基于滑模方法的不确定分数阶广义系统的鲁棒无源控制  

Robust Passive Control of Uncertain Fractional Order Singular System via Sliding Mode Approach

作　　者：张程程 任启峰[1] 考永贵 高存臣[1] Zhang Chengcheng;Ren Qifeng;Kao Yonggui;Gao Cunchen(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China;School of Science,Harbin Institute of Technology(Weihai),Weihai 264209,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100 [2]哈尔滨工业大学(威海)理学院,山东威海264209

出　　处：《中国海洋大学学报（自然科学版）》2023年第7期147-152,共6页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2019MF027)资助。

摘　　要：本文研究了基于滑模控制的一类不确定分数阶广义系统的可容许性和鲁棒无源性问题。首先,设计了一种含有奇异矩阵的分数阶积分型切换函数,对其求分数阶导数推导出等效控制,进而得到滑动模态方程。其次,针对滑动模态方程和系统输出方程,利用线性矩阵不等式技巧,给出了系统滑动模态具有鲁棒无源性和可容许性的充分性判据,并进一步建立了鲁棒无源可容许的可解性条件。同时,设计的分数阶滑模控制律保证了闭环系统状态轨迹能够到达预设的切换面。最后,通过一个仿真实例验证了本文结果的有效性。The admissibility and robust passivity of uncertain fractional order(FO)singular system via sliding mode control(SMC)is studied.Firstly,a FO integral-type switching function with singular matrix is designed,and the equivalent control is derived by calculating the FO derivative,and then the sliding mode equation is obtained.Secondly,in view of the sliding mode equation and the system output equation,the sufficient criteria for the robust passivity and admissibility of the sliding mode of the system are given by using the technique of linear matrix inequality,and the conditions for the robust admissibility with passive performance of the solvable are further established.At the same time,the FO SMC law is designed to ensure that the state trajectories of the closed-loop system can reach the pre-designed switching surface.Finally,a simulation example is provided to verfity the effectiveness of the results.

关 键 词：分数阶 广义系统 滑模控制 鲁棒无源性 可容许性 

分 类 号：O231.2[理学—运筹学与控制论]