Comparative Study of VSS Controls with Sliding Mode via the Ball and Beam System

H. Allamehzadeh (USA)


Sliding Mode, Variable Structure, Ball & Beam, Robust Control


In this paper, The Ball and Beam System (BBS) is introduced briefly; then the dynamic equation of the BBS is explained and its state space representation and input output nonlinear model are derived. Since the relative degree of BBS in input-output form is not well defined, a BBS model based on error and its derivatives are derived. Furthermore, the concept of variable structure control with sliding mode is explained. Then, the classical sliding mode control of a special class of nonlinear systems is discussed. To force all trajectories of a system toward a sliding plane, various reaching laws with their advantages and disadvantages are reviewed and explained. The Sliding Mode Control (SMC) with various reaching laws was applied to BBS with various initial conditions and nominal points. Finally, the performance of each class of sliding mode controllers was evaluated.

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