of complex physical systems, advanced control techniques, trajectory planning, control in automotive systems Dr. Walter LHOMME L2EP, University Lille1, MEGEVH, France PhD on Hybrid Electric Vehicles at University Lille1, 2007 Engineer at AVL (UK) ( ) Associate Prof. at Univ. Lille1 (2008) Research topics: EMR, EVs and HEVs Prof. Alain BOUSCAYROL University Lille 1, L2EP, MEGEVH, France Coordinator of MEGEVH, French network on HEVs PhD in Electrical Engineering at University of Toulouse (1995) Research topics: EMR, HIL simulation, tractions systems, EVs and HEVs 26

27 References 27 [1] F. Grossi, W. Lhomme, R. Zanasi, A. Bouscayrol, Modelling and control of a vehicle with tireroad interaction using POG and EMR formalisms, ELECTROMOTION 2009, EPE Chapter Electric Drives 8 th International Symposium on Advanced Electromechanical Motion Systems, Lille, France, July 2009 (common paper University of Modena and L2EP Lille) [2] F. Grossi, W. Lhomme, R. Zanasi, A. Bouscayrol, Modelling and control of a vehicle with tireroad interaction using energy-based techniques IEEE VPPC 2009 (Vehicular Power and Propulsion Conference), Dearborn, Michigan, USA, September 2009 common paper University of Modena and L2EP Lille). [3] R. Zanasi, F. Grossi, Modelling Hybrid Automotive Systems with the POG Technique, Journal of Asian Electric Vehicles, Vol. 8, Nr. 1, June [4] R. Zanasi The Power-Oriented Graphs Technique: system modeling and basic properties, IEEE VPPC 2010 (Vehicular Power and Propulsion Conference), Lille, France, September [5] W. Lhomme, R. Zanasi, G.-H. Geitner, A. Bouscayrol, Different graphical descriptions of clutch modelling for traction systems, ElectrIMACS 08, Québec (Canada), May 2008 (common paper L2EP Lille, University of Modena and University of Dresden) [6] F.Grossi, Dynamic Modeling and Control of Hybrid Automotive Systems, PhD Dissertation