Magnetic Levitation Systems are used to levitate a ferromagnetic object in the air. It has a wide area of applications because it eradicates energy losses that occur due to friction of the surface. In this paper, nonlinear controllers have been designed by using backstepping, integral backstepping and synergetic control techniques to obtain certain control objectives. Nonlinear controllers have been designed because of nonlinear dynamics present in the system model. It is required to generate a certain amount of flux by applying control input to the system. The magnetic flux is then used to levitate the body in air at a certain distance from the coil so that the movement of the body within that magnetic flux is negligible. The magnetic force provides an acceleration against the earth gravitational force to lift the body towards the coil. For each nonlinear controller, Lyapunov based theory has been used to check the global asymptotic stability of the system. MATLAB/Simulink environment is then used to analyze the system's performance for the proposed controllers. Moreover, a comparative analysis of proposed controllers has been given with linear (PI) controller. INDEX TERMS Magnetic levitation (MAGLEV) system, nonlinear controller, integral backstepping (IBS) controller, synergetic controller, backstepping controller.
Exponential decrease in oil and natural gas resources, increasing global warming issues and insufficiency of fossil fuels has shifted the focus to fuel cell hybrid electric vehicles (FHEVs). FHEV model used in this work consists of fuel cell, ultracapacitor and battery. Non-linearities present in the vehicle model dominate because of extreme driving conditions like rough terrains, slippery roads or hilly areas. Behavior of components like energy sources, induction motors and power processing blocks deviate significantly from their normal behavior when driving in highly demanding situations. To tackle these shortcomings, non-linear controllers are preferred because of their efficiency. In literature, different controllers have been proposed for either the energy sources or the induction motor separately, whereas this research work focuses on a unified hybrid electric vehicle (HEV) model to simultaneously control the energy sources and the induction motor. The model used is a complete representation of electric system of FHEV and increases the performance of the vehicle. This unified model provides improved DC bus voltage regulation along with speed tracking when subjected to European extra urban drive cycle (EUDC). In this work, Robust Integral Backstepping and Robust Backstepping controllers have been designed. Lyapunov based analysis ensures the global stability of the system. Performance of proposed controllers is validated in MATLAB/Simulink environment. A comparative analysis is also given to illustrate the importance of the unified model proposed in this work. INDEX TERMS Hybrid electric vehicles, unified model, non-linear control, integral backstepping control, backstepping control, stabilizing functions.
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