The paper presents a gradient-based algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-intime recurrent structure similar to the backpropagation-throughtime algorithm, which is mostly used as a learning algorithm for dynamic neural networks. Other main features of the algorithm include the use of higher order Adams time-discretization schemes, numerical calculation of Jacobians, and advanced conjugate gradient methods for favorable convergence properties. The algorithm performance is illustrated on an example of off-line vehicle dynamics control optimization based on a realistic high-order vehicle model. The optimized control variables are active rear differential torque transfer and active rear steering road wheel angle, while the optimization tasks are trajectory tracking and roll minimization for a double lane change maneuver.
Powertrain size optimisation based on vehicle class and usage profile is advantageous for reducing emissions. Backwardfacing powertrain models, which incorporate scalable powertrain components, have often been used for this purpose. However, due to their quasi-static nature, backwardfacing models give very limited information about the limits of the system and drivability of the vehicle. This makes it difficult for control system development and implementation in hardware-in-the-loop (HIL) test systems. This paper investigates the viability of using forward-facing models in the context of powertrain component sizing optimisation. The vehicle model used in this investigation features a conventional powertrain with an internal combustion engine, clutch, manual transmission, and final drive. Simulations that were carried out have indicated that there is minimal effect on the optimal cost with regards to variations in the driver model sensitivity. This opens up the possibility of using forwardfacing models for the purpose of powertrain component sizing.
Active differentials are used to improve the overall performance of traction control and vehicle dynamics control systems. This paper presents the development of a unified mathematical model of active differential dynamics using the bond graph modeling technique. The study includes active limited slip differential and various common types of torque vectoring differentials. Different levels of model complexity are considered, starting from a second-order model with lumped input and output inertia toward higher-order models including the gear inertia and half-shaft compliance. The model is used for a theoretical analysis of drivability and time response characteristics of the active differential dynamics. The analysis is illustrated by simulation results.
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