Abstract:

In order to solve the problem that the arctangent tracking differentiator has difficulty in setting parameters and slow convergence near the equilibrium, the author has designed a fast convergence arctangent tracking differentiator. A rapid arctangent tracking differentiator is constructed by introducing linear functions and terminal attractor functions into the arctangent function and its stability is proved, which makes the system far from the equilibrium and close to the equilibrium point convergence rapidly and stably to the equilibrium point. This continuous function form of linear and nonlinear combination enhances the tracking ability of the system, and effectively suppresses the noise, which can realize fast and precise signal differential and tracking, and the form is simple and easy to implement. The simulation results show that the rapid arctangent tracking differentiator has excellent performance.

Key words: Tracking differentiator, nonlinear, terminal attractor function, arctangent function

摘要： 针对反正切跟踪微分器存在整定参数困难和在平衡点附近收敛慢等问题，设计了一种快速收敛的反正切跟踪微分器。在反正切函数中引入线性函数和终端吸引子函数构造了快速反正切跟踪微分器，并证明了其稳定性，使系统在远离平衡点和接近平衡点都能快速并稳定地向平衡点收敛。这种线性与非线性组合的连续函数形式，提高了系统的跟踪能力，并且有效地抑制了噪声。可实现对信号快速而精确的微分和跟踪，且形式简单、易于实现。仿真结果表明快速反正切跟踪微分器具有优良的性能。

关键词: 跟踪微分器, 非线性, 终端吸引子函数, 反正切函数