Markus Schori

Calibration of Parallel Hybrid Vehicles Based on Hybrid Optimal Control Theory

Abstract Most energy management systems for hybrid electric vehicles rely on information stored in lookup tables, to define the current mode of operation under certain circumstances. In this paper it is demonstrated how the theory of hybrid optimal control can be used to calculate an initial parameter set for the calibration of parallel hybrid electric vehicles. After solving a hybrid optimal control problem for the fuel optimal operation of the vehicle, taking into account continuous as well as discrete dynamics, the results can be used to automatically calculate lookup tables for optimal gear shifts, optimal torque-split between motor/generator and internal combustion engine and the determination of the drive mode (electric or hybrid mode). The algorithms proposed are easy in their application and can be used for other hybrid vehicle configurations as well and therefore constitute a valuable tool for the initial calibration.

Solution of a Hybrid Optimal Control Problem For a Parallel Hybrid Vehicle

Abstract In this paper, an algorithm for solving a nonlinear hybrid optimal control problem for the fuel-optimal operation of a parallel hybrid electric vehicle is proposed. The proposed algorithm is very simple in its application and allows for finding the optimal controls in hybrid drive mode, as well as optimal discrete dynamics. In particular, the discrete decisions gear choice and drive mode are regarded. The algorithm uses an indirect variation of extremals approach based on necessary conditions for hybrid optimality. For better solvability, we accept the fact, that the solution becomes suboptimal, when encountering state constraints. It will be shown that the solution obtained provides a set of valuable information for the definition of the energy management for a given vehicle. The algorithm can be adapted to other configurations of hybrid vehicles and can be used to determine optimal controls on any drive cycle.

Optimal Calibration of Map-Based Energy Management for Plug-In Parallel Hybrid Configurations: A Hybrid Optimal Control Approach

In this paper, an optimization framework for the calibration of energy management in plug-in hybrid electric vehicles (PHEVs) is proposed. The framework is based on the modeling of hybrid vehicles as hybrid systems in the mathematical sense, i.e., as a system, whose input is composed of continuous and discrete variables. This allows for the flexible integration of discrete decisions, such as drive modes and gear selection. Hybrid optimal control problems are then formulated, which seek optimal continuous and discrete system inputs, and methods for the efficient solution are described. The framework also allows for the incorporation of losses that occur due to a change in a discrete variable. The results can then be used to automatically calculate lookup tables for optimal gear shifts, optimal torque split between the motor/generator and the internal combustion engine, and the determination of the drive mode (electric or hybrid mode). It is demonstrated that when switching cost is disregarded, the main challenge is still finding the initial costate value. Practical strategies for determining the costate value online are described, containing a rule-based method, a CO2 optimal method, and predictive energy management. The most important implementation issues are discussed, and the results of real-world experiments of predictive energy management are shown.

Solution of a hybrid optimal control problem for parallel hybrid vehicles subject to thermal constraints

The class of dynamical systems that exhibit both continuous and discrete dynamics can be referred to as hybrid systems. One example of hybrid systems constitute nowadays parallel hybrid electric vehicle (HEV) configuration, that provide continuous dynamics, such as the torque-split between motor/generator and the internal combustion engine, as well as discrete decisions, such as choice of driving mode and catalytic converter heat-up. In this paper, an algorithm that combines the advantages of direct and indirect methods for solving optimal control problems is proposed. The applicability of the proposed algorithm is demonstrated on a simulated parallel HEV.

A predictive energy management for hybrid vehicles based on optimal control theory

In this paper we propose a predictive energy management for a hybrid electric vehicle with compound power-split powertrain configuration. The strategy relies on information on the future driving trip provided by modern navigation systems. Based on this information a simplified optimal control problem is solved via an indirect variation of extremals algorithm to determine a feasible start value of the adjungated variable. The powertrain controls are then determined from offline calculated maps using the value of the adjungated variables, the current vehicle speed and the requested wheel-torque. The strategy is implemented into a model-based simulation environment and has shown fuel savings on real world driving cycles. It has proven to be real-time applicable and very robust against low accuracy of the predicted driving trip.

Multi-objective optimal powertrain design of parallel hybrid vehicles with respect to fuel consumption and driving performance

In the past decade, Hybrid Electric Vehicles have been demonstrated to significantly reduce the fuel consumption and emissions. However, this capability strongly depends on the sizing of the components and on the quality of the energy management. These challenges require new optimization procedures for a systematical exploration of the design space to find the optimal component sizings and control trajectories. A novel two-layer optimization strategy based on a multi-objective problem formulation is proposed. The first layer consists of a multi-objective genetic algorithm for determining the best system design parameters with respect to fuel consumption and driving performance. The second layer solves a deterministic hybrid optimal control problem (HOCP) to find for each individual of the population pool the optimal continuous and discrete control trajectories for the energy management. The proposed optimization strategy is benchmarked to a one-layer genetic algorithm approach on a parallel hybrid design study.

Switching time optimization for discontinuous switched systems

In this paper, an algorithm for switching time optimization for switched systems that exhibit discontinuities in the state trajectory on a switching is proposed. A derivative of the cost function with respect to the switching time is derived using a dynamic programming argumentation. Based on this derivative, a two-stage algorithm is described that alternates between solving an optimal control problem with fixed switching sequence and improving the switching times.

Costate approximation from direct methods for switched systems with state jumps

This paper demonstrates, how an approximation of the costate trajectory can be obtained for switched systems with state jumps, when an optimal control problem with fixed switching sequence is solved using a direct method, i.e. direct shooting or collocation. The obtained trajectories include the jump conditions for the costate given by necessary conditions for optimal control of switched systems.

A robust predictive energy management for plug-in hybrid vehicles based on hybrid optimal control theory

This paper presents a predictive energy management for plug-in hybrid vehicles, feasible for the implementation on an electronic control unit. An optimal reference trajectory for the batterys state of charge is calculated by solving a hybrid optimal control problem that considers continuous controls as well as discrete decisions, such as the switching between drive modes. The problem is solved via an indirect variation of extremals approach, expanded for hybrid systems. To decrease calculation time, information necessary for solving the problem is calculated offline and stored in lookup tables. The information necessary for the formulation of the hybrid optimal control problem are obtained using information from modern navigation systems for each segment of the route. A driver model transforms this set of information into a continuous driving profile that contains all necessary information for solving the hybrid optimal control problem. A PI-controller is implemented to follow the reference trajectory of the batterys state of charge. The controller output is an offset to the costate obtained from the solution of the hybrid optimal control problem. The energy management was implemented in a pilot-production plug-in-hybrid vehicle. Results obtained from real world measurements are presented as well as simulation results to investigate the energy managements robustness.

Control Optimization of Discontinuous Hybrid Systems Using Embedding

Abstract In this paper, a framework for the approximation of optimal controls for a class of hybrid systems that exhibit discontinuities in the states on a change of the active subsystem is proposed. Via a discretization, the hybrid optimal control problem is first transcribed to a nonlinear program with integer constraints. The integer constraints are then relaxed and the height of the jump is approximated by a function that is continuous but nonsmooth with respect to the discrete optimization variables. The resulting nonsmooth nonlinear program can in many cases be solved using standard variable metric methods. A blackbox method is used to provide gradients, where the model is nonsmooth. The proposed method is demonstrated on the problem of an optimal energy management of a hybrid vehicle with different drive modes.