This paper presents a proposed optimum tire force distribution method in order to optimize tire usage and find out how the tires should share longitudinal and lateral forces to achieve a target vehicle response under the assumption that all four wheels can be independently steered, driven, and braked. The inputs to the optimization process are the driver’s commands (steering wheel angle, accelerator pedal pressure, and foot brake pressure), while the outputs are lateral and longitudinal forces on all four wheels. Lateral and longitudinal tire forces cannot be chosen arbitrarily, they have to satisfy certain specified equality constraints. The equality constraints are related to the required total longitudinal force, total lateral force, and total yaw moment. The total lateral force and total moment required are introduced using the model responses of side-slip angle and yaw rate while the total longitudinal force is computed according to driver’s command (traction or braking). A computer simulation of a closed-loop driver-vehicle system subjected to evasive lane change with braking is used to prove the significant effects of the proposed optimal tire force distribution method on improving the limit handling performance. The robustness of the vehicle motion with the proposed control against the coefficient of friction variation as well as the effect of steering wheel angle amplitude is discussed.

The objective of this research was to design a low cost parabolic solar dish concentrator with small-to moderate size for direct electricity generation. Such model can be installed in rural areas which are not connected to governmental grid. Three diameters of the dish; 5, 10 and 20m are investigated and the focal point to dish diameter ratio is set to be 0.3 in all studied cases. Special attention is given to the selection of the appropriate dimensions of the reflecting surfaces to be cut from the available sheets in the market aiming to reduce both cutting cost and sheets cost. The dimensions of the ribs and rings which support the reflecting surface are optimized in order to minimize the entire weight of the dish while providing the minimum possible total deflection and stresses in the beams. The study applies full stress analysis of the frame of the dish using Autodesk Inventor. The study recommends to use landscape orientation for the reflective facets and increase the ribs angle and the distance between the connecting rings. The methodology presented is robust and can be extended to larger dish diameters

The aim of this paper is not only to present various methods for combining lateral force and yaw moment control but also to find out how the mix between them should be applied to maximize the stability limit as well as vehicle responsiveness. Approximated two-degree-of-freedom (2DOF) vehicle model responses of side-slip angle and yaw rate are used to introduce the required total lateral force and yaw moment control. Three different cases of combining lateral force and direct yaw moment control have been investigated using computer simulations. A direct yaw moment control to follow the yaw rate response only is taken as a comparison case in order to show the effect of the combined control on vehicle stability and responsiveness. A computer simulation of a closedloop driver-vehicle system subjected to quick lane change with braking is used to prove the influence of the combined control. It is found that the influence of the combined control on vehicle stability and responsiveness is significant.

Aiming to maximize not only stability limit but also vehicle responsiveness combined yaw moment and lateral force control as a cooperative control is presented. The total lateral force for front and rear wheels as well as direct yaw moment are introduced using the models response of side-slip angle and yaw rate. The side-slip response is the 2DOF vehicle response while the yaw rate response is a suggested first order lag to prevent oscillation in relation to steering input. Three different cases of combining lateral force and direct yaw moment control have been investigated using computer simulations. In order to show the effect of the cooperative control on vehicle stability and responsiveness, a direct yaw moment control to follow the yaw rate response is taken as comparison case. The effect of cooperative control is proved by computer simulations of the vehicle response to a single sine wave steer input with braking.