基于反双曲正切函数的跟踪微分器设计与应用

doi:10.3969/j.issn.1001-506X.2020.12.25

摘要/Abstract

摘要：

通过引入反双曲函数与终端吸引子函数,构造了一种新型跟踪微分器。反双曲正切函数在平衡点较近处优异的线性特性可以保证系统收敛的平滑性,远离平衡点处的非线性特性能保证收敛的快速性。通过引入终端吸引子函数,降低了高频信号引起的抖振,增强了噪声抑制能力。通过扫频测试总结得出了参数整定规则后，与典型的跟踪微分器进行对比仿真,测试了所设计新型跟踪微分器的性能。最后，在控制器设计时,基于所提出的新型跟踪微分器构造了干扰观测器。通过仿真对比,证明所构造的干扰观测器实现了对模型不确定项的有效估计。

关键词: 跟踪微分器, 反双曲正切函数, 终端吸引子函数, 干扰观测器

Abstract:

A type of tracking differentiator is constructed by introducing the inverse hyperbolic function and the terminal attractor function. The linear property of the inverse hyperbolic tangent function which is close to the equilibrium point can ensure the smoothness of the convergence of the system, and the nonlinear characteristic which is far away from the equilibrium point ensures the fast convergence. By introducing the terminal attractor function, the chattering which is caused by the high frequency signal is reduced, and the noise suppression capability is enhanced. The parameter tuning rules are obtained by sweeping test. Then, the performance of the new tracking differentiator is tested by comparing with the typical tracking differentiator. Finally, in the design of the controller, the disturbance observer is constructed based on the proposed tracking differentiator. The simulation results show that the constructed disturbance observer can effectively estimate the uncertainties of the model.

Key words: tracking differentiator, inverse hyperbolic tangent function, terminal attractor function, disturbance observer

中图分类号:

TJ273

鲁力, 王洁, 袁成人, 吴亚晖. 基于反双曲正切函数的跟踪微分器设计与应用[J]. 系统工程与电子技术, 2020, 42(12): 2875-2883.

Li LU, Jie WANG, Chengren YUAN, Yahui WU. Design and application of tracking differentiator based on inverse hyperbolic tangent function[J]. Systems Engineering and Electronics, 2020, 42(12): 2875-2883.

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测试可变参数	参数值
R=7, 10, 15, 20, 30	a₁=4, a₂=9, b=0.9
a₁=1, 2, 3, 4, 5	R=20, a₂=9, b=0.9
a₂=10, 15, 20, 30, 50	R=20, a₁=4, b=0.9
b=0.1, 0.3, 0.5, 0.7, 0.9	R=20, a₁=4, a₂=9

TD的类型	参数值
IHTD	R=35, a₁=0.75, a₂=0.63, b=0.01
HSMD	L₀=3π, Γ₁=1.1, Γ₂=1.5
MATD	R=15, λ₁=4, λ₂=2, b=0.9
HNTD	R=35, a₁=0.75, a₂=0.63, γ₁=1, γ₂=1, b=0.01

TD类型	参数值
IHTD	R=60, a₁=0.15, a₂=0.09, b=0.33
HSMD	L₀=3π, Γ₁=1.1, Γ₂=1.5
MATD	R=15, λ₁=4, λ₂=2, b=0.9
HNTD	R=20, a₁=10, a₂=1, γ₁=1, γ₂=1, b=0.01

干扰观测器类型	参数值
IHTD	R=70, a₁=90, a₂=1, b=0.33
SMTD	Z_V0=1.5, Z_V1=1.1
INTD	R=220, a₁=1, a₂=1, a₃=1, a₄=1.14, b=3

干扰观测器类型	参数值
IHTD	R=2, a₁=10, a₂=1, b=0.33
SMTD	Z_V0=1.5, Z_V1=1.1
INTD	R=2, a₁=5, a₂=5, a₃=1, a₄=1.14, b=3