Some optimal control problems in electric vehicles

Ahıska, Kenan
Conventional internal combustion engine-powered vehicles are the mainstream mean in nowadays private transportation. However, their fuel consumption results in environmental problems. Electric vehicles, on the other hand, have zero pollutant emission and benefit from high highly-efficient electric motor technology. These make the electric vehicles as the most promising alternative in private transportation. However, limitations in current battery technology aggravate the widespread usage of electric cars. The question of optimal solutions even for the small travel distances in urban traffic are very intriguing. In this thesis, several optimal control problems concerning electric vehicles are studied: (1) energy optimality of electric vehicles moving along roads with uphill and downhill sections, (2) energy and time optimality of electric vehicles cornering arcs with various radii along asphalt road and the Pareto-front between these two objectives, and (3) vehicle handling of electric cars cornering around arcs with various radii along icy roads. A mathematical model for electric vehicles including longitudinal, lateral and rotational dynamics is constructed. Wheel skidding kinematics and battery dynamics are incorporated into the mathematical model. This model is derived through necessary simplification of a previously derived more comprehensive mathematical model that includes the suspension characteristics as well. The simplified model is named gross motion model and it is verified with in several tests. Energy and time optimality problems are solved with methods based on classical optimal control theory. A solution method for these two-point boundary value problems with defined state boundaries and free final time has been developed and the obtained solutions are compared with constant velocity cruise controllers. For roads including icy uphill and downhill sections a skidding compensation logic is proposed to reduce the wheel slippage. It has been observed that the optimal control solution has superiority in energy management against the cruise controllers and it reaches a solution near the global optimum without being influenced by the skidding compensation logic. The sensitivity of the energy optimal controller on passenger seating configurations and initial state-of-charge of the battery turns out to be smaller in magnitude compared to the changes in the parameters. The superiority of the energy optimal controller against the cruise controllers becomes more evident in the scenarios where the battery is far from being fully charged. The vehicle cornering problems for electric vehicles are evaluated in terms of both energy and time optimality. Significant improvements compared to the cruise control solutions for both objectives are obtained with the solutions based on classical optimal control approach. A Pareto-front analysis is carried out with multi-objective energy and time minimization. The analysis provides a multi-objective solution to the vehicle cornering problem with a compromise between travel time and energy consumption that enables the vehicle to travel over the corner with minimum energy consumption within the given speed limits. The optimality of the Pareto-front results is discussed. Furthermore, a sensitivity analysis is performed and it is confirmed that the optimal control solution is insensitive to the different passenger seating arrangements. The vehicle handling problem for electric cars cornering around roads with low friction coefficients is studied and an autopilot design is proposed to satisfy desired handling performance. A novel hierarchical optimization approach is presented to generate off-line solutions for cornering along roads with different friction coefficients and radii of curvature. Vehicle motion as the output of this optimization process, together with vehicle states and control commands at each sampling time are generated and stored for different selected scenario parameters with various rotation radii and friction coefficients. A vehicle status definition is presented as a function of vehicle states that contains the most informative data to evaluate the vehicle handling performance. The vehicle statuses at each decision instant among these off-line optimized data are clustered with the k-means clustering technique. These are associated with the control commands applied. A cluster centre-control command corresponds to a rule that produces the unique control command to be applied as a function of vehicle status. The autopilot is constructed by a convex combination of these rules. This basic idea of autopilot design has been extended for motions along a specific rotation radii and friction coefficients; the control commands corresponding to arbitrary scenario parameters are obtained by a runtime scheduling of the weighted-interpolation among the control commands corresponding to different scenario parameters.