摘要
Signal filtering and differential acquisition are classic yet challenging issues in control engineering.The discrete-time optimal control(DTOC)based on classic tracking differentiator(TD)can effectively extract differentiation signals and filter signals,while eliminating the chattering problem that arises during the discretization of the continuous solution.However,under external disturbance,the convergence mode may change,leading to overshoot and noise amplification.In this paper,a dual-switching strategy is proposed,which can alternate between the base double-integral system and its dual system according to the quadrant of the system’s state.And a novel linearized control law is also introduced,deriving a novel dual-switch tracking differentiator.Further analysis of system convergence and time optimality is provided.Simulation results show that the application of this dual-switching strategy notably reduces overshoot in both tracking and differential signals while enhancing noise filtering performance.Moreover,experiments conducted on a permanent magnet synchronous motor(PMSM)platform,where the proposed TD acts as a filter in the speed feedback loop,demonstrate that the standard deviation between the reference speed and the target speed(at a constant speed of 378 r/min)decreased from 5.63 r/min to 4.93 r/min,compared to the moving average algorithm.
信号的跟踪和微分一直是控制工程中经典且具有挑战性的问题,现有的基于离散时间控制的经典跟踪微分器(TD),解决了连续时间控制在离散化过程中所出现的抖振问题。然而,受制于外部扰动,系统的收敛模态可能发生改变,造成超调和噪声放大。本文提出了一种对偶切换策略,通过修改系统的离散形式,使其根据系统状态象限在双积分系统与其对偶系统间进行切换。同时提出了一种线性化的控制综合函数,综合构造了新型的对偶变结构离散跟踪微分器,并对这一对偶切换算法给出了收敛性证明和时间最优性分析。仿真结果表明,对于非连续或非光滑信号,应用对偶切换策略显著减少了跟踪及微分信号的过冲量,相较于经典跟踪微分器提高了噪声滤波性能。此外,在永磁同步电机平台上进行的实验表明,所提出的TD作为速度反馈回路中的滤波器,相较于滑动平均算法,闭环速度与目标速度间的标准差由5.60 r/min降至4.93 r/min(定速380 r/min),表明其在工程实践中能够平稳、有效运行。
基金
Project(QZKFKT2023-012)supported by the State Key Laboratory of Heavy-duty and Express High-power Electric Locomotive,China。
作者简介
Corresponding author:HAN Kun,PhD,Associate Professor,E-mail:hkun@csu.edu.cn,ORCID:https://orcid.org/0000-0003-4091-327 X。
