针对非奇异快速终端滑模在趋近阶段收敛速率较慢的问题, 提出一种时变非奇异快速终端滑模控制算法, 提高了系统收敛速率. 首先, 提出一种时变非奇异快速终端滑模, 使系统在滑动阶段能有限时间收敛到平衡点, 并在趋近阶段保持较快的收敛速率. 同时, 提出一种新型双幂次趋近律, 使其与经典双幂次趋近律相比具有更好的运动品质, 同时改善系统鲁棒性. 根据设计的滑模和趋近律提出一种时变非奇异快速终端滑模控制算法. 通过Lyapunov理论证明: 当系统扰动为0时, 系统能实现有限时间收敛到平衡点; 当系统扰动不为0时, 系统滑模和其导数能有限时间收敛到一个剩余集,提高了系统控制精度. 通过Matlab仿真表明, 与传统非奇异快速终端滑模控制算法相比, 该方法能有效提高系统收敛速率和控制精度, 改善鲁棒性.

In order to improve convergent rate of conventional non-singular fast terminal sliding mode (NFTSM) control in reaching phase, a time-varying non-singular fast terminal sliding mode (TVNFTSM) control scheme is proposed so as to enhance convergence of systems. Firstly, a TVNFTSM structure is proposed to achieve finite-time convergence in sliding phase and faster convergence in reaching phase. Also, a new double power reaching law is designed and further improves convergence and robustness in comparison with classical double power reaching law. By applying Lyapunov theory, it can be proved that system can achieve finite-time stability without perturbation and sliding mode and its derivation can converge to a small residual set in finite time with perturbation, respectively. Finally, the simulation results verify that the faster convergence rate, higher control precision and stronger robustness can be achieved in comparison with the conventional NFTSM control scheme.