New system technologies are continuously improving the performance of vehicles with regard to safety, comfort, stability and the environment. The development of control systems based on anti-lock braking system, active steering control, adaptive cruise control, collision avoidance, electronic stability programme or roll-over prevention systems, facilitated these improvements. In order to maximise the benefits from such devices, information about the tyre/road friction parameter is required in real-time. As it is impractical to measure the tyre/road friction coefficient, estimation from other available parameters is essential.\ud In this thesis, the main theoretical contribution is the development of sliding mode schemes for tyre/road friction estimation. In the first part of this thesis, a sliding mode based scheme is designed for a braking scenario. The scheme is designed to maintain the longitudinal slip value associated with the tyre road contact patch at an optimum value utilising a sliding mode controller, subject to varying road conditions. The stability of the controller is proven using a Lyapunov function and Linear Matrix Inequality (LMI) method. An analysis of the designed scheme in the presence of imperfect measurement of wheel angular velocity is also presented. The sliding mode scheme is also compared with an adaptive scheme from the literature. The comparison study shows that the sliding mode based scheme appears more robust than the adaptive scheme, and the simulation results are supported by the analysis. Another key contributions in this thesis is the development of a sliding mode based scheme which is independent of the underlying friction model.\ud This distinguishes the work proposed in this thesis from the existing literature. Finally a comparative study is presented for the observers considered in this thesis using three different friction models. The results for different road conditions show that the sliding mode based schemes out-perform the adaptive scheme for the tests undertaken
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