一类新的二阶滑模控制方法及其在倒立摆控制中的应用

摘要

Second-order sliding mode, as a special case of high-order sliding mode, not only has strong robustness and insensi-tiveness to external disturbance, but also eliminates the chat-tering phenomenon existing in the traditional first-order sliding mode. A new second-order sliding mode control algorithm is developed in this paper. The advantage of the algorithm lies in that it can be used to handle the uncertainty bounded by a known positive function rather than a positive constant. Con-sequently, the algorithm can be applied to a more general class of systems. In addition, the adding a power integrator tech-nique guarantees the global finite-time stability rather than the finite-time convergence. Finally, the application to control of an inverted pendulum shows the effectiveness of the algorithm.%二阶滑模作为高阶滑模的特殊情形，不仅具有传统滑模鲁棒性强、对外界干扰不敏感的特点，而且能够有效地消弱传统一阶滑模中存在的“抖振”现象。本文设计了一种新的二阶滑模控制算法。该算法的优点是假设不确定性是由非负函数限制而不是由常数限定。因此，该算法在实际应用中具有更广的应用范围。此外，算法中的加幂积分技术保证了系统在有限时间内稳定，而不是传统二阶滑模中普遍存在的有限时间收敛，并给出了严格的数学证明。最后，在倒立摆控制中的应用验证了该算法的有效性。