Sliding Mode Control (SMC) as a result of being a powerful robust control design is widely use in control system to analyze non-linear systems and to endow them of stability and performance. Sliding Mode Control is characterized by a suite of feedback control laws and a decision rule. The decision rule, termed the switching function, has as its input some measure of the current system behavior and produces as an output the feedback controller which should be used at that instant in time. The main advantages of SMC are that the dynamic behavior of the system may be tailored by the choice of switching function and the closed-loop response becomes totally insensitive to a particular class of uncertainty in the system which means that even in the presence of chattering, the controller can be designed with bounds for its chattering. However, If the bounds are not defined, robust control seizes to deliver the claimed robustness. To mitigate the problems of uncertainties / perturbations bounds knowledge, an adaptive law is introduced to update the controller gain to obtain a robust sliding mode adaptive gain control law. This thesis demonstrates the design principles of a sliding mode controller with an adaptive law for updating the gain following the new methodology for adaptive sliding mode control [1] proposed by F. Plestan, Y. Shtessel, V. Bregeault and A. Pozniak. The proposed approaches consist in having a dynamical adaptive control gain that successfully establishes a sliding mode in finite time and does not overestimate the magnitude of external disturbances, thus preventing high level of chattering. The efficacy of the proposed algorithms will be discussed while it is implemented on a linear and nonlinear mathematically modeled real time ball and beam system.

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