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Mathematical Problems in Engineering
Volume 2012, Article ID 287195, 31 pages
Research Article

Vehicle Sliding Mode Control with Adaptive Upper Bounds: Static versus Dynamic Allocation to Saturated Tire Forces

Department of Mechanical Engineering, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran

Received 20 December 2011; Accepted 13 February 2012

Academic Editor: Alexander P. Seyranian

Copyright © 2012 Ali Tavasoli and Mahyar Naraghi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Nonlinear vehicle control allocation is achieved through distributing the task of vehicle control among individual tire forces, which are constrained to nonlinear saturation conditions. A high-level sliding mode control with adaptive upper bounds is considered to assess the body yaw moment and lateral force for the vehicle motion. The proposed controller only requires the online adaptation of control gains without acquiring the knowledge of upper bounds on system uncertainties. Static and dynamic control allocation approaches have been formulated to distribute high-level control objectives among the system inputs. For static control allocation, the interior-point method is applied to solve the formulated nonlinear optimization problem. Based on the dynamic control allocation method, a dynamic update law is derived to allocate vehicle control to tire forces. The allocated tire forces are fed into a low-level control module, where the applied torque and active steering angle at each wheel are determined through a slip-ratio controller and an inverse tire model. Computer simulations are used to prove the significant effects of the proposed control allocation methods on improving the stability and handling performance. The advantages and limitations of each method have been discussed, and conclusions have been derived.