The mathematical model for the magnetically levitated linear compressor (MLLC), which consists of a magnetic linear actuator (MLA), a pair of active magnetic bearings (AMBs), and a drive rod, is developed. To prevent any potential wear or collision by the drive rod against conventional bearings and certainly reduce noise, the AMB pair is employed to regulate the lateral position deviation of the drive rod. The integral sliding-mode control (ISMC) is synthesized to account for state-dependent system parameters and input nonlinearities for the MLLC system. In addition, the closed-loop stability, under the presence of the reaction force by gas in chamber, is proven by Lyapunov direct method. Finally, the efficacy of the ISMC is verified by intensive computer simulations to ensure its superior regulation capability for lateral position deviation on the drive rod, retention of constant stroke of the piston, and counterbalance against the reaction force by gas during Otto cycle.

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