A Novel Fractional-Order Second-Order Sliding-Mode Control for Nonlinear Systems Under Matched and Mismatched Uncertainties

—To overcome traditional limitations in handling complex disturbances, a novel fractional-order second-order sliding mode control (FOSOSMC) is developed for a class of nonlinear systems in the presence of matched and mismatched uncertainties, ensuring the properties of stability and dynamic performance. The main novelties are highlighted as follows. Firstly, a structurally flexible continuous SOSMC manifold incorporating FO calculus is constructed by taking into account the design of a family of sliding variables, which ensures that the state trajectory can converge to the equilibrium point accurately in a finite time and address the chattering problem owing to its memory and hereditary properties, while uniformly compensating for mismatched uncertainties. Furthermore, the straightforward sliding manifold structure allows for diverse designs of control laws. For simple single-input single-output systems, their fast convergence and high precision under lumped uncertainties can be guaranteed by combining the FOSOSM manifold and a fast-terminal sliding mode-type reaching law. For complex multi-input multi-output systems, a state-dependent adaptive gain is fitted to the FOSOSM manifold to obtain stronger robustness without sacrificing control accuracy or complicating parameter tuning. The global finite-time stability of the closed-loop dynamics is demonstrated by means of Lyapunov functions. Finally, simulation and experimental results verify the excellent control performance of the proposed method for nonlinear systems with uncertainties. Note to Practitioners—For nonlinear industrial systems such as DC-DC converters and flexible manipulators, ensuring stable operation while resisting disturbances is critical to automation efficiency and component durability. Existing second-order sliding mode can reduce chattering, yet it it often has a complex structure and fails to balance fast convergence and high precision under coexisting matched and mismatched uncertainties. To address these issues, this paper develops a novel fractional-order second-order sliding mode control structure, a cohesive framework where fractional-order properties are inherently integrated into a re-designed uniform second-order sliding mode. This framework allows for targeted control law selection based on specific system requirements, which has been verified in different application scenarios: it caters to the rapid response demand of buck converters and meets the high-precision operation need of flexible manipulators, effectively counteracting complex uncertainties in both cases. This design offers engineers intuitive parameter tuning based on derived stability ranges, facilitating straightforward practical application. It can also be extended to other industrial nonlinear systems like servo drives and chemical reactors, providing reliable dynamic performance and stability in diverse real-world scenarios.