The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)
针对传统幂次趋近律存在的抖振以及全局收敛缓慢的问题, 提出一种新型复合趋近律, 该趋近律通过引入正切函数以及对传统幂次趋近律的改进, 实现趋近律的快速收敛和无抖振特性. 首先, 引入了正切函数, 在初始状态已知的情况下能够使系统更快地收敛; 其次, 设计的趋近律改进传统幂次趋近律中含符号函数乘积项容易引起的抖振. 本文通过理论证明了新型复合趋近律能够快速收敛且无抖振, 并推导出趋近速率及稳态误差界. 最后, 通过直线磁悬浮同步电动机磁悬浮系统仿真进一步验证了新型复合趋近律的有效性.
To address the chattering problem of the traditional power reaching law and the slow global convergence, a new compound reaching law is proposed. By introducing the tangent function and improving the traditional power reaching law, the fast convergence and chattering free property of the reaching law are realized. Firstly, the tangent function is introduced, which can make the system converge faster when the initial state is known. Secondly, the proposed approach law improves the chattering problem caused by the product term of the signed function in the traditional power approach law. In this paper, it is proved theoretically that the new compound reaching law can converge quickly without chattering, and the reaching rate and steady-state error bound are derived. Finally, the effectiveness of the new compound reaching law is further verified by the magnetic levitation system simulation of Linear Magnetic Levitation Synchronous Motor.