Variable parameter linear tracking differentiator and its application in altazimuth large area telescope

YANG Xiaoxia; DENG Yongting; ZHAOJinyu; ZHANG Bin

doi:10.37188/OPE.20223023.3045

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Variable parameter linear tracking differentiator and its application in altazimuth large area telescope

更新时间：2026-09-12

- Variable parameter linear tracking differentiator and its application in altazimuth large area telescope
- Optics and Precision Engineering Vol. 30, Issue 23, Pages: 3045-3057(2022)
- 作者机构：
  
  中国科学院长春光学精密机械与物理研究所，吉林长春 130033
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20223023.3045
  CLC： TP273
- Received：30 September 2022，
  
  Revised：2022-11-26，
  
  Published：10 December 2022
- 稿件说明：
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杨晓霞,邓永停,赵金宇等.变参数线性跟踪微分器及其在地平式大视场望远镜中的应用[J].光学精密工程,2022,30(23):3045-3057.

YANG Xiaoxia,DENG Yongting,ZHAOJinyu ,et al.Variable parameter linear tracking differentiator and its application in altazimuth large area telescope[J].Optics and Precision Engineering,2022,30(23):3045-3057.
杨晓霞,邓永停,赵金宇等.变参数线性跟踪微分器及其在地平式大视场望远镜中的应用[J].光学精密工程,2022,30(23):3045-3057. DOI： 10.37188/OPE.20223023.3045.

YANG Xiaoxia,DENG Yongting,ZHAOJinyu ,et al.Variable parameter linear tracking differentiator and its application in altazimuth large area telescope[J].Optics and Precision Engineering,2022,30(23):3045-3057. DOI： 10.37188/OPE.20223023.3045.

摘要

为了对具有速度和加速度限制的物理信号安排合理的过渡过程，提出了一种带有速度和加速度饱和限制的变参数线性跟踪微分器。将跟踪微分器的快速因子设计为跟踪误差减函数的形式，即使在初始跟踪误差非常大的时候也不会产生非常大的加速度，同时结合速度和加速度饱和的限制，使用同一组参数就可以对大范围的阶跃信号给出与物理系统反馈能力相匹配的过渡过程信号。仿真计算表明，所设计的跟踪微分器的跟踪效果与经典的非线性跟踪微分器几乎相同，计算复杂度却明显降低。将所设计的跟踪微分器应用于地平式大视场望远镜的快速调转定位中，与工程中常用的位置分段方式进行对比，响应时间缩短了大约15%~37%，有效提高了望远镜的搜索效率。变参数跟踪微分器不但能够起到过渡作用，还能最大限度地激发物理系统的反馈能力。该方法参数设置简单，易于工程中的调试和实现。

Abstract

To develop a reasonable transition process for physical signals with speed and acceleration limits， we propose a variable parameter linear tracking differentiator with speed and acceleration saturations. The parameter of the tracking differentiator is designed as a decreasing function of the tracking error， which avoids large acceleration shock in the initial stage when the tracking error is relatively large. Using the same set of parameters， the designed tracking differentiator can give reasonable transition signals that match the feedback capabilities of physical systems for a wide range of step signals. Simulation results show that the proposed tracking differentiator can produce nearly the same tracking effect as that of the classical nonlinear tracking differentiator and with reduced computational complexity. We applied the designed tracking differentiator to the rapid positioning of an altazimuth large area telescope. Compared with the commonly used position segmentation method， the response time was reduced by 15%–37%， thereby improving the search efficiency of the telescope. The proposed variable parameter tracking differentiator can not only play a transitional role but can also maximize the feedback capabilities of physical systems. The parameter setting of the proposed method is simple as well as easy to debug and implement in engineering practice.

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