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

Abstract

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

CLC Number:

TJ273

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.

Figures/Tables 14

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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

Design and application of tracking differentiator based on inverse hyperbolic tangent function

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