Variable structure control design with sliding sector for a class of nonlinear systems

In this study, Variable Structure Control Systems are considered and Sliding Sector Variable Structure Control (SSVSC) method is proposed for the control of a class of nonlinear systems together with the comparison of Sliding Mode Control (SMC) and SSVSC algorithms.The method which is presented in this study based on a stable subset of the state space called sliding sector inside which some norm of the system state decreases without any control action. Thus, relatively smoother control signal is obtained as the system is left free inside the predefined sliding sector. Therefore there is no need to high frequency control signal which occurs when the system trajectories are confined to stay on the sliding surface during the implementation of SMC. Although various SSVSC design algorithms are suggested for Linear Time Invariant (LTI) systems, there is no systematic design method for the control of nonlinear systems. In this thesis, a new approach, which provides nonlinear time varying sliding sector design by the solution of State Dependent Riccati Equation (SDRE), is proposed for the control of a class of nonlinear systems where the nonlinear system is frozen at some certain control intervals to get a set of LTI systems.The proposed method is illustrated by using nonlinear inverted pendulum model and its control is successfully satisfied under the effect of uncertainties. The robustness and effectiveness of the proposed method for nonlinear systems is simulated by comparing the method with the SMC and LQR State Feedback Control.Key Words : Nonlinear Control, Sliding Sector, Variable Structure Control, Sliding Mode Control, Riccati Equation