This paper presents a robust fuzzy $H_{\infty }$ control strategy for improving vehicle lateral stability and handling performance through integration of direct yaw moment control system (DYC) and active front steering. Since vehicle lateral dynamics possesses inherent nonlinearities, the main objective is dedicated to deal with the nonlinear challenge in vehicle lateral dynamics by applying Takagi-Sugeno (T-S) fuzzy modeling approach. First, the nonlinear Brush tire dynamics and the nonlinear functions of longitudinal velocity are represented via a T-S fuzzy modeling technique, and vehicle parametric uncertainties are handled by the norm-bounded uncertainties. An uncertain nonlinear vehicle lateral dynamic T-S fuzzy model is then obtained with multi-fuzzy-rules. The resulting robust fuzzy $H_{\infty }$ state-feedback controller is designed with the parallel-distributed compensation strategy and premise variables, and solved via a set of linear matrix inequalities derived from Lyapunov asymptotic stability and quadratic $H_{\infty }$ performance. Simulations for two different maneuvers are implemented with a high-fidelity, CarSimⓇ, full-vehicle model to verify the effectiveness of the developed approach. It is confirmed from the results that the proposed controller can effectively preserve vehicle lateral stability and enhance yaw handling performance.

Improving Vehicle Handling Stability Based on Combined AFS and DYC System via Robust Takagi-Sugeno Fuzzy Control

Electric vehicles (EVs) with four individually controlled drivetrains are over-actuated systems, and therefore, the total wheel torque and yaw moment demands can be realized through an infinite number of feasible wheel torque combinations. Hence, an energy-efficient torque distribution among the four drivetrains is crucial for reducing the drivetrain power losses and extending driving range. In this paper, the optimal torque distribution is formulated as the solution of a parametric optimization problem, depending on the vehicle speed. An analytical solution is provided for the case of equal drivetrains, under the experimentally confirmed hypothesis that the drivetrain power losses are strictly monotonically increasing with the torque demand. The easily implementable and computationally fast wheel torque distribution algorithm is validated by simulations and experiments on an EV demonstrator, along driving cycles and cornering maneuvers. The results show considerable energy savings compared to alternative torque distribution strategies.

A Fast and Parametric Torque Distribution Strategy for Four-Wheel-Drive Energy-Efficient Electric Vehicles

This paper proposes a novel unified structure to estimate tire forces. The proposed structure uses estimation modules to calculate/estimate tire forces by means of nonlinear observers. The novelty in the proposed approach lies in the independence of the estimates from the vehicle tire model, thereby making the structure robust against variations in vehicle mass, tire parameters due to tire wear, and, most importantly, road surface conditions. In the proposed structure, we have a dedicated module to estimate the longitudinal tire forces and another to calculate the vertical tire forces. Subsequently, these forces are fed into a third module that utilizes a nonlinear observer to estimate lateral tire forces. The proposed structure is validated through experimental studies.

Novel Tire Force Estimation Strategy for Real-Time Implementation on Vehicle Applications

The safety benefits of torque-vectoring control of electric vehicles with multiple drivetrains are well known and extensively discussed in the literature. Also, several authors analyze wheel torque control allocation algorithms for reducing the energy consumption while obtaining the wheel torque demand and reference yaw moment specified by the higher layer of a torque-vectoring controller. Based on a set of novel experimental results, this study demonstrates that further significant energy consumption reductions can be achieved through the appropriate tuning of the reference understeer characteristics. The effects of drivetrain power losses and tire slip power losses are discussed for the case of identical drivetrains at the four vehicle corners. Easily implementable yet effective rule-based algorithms are presented for the set-up of the energy-efficient reference yaw rate, feedforward yaw moment and wheel torque distribution of the torque-vectoring controller.

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Energy-Efficient Torque-Vectoring Control of Electric Vehicles With Multiple Drivetrains

Motion stabilization for electric vehicles with four in-wheel motors has been extensively studied in recent years. While most of the previous works have tended to focus on the development of optimization algorithms for driving force distribution, this paper considers a global–local control scheme: the global controller coordinates wheel and vehicle motions to generate reference driving forces and the local controller further controls the generated force commands. Specifically, two approaches with different global control concepts are proposed. The first approach considers the redesign of weighting factors for a conventional driving force optimization algorithm, and based on the first method, the second approach formulates the objective function and equality constraints in a two degree-of-freedom control framework. As an example, vehicle start off on an instantaneous split-friction road is employed to verify the proposed methods in both simulations and experiments.

Driving Force Distribution and Control for EV With Four In-Wheel Motors: A Case Study of Acceleration on Split-Friction Surfaces

In this paper, an optimal torque distribution approach is proposed for electric vehicle equipped with four independent wheel motors to improve vehicle handling and stability performance. A novel objective function is formulated which works in a multifunctional way by considering the interference among different performance indices: forces and moment errors at the centre of gravity of the vehicle, actuator control efforts and tyre workload usage. To adapt different driving conditions, a weighting factors tuning scheme is designed to adjust the relative weight of each performance in the objective function. The effectiveness of the proposed optimal torque distribution is evaluated by simulations with CarSim and Matlab/Simulink. The simulation results under different driving scenarios indicate that the proposed control strategy can effectively improve the vehicle handling and stability even in slippery road conditions.

An optimal torque distribution control strategy for four-independent wheel drive electric vehicles

© SAE, Athari, A., Fallah, S., Li, B., Khajepour, A. et al., "Optimal Torque Control for an Electric-Drive Vehicle with In-Wheel Motors: Implementation and Experiments," SAE Int. J. Commer. Veh. 6(1):82-92, 2013, doi:10.4271/2013-01-0674.

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Baktiar Litkouhi

Papers

An optimal torque distribution control strategy for four-independent wheel drive electric vehicles

Optimal Torque Control for an Electric-Drive Vehicle with In-Wheel Motors: Implementation and Experiments