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中南大学学报(自然科学版)

Journal of Central South University

第45卷    第9期    总第241期    2014年9月

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文章编号:1672-7207(2014)09-3068-08
一类高阶非线性系统的鲁棒反推终端滑模控制
苏磊1,姚宏2,杜军1,冀捐灶1

(1. 空军工程大学航空航天工程学院,陕西 西安,710038;
2. 空军工程大学理学院,陕西 西安,710051
)

摘 要: 针对一类高阶非匹配不确定非线性系统,结合动态面控制方法,设计一种鲁棒自适应反推终端滑模控制方案,在消除控制抖振的同时,提高系统对不确定性的鲁棒性。设计非线性干扰观测器,对系统中由外界干扰引起的非匹配不确定性进行观测补偿。在反推过程中,基于动态面控制方法引入低通滤波器,有效降低控制器复杂 性。引入边界层厚度设计系统建模误差自适应律。在反推最后一步,采用双曲正切函数替换符号函数降低控制抖振。给出观测器和系统在设计控制方案下的稳定性定理及证明,观测误差和跟踪误差一致终结有界。通过对比仿真,验证观测器对系统不确定性的精确观测能力。研究结果表明:设计的控制方案对系统非匹配不确定性和建模误差具有较好的鲁棒性。

 

关键词: 非匹配不确定性;终端滑模;自适应反推;动态面控制;非线性干扰观测器

Robust backstepping terminal sliding mode control for a class of high-order nonlinear systems
SU Lei1, YAO Hong2, DU Jun1, JI Juanzao1

1. School of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi’an 710038, China;
2. School of Science, Air Force Engineering University, Xi’an 710051, China

Abstract:Combined with dynamic surface control (DSC) method, a robust adaptive backstepping terminal sliding mode (TSM) control method was proposed for a class of high-order nonlinear systems with unmatched uncertainties. The chattering of control signal was eliminated. Moreover, system’s robustness for uncertainties was recovered and strengthened. Nonlinear disturbance observers (NDOs) were designed for compensation of the unmatched uncertainties caused by external disturbances. In the procedure of backstepping, law pass filters (LPFs) were employed to simplify the design of controller, which was based on DSC method. An adaptive law was designed for system modelling error, in which the boundary layer thickness was used. In the last step of backstepping, hyperbolic tangent function was employed to replace the sign function in traditional sliding mode. The chattering of control signal was effectively suppressed. The stability theories and proofs of NDOs and close-loop system were presented. The observation errors and tracking error were uniformly ultimately bounded. Simulation results and comparisons were given. The results show that the control method can validate the accurate observation ability of designed NDOs and the robustness of the proposed control method for both system uncertainties and modelling errors.

 

Key words: unmatched uncertainties; terminal sliding mode; adaptive backstepping; dynamic surface control; nonlinear disturbance observer

中南大学学报(自然科学版)
  ISSN 1672-7207
CN 43-1426/N
ZDXZAC
中南大学学报(英文版)
  ISSN 2095-2899
CN 43-1516/TB
JCSTFT
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