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1. 华北科技学院 电子信息工程学院, 北京 101601;
2. 中央新影集团 CCTV证券资讯频道, 北京 100080

A direct adaptive fuzzy sliding mode control method for discrete nonlinear systems
ZHANG Xiaoyu1, LIU Binbo2
1. Department of Electronics and Information Engineering, North China Institute of Science and Technology, Beijing 101601, China ;
2. CCTV Securities Information Channel, Beijing 100080, China
Abstract: In order to obtain chatter-free sliding mode control for a class of discrete nonlinear systems, an adaptive fuzzy sliding mode control (FSMC) is constructed on the basis of the adaptive fuzzy logic system (AFLS). Firstly, the online adaptive law is applied to regulate the parameters of the AFLS, in order to make the output of the AFLS approximate to the pre-designed sliding mode control (SMC); then the convergence of the approximation errors and the reachability of the SMC are proofed by using the Lyapunov method. The simulation results of the inverted pendulum system verify the effectiveness of the presented design. Therefore, the proposed discrete controller drives the system state onto the sliding mode, and its robustness is enhanced.
Key words: discrete system     fuzzy logic system     sliding mode control     adaptive control     nonlinear systems     robust control     variable structure control     chattering

1 离散非线性系统的SMC

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)
 (7)
 (8)

 (9)

2 模糊自适应SMC

2.1 自适应模糊逻辑系统

 (10)

2.2 自适应率

 (11)
2.3 DAFLS逼近滑模控制

 (12)

 (13)

 (14)

 (15)

 (16)

3 主要结果 3.1 动态AFLS的逼近误差

 (17)

Cb=1, 式(17)变为

3.2 近似逼近下的滑模可达性

 (18)

4 倒立摆系统应用仿真

 图 1 SMC和DAFLSMC控制下摆角位移曲线对比 Fig. 1 Angle displacement contract curves of pendulum for SMC and DAFLSMC
 图 2 SMC和DAFLSMC控制下电压曲线对比 Fig. 2 Control voltage contract curves for SMC and DAFLSMC

 图 3 滤波器前后的控制电压曲线对比 Fig. 3 Control voltage comparison of AFLSMC and DAFLSMC

 图 4 DAFLS控制下摆角位移受扰曲线 Fig. 4 The angle excursion curve when disturbed under DAFLSMC control
 图 5 DAFLS控制下受扰时控制电压曲线 Fig. 5 The control volt curve when disturbed under DAFLSMC control
5 结束语

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DOI: 10.3969/j.issn.1673-4785.201303034

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#### 文章信息

ZHANG Xiaoyu, LIU Binbo

A direct adaptive fuzzy sliding mode control method for discrete nonlinear systems

CAAI Transactions on Intelligent Systems, 2014, 9(2): 197-203
http://dx.doi.org/10.3969/j.issn.1673-4785.201303034