Energetic Macroscopic Representation and Inversion-based Control: Application to an Electric Vehicle with an Electrical Differential

Chen, Keyu; Bouscayrol, Alain; Lhomme, Walter · 2008 · OpenAlex-citations

DOI: 10.4130/jaev.6.1097

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Summary

This paper introduces Energetic Macroscopic Representation (EMR), an energy-based graphical modeling tool, and demonstrates its application to the design of inversion-based control systems for complex electromechanical applications. The authors address the challenge of organizing the modeling and control of energetic systems, noting that while previous tools like Bond Graphs and Causal Ordering Graphs (COG) contributed to system modeling, they lacked direct pathways for control design. EMR is presented as a functional modeling approach that emphasizes physical causality and energy flow, enabling the systematic derivation of control structures. The methodology relies on the action-reaction principle and integral causality, where inputs are causes (integrand) and outputs are effects (integrals). EMR utilizes four element types: sources, converters, accumulators, and couplings. Control design is achieved by inverting the EMR model. Tuning chains are defined based on system objectives, and control chains are derived by inverting these elements. Conversion and coupling elements are inverted directly, while accumulation elements require indirect inversion using controllers to avoid physical derivation. This process yields a "Maximum Control Structure," which can be simplified into a practical implementation. The paper applies this framework to an electric vehicle (EV) equipped with an electrical differential, where two permanent magnet DC machines drive the front wheels independently via choppers supplied by a common battery. The EMR model maps the energy flow from the battery through the choppers, machines, gears, and wheels to the chassis dynamics. The control structure is designed to regulate vehicle velocity. The inversion process defines reference values for traction force, wheel forces, gear torques, machine currents, and chopper modulations. A supplementary input $k_D$ is used to distribute traction force between the wheels, set to 0.5 for equal distribution. Simulation results using Matlab-Simulink under an urban driving cycle demonstrate the effectiveness of the proposed control. During straight-line driving, both wheels exhibit identical velocities and torques. During a curve, the external wheel rotates faster with lower torque, while the internal wheel rotates slower with higher torque, correctly simulating the behavior of an electrical differential. The study concludes that EMR provides clear physical insights and facilitates the systematic design of control and energy management strategies for complex electromechanical systems.

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