弹性伺服系统高性能位置控制器设计及增益边界分析

doi:10.19595/j.cnki.1000-6753.tces.241047

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摘要

针对弹性伺服系统带宽受反谐振频率限制问题,提出了两种基于状态反馈的位置控制器设计方法。含积分的状态反馈控制采用零极点对消法降低了闭环系统的阶数,频域上最优速度前馈设计提高了动态性能。无积分的状态反馈控制取消了速度环积分部分,用观测扰动补偿输出转矩,消除稳态误差。采用最大峰值灵敏度理论分析可得,取消速度环积分的设计有更大的增益边界,且所得极限增益为实际应用中带宽选择提供了合理的指导。在同步带轮伺服系统上验证了所提方法的有效性,实验表明,所提状态反馈位置控制具有良好的动态响应和较宽的增益选择范围。

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关键词 ：伺服控制, 双惯量系统, 状态反馈控制, 增益边界

Abstract：

High-performance servo drives are critical for the quality of industrial production. In traditional servo control schemes, motor position feedback modifies the speed closed-loop transfer function, characterized by two parameters: proportional and integral. For elastic mechanical loads, it is impossible to balance damping and dynamic response within the system. State feedback control (SFC) effectively improves speed dynamic response and suppresses residual vibration. This paper proposes two types of position controller design methods based on state feedback to address the bandwidth restrictions imposed by anti-resonance frequencies in elastic servo systems.
Firstly, the numerator polynomial in the speed proportional-integral (PI) structure has freedom restrictions. The proposed state feedback position control (SFPC) with an integral part combines PI with integral-proportional (IP) for a more flexible zero design. Zero-pole cancellation reduces the order of the closed-loop system, and optimal speed feedforward in the frequency domain improves dynamic performance. Secondly, the state feedback controller without an integral part removes the integral component from the speed loop, where estimated disturbances are compensated on the output torque. The disturbance function is modified with a parameter k_L to provide a high-pass filter characteristic. Zero-pole cancellation is unnecessary for this simplified structure. Furthermore, the gain boundaries of these two SFPCs are analyzed using maximum peak sensitivity, demonstrating that the speed loop without an integral part has a larger gain boundary than the series structure. The maximum gain offers a reasonable guideline for bandwidth selection in practical applications. Finally, the effectiveness of the proposed methods is verified on a tooth belt servo system. The proposed SFPCs have good dynamic response and a wide gain selection boundary.
The following conclusions can be drawn. (1) The proposed SFPC with an integral part reaches the target position faster than the traditional method, with less overshoot and a 44% reduction in settling time. (2) Compared to state feedback speed control cascading a position loop, the response characteristics of the proposed SFPC remain consistent across different gains. (3) The position response of the SFPC with an integral part is in good agreement with the method that includes an integral, which achieves the same positional dynamic response at the same gain. (4) The optional gain boundaries of the two methods differ. The gain of the SFPC with and without an integral can approach 1.4ω_ares with oscillations and 1.8ω_ares without oscillations. The non-integral SFPC increases the gain boundary by 28%.
The proposed SFPC can balance dynamic response and residual vibration, broadening the maximum gain boundary to 1.8ω_ares, which is beneficial for improving servo driver performance under elastic mechanical loads.

Key words： Servo control two-mass system state feedback control gain boundary

收稿日期: 2024-06-18

PACS:

TM383.4

基金资助:

中央高校基本科研业务费资助项目（NT2023007）

通讯作者: 黄文新男,1966年生,教授,博士生导师,研究方向为电机系统及其控制、新型风力发电技术、电能变换、航空电源等。E-mail: huangwx@nuaa.edu.cn

作者简介: 牛泽农男,1993年生,博士研究生,研究方向为永磁同步电机低载波比控制、高性能伺服控制系统设计。E-mail: niuzenong@nuaa.edu.cn

引用本文:

牛泽农, 黄文新, 卜飞飞, 赵亚俊. 弹性伺服系统高性能位置控制器设计及增益边界分析[J]. 电工技术学报, 2025, 40(16): 5234-5246. Niu Zenong, Huang Wenxin, Bu Feifei, Zhao Yajun. High-Performance Position Controller Design and Gain Boundary Analysis for Elastic Servo Systems. Transactions of China Electrotechnical Society, 2025, 40(16): 5234-5246.

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