Magnetic Levitation systems are nonlinear, frictionless and noiseless which use electromagnetic fields to hover ferromagnetic objects in air. For this purpose, we have proposed Supertwisting and Integral Backstepping sliding mode controllers. The designed controllers ensure the air gap to be maintained at the desired value while tracking the magnetic flux and momentum to their respective references. The stability analysis of the proposed controllers has been presented using Lyapunov theory which proves the global asymptotic stability of the system. The performance of the proposed controllers is analyzed using ODE 45 solver in MATLAB/Simulink environment. The proposed controllers reduce the chattering and improves the dynamic response of the system. Robustness of the proposed controllers has been checked by adding noise and disturbance in system's state space model. Furthermore, comparison of proposed controllers with each other, with conventional PI and recently published nonlinear controllers for MagLev system in terms of dynamic response has also been presented. The results show that the dynamic behavior of supertwisting sliding mode controller is best among analyzed controllers. INDEX TERMS Magnetic levitation (MagLev), integral backstepping sliding mode controller (IBS-SMC), supertwisting sliding mode controller (ST-SMC), Lyapunov stability.

The problem of extracting maximum power from a photovoltaic (PV) system with negligible power loss is concerned with the power generating capability of the PV array and nature of the output load. Changing weather conditions and nonlinear behavior of PV systems pose a challenge in tracking of varying maximum power point. A robust nonlinear controller is required to ensure maximum power point tracking (MPPT) by handling nonlinearities of a system and making it robust against changing environmental conditions. Sliding mode controller is robust against disturbances, model uncertainties and parametric variations. It depicts undesirable phenomenon like chattering, inherent in it causing power and heat losses. In this paper, a supertwisting sliding mode algorithm based nonlinear robust controller has been designed for MPPT of a PV system which not only removes the chattering but also enhances the overall system’s dynamic response. Moreover, supertwisting sliding mode controller is robust against changing environmental conditions like change in temperature and irradiance. Noninverting DC-DC Buck-Boost converter has been used as an interface between source and the load. The efficiency of MPPT of a PV system depends upon the accuracy of reference for peak power voltage, therefore an efficient mechanism for reference generation has also been proposed in this work. The reference for peak power voltage has been generated by using a trained artificial neural network, which is to be tracked by proposed nonlinear controllers. Sliding mode controller (SMC) and synergetic controllers have also been designed for MPPT of a PV system in order to compare them with supertwisting sliding mode controller (ST-SMC). Global asymptotic stability of the system has been ensured by using Lyapunov stability criterion. The performance of the proposed nonlinear controllers has been validated in MATLAB/Simulink ODE 45 environment. ST-SMC has also been compared with recently proposed integral backstepping controller and other conventional MPPT controllers given in the literature. The simulation results show the better performance of ST-SMC in terms of best dynamic response and robustness.

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