Sliding mode control design for a class of uncertain nonlinear systems

Demands for higher accuracy in the presence of disturbance and parameter uncertainty have been the prime motivation for designing controllers that guarantee the stability with good tracking and regulating characteristics of the nonlinear systems. This is achieved by robust control methods; one of which is the sliding mode control. It is very difficult for traditional controllers to handle complex systems, affected by disturbances and incomplete knowledge and to provide good response. The fuzzy logic control has been one of the most useful approaches for utilizing expert knowledge. With the universal approximation ability of fuzzy systems, the plant model is approximated by adaptive fuzzy systems to construct the control law. To improve the tracking performances, the adaptation laws are synthesized from the stability analysis in the sense of Lyapunov.In this study, different sliding mode controllers are investigated for a class of nonlinear systems. One of these controllers is the modified adaptive fuzzy sliding mode controller. In this method, the first fuzzy models are constructed to describe the dynamics of the ill-defined system. The control law is then formulated from the sufficient condition for driving asymptotically the trackingerror to zero for any initial states. Then, based on Lyapunov function the adaptive laws are derived.The modified adaptive laws are obtained from incorporating the modeling error with the tracking error. The control algorithm derivation for SISO systems is presented, and then extended to cover MIMO systems too. The method is applied to different classes of nonlinear systems and compared with the indirect adaptive fuzzy sliding mode control. The controller is tested by applying it to a first order nonlinear system and duffing oscillator system. It is also applied to a coupled double pendulum system and two-link robotic arm to demonstrate the control performance. It is shown that method can achieve regulation and tracking in spite of the presence of disturbance and unknown dynamics of plant. The design can be applied to a large class of mechanical systems.