不确定分数阶广义系统的滑模控制器设计与仿真

doi:10.12068/j.issn.1005-3026.2022.11.001

摘要/Abstract

摘要： 针对一类含有外部扰动的分数阶广义系统进行滑模控制研究，提出了一种改进的指数趋近律从理论上消除了抖振.通过构造分数阶反馈控制器的方法将分数阶广义系统正常化.采用积分滑模面以消除滑模运动的趋近阶段.分数阶次α分0<α<1和1<α<2两种情况讨论，运用Kronecker积与LMI方法，分别设计增益矩阵使得滑动模态方程稳定.在滑模控制器的设计中，对指数趋近律进行了性能的改进，以所设计的连续函数代替符号函数，使得当状态趋近滑动模态时可以与滑动模态实现光滑过渡.最后，通过Simulink建立滑模控制仿真实验，验证了0<α<1和1<α<2两种情况下算法的有效性.

关键词: 滑模控制；指数趋近律；分数阶系统；广义系统；积分滑模面；LMI

Abstract: In this paper， sliding mode control is studied for a class of fractional-order singular systems with external disturbances， and an improved exponential reaching law is proposed to eliminate chattering in theory. The integral sliding surface is used to eliminate the approaching phase of sliding mode movement. Kronecker product and LMI method are used to design the gain matrix in order to stabilize the sliding mode equation in both cases: 0<α<1 and 1<α<2. In the design of sliding mode controller， the performance of exponential reaching law is improved， and the sign function is replaced by the designed continuous function， so that when the state approaches the sliding mode， the smooth transition can be achieved with the sliding mode. Finally， the simulation experiments of sliding mode control are established by Simulink to verify the effectiveness of the algorithm in both cases: 0<α<1and 1<α<2.

Key words: sliding mode control; exponential reaching law; fractional-order systems; singular systems; integral sliding surface; LMI

中图分类号:

TP13

李惜笑，杨冬梅. 不确定分数阶广义系统的滑模控制器设计与仿真[J]. 东北大学学报（自然科学版）, 2022, 43(11): 1521-1528.

LI Xi-xiao， YANG Dong-mei. Design and Simulation of Sliding Mode Controllers for Fractional-Order Singular Systems with Uncertainties[J]. Journal of Northeastern University(Natural Science), 2022, 43(11): 1521-1528.

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