New methods for eliminating the chattering problem in variable structure control input

In this study, variable structure control methods are considered for linear and nonlinear systems and control methods are proposed in order to avoid chattering problem in variable structure control. In this context, firstly, second order sliding mode control on stable manifold method is proposed. The method is based on designing a stable manifold of a proper dimension and using the stable manifold as a sliding surface. Then the system is controlled by second order sliding mode control algorithms. Secondly, sliding sector method is considered. Sliding sector is a stable region which includes the sliding surface. In this method, the system is controlled by forcing the trajectories inside the sliding sector. In this thesis study, design approaches of variable structure control systems with nonlinear time varying sliding sector and state dependent sliding sector are proposed for nonlinear system with matched uncertainty. Lastly, sliding sector control method based on successive approximation method is proposed. The method is based on linear time varying approximations of the nonlinear system. With the help of approximations, sliding sector control problem for nonlinear systems is transformed to sliding sector control problem for linear time varying systems. By using the linear time varying system models, sliding sector and sliding sector controller are designed and the convergence conditions of the method are given. The proposed methods are applied to some mathematical models, including robot manipulator model with elastic joints and invert pendulum model. Then simulation results are compared with sliding mode control method. The successes of suggested methods are analyzed in terms of decreased chattering phenomenon.