A Composite Sliding Mode Control for Hybrid Magnetic Levitation Systems Based on a Novel Compound Reaching Law With High-Order Sliding Mode Observer

Achieving finite-time fast convergence and chattering suppression simultaneously presents a significant challenge in the sliding mode control (SMC) of permanent magnetic-electromagnetic hybrid levitation systems (PM-EMHLSs). To address this challenge, this study proposes a composite fast non-singular terminal sliding mode approach based on a novel compound reaching law (NCRL) integrated with a high-order sliding mode observer (HOSMO). The proposed method integrates an NCRL to address the trade-off between fast convergence rate and chattering reduction found in conventional reaching laws. The stability of NCRL is formally proven, and its convergence time is derived. To enhance system robustness via the estimation of levitation velocity and external disturbances, the NCRL-based fast non-singular terminal sliding mode controller, named composite fast non-singular terminal sliding mode controller (CFNTSMC), is combined with an HOSMO. The overall stability is ensured through the Lyapunov stability theory. Comparative simulation and experimental results demonstrate the superiority of the HOSMO-CFNTSMC strategy over the exponential reaching law (ERL) method and terminal sliding mode method in terms of disturbance rejection, high estimation precision, and reduced chattering. The analysis demonstrates the effectiveness of the proposed approach in ensuring fast convergence in finite time while having the ability to suppress chattering.