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The fast rotating machines are susceptible to rotor deviation, and therefore, active magnetic bearing (AMB) systems are used to support the shaft through controlled electromagnetic forces. The five degrees of freedom (DOF) AMB system is a highly coupled nonlinear dynamical system that is often subjected to parametric uncertainties, unmodelled dynamics, external harmonic and electromagnetic disturbances, measurement noises, etc. With the above challenges in mind, this paper investigates the robust controller design for regulating the 5 DOF AMB system using an adaptive second-order super twisting sliding mode control algorithm. The second-order super-twisting scheme enables the controller to attain a faster response, finite-time convergence, and enhanced chattering alleviation without compromising its invariance property. The adaptation law self tunes the switching gains to avoid using conservative assumptions about apriori information of disturbance upper bound. The Lyapunov analysis guarantees the finite-time stability of the closed-loop system states to the neighborhood of zero. The performance of the proposed controller is also validated and compared with existing techniques using numerical simulations. The comparative results manifest the effectiveness of the designed scheme based on various performance measures.