%0 Journal Article
%T 跟踪微分器的等效线性分析及优化
%A 劳立明
%A 陈英龙
%A 赵玉刚
%A 周华
%J 浙江大学学报(工学版)
%D 2018
%R 10.3785/j.issn.1008-973X.2018.02.003
%X 为了解决跟踪微分器跟踪函数选取多样、参数调整困难的问题，研究跟踪微分器在平衡点附近的等效线性模型.提出平衡点附近非线性跟踪微分器的统一型式，用Lyapunov方法证明统一模型的稳定性.将统一模型在平衡点处线性化，得到不同非线性结构对线性化参数的影响，仿真算例验证了线性化模型的等效性.基于等效线性模型的频率特性分析跟踪微分器的滤波性能及相位滞后，据此提出跟踪微分器的参数优化方法.提出前馈补偿的复合跟踪微分器，减小相位滞后并抑制前馈噪声.数值仿真结果验证了跟踪微分器参数优化方法的可行性，表明所提复合跟踪微分器具有最佳的跟踪误差与微分误差组合.</br>Abstract: The equivalent linear tracking differentiator near the equilibrium point was analyzed in order to solve the difficulties of various tracking functions selection and parameters setting. A unified model of the nonlinear tracking differentiator near the equilibrium point was presented. Then the asymptotic stability was proven by the Lyapunov method. The unified nonlinear model was further linearized near the equilibrium point and the effect of different nonlinear structures on linearized parameters was analyzed. Simulation examples verified the effectiveness of the equivalent linear model. The filtering property and the resulted phase lag were analyzed by the frequency response of the linearized model, and a decoupled parameter optimization method was proposed. A compound tracking differentiator with feedforward was proposed to reduce the phase lag and suppress the noise introduced by feedforward. Simulations showed the effectiveness of proposed parameter tuning method. The compound tracking differentiator achieved the best combination of tracking error and differential error.
%U http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2018.02.003