基于自适应分数阶正位置反馈的垂尾振动主动控制

doi:10.12382/bgxb.2023.0570

摘要/Abstract

摘要：

针对自适应正位置反馈(Adaptive Positive Position Feedback, APPF)控制器在控制效果与分数阶正位置反馈(Fractional Order Positive Position Feedback, FOPPF)控制器在针对摄动区间小的不足,提出一种分数阶APPF(Fractional Order Adaptive Positive Position Feedback, FOAPPF)控制器,使得控制器在控制效果提升的同时兼具强鲁棒性。基于不同参数对FOPPF控制器的影响,推导参数的最佳范围,将系统多个摄动模型的正弦扫频响应进行综合加权处理,并考虑系统远离共振频段的控制性能,构建附带约束条件的控制设计的目标函数。以粘有宏纤维复合材料(Macro Fiber Composites, MFC)的垂尾模型及其摄动模型为被控对象,设计相应的FOAPPF控制器。研究结果表明:相比FOPPF控制器,FOAPPF控制器闭环极点对参数摄动不敏感;相比APPF控制器,FOAPPF控制器的相频曲线在摄动频带内变化平缓,其控制效果受固有频率在线估计误差的影响更小;多种试验工况表明,FOAPPF控制器在不同摄动模型下均具有较好的控制效果,垂尾抖振响应均方根值至少降低了55%,且具有较好的鲁棒性,因此该控制器对垂尾结构的振动主动控制具有良好应用潜力。

关键词: 正位置反馈, 固有频率在线估计, 摄动结构, 自适应控制, 分数阶控制

Abstract:

Aiming at the deficiencies of the adaptive positive position feedback (APPF) controller in the control efficiency and the fractional order positive position feedback (FOPPF) controller for the small perturbation interval, a fractional order adaptive positive position feedback (FOAPPF) controller is proposed, which aims to enhance control effectiveness while maintaining robustness. The distinct impacts of various parameters on the FOPPF controller are evaluated to derive the optimal parameter range. The sine sweep responses of multiple perturbation models of the system are comprehensively weighted. Additionally, the system's control performance far from the resonance frequency band is considered, leading to the formulation of an objective function for control design incorporating necessary constraints. The FOAPPF controller is designed based on the vertical tail model attaching macro fiber composites (MFC) and its perturbation model. Compared with FOPPF controller, the poles in the closed-loop system of FOAPPF controller are insensitive to the parameter perturbation. Moreover, compared with the APPF controller, the slope of the phase-frequency curve of FOAPPF controller is smooth in the perturbation frequency band, and its control efficiency is less affected by the online estimation error of natural frequency. Various experimental conditions show a significant improvement in the control effectiveness of FOAPPF controller across different perturbation models. Furthermore, the RMS value of the vertical tail buffeting response is reduced by at least 55%, indicating substantial robustness. Therefore, the FOAPPF controller demonstrates the promising potential for active vibration control of vertical tail structures.

Key words: positive position feedback, online estimation of natural frequency, perturbation structure, adaptive control, fractional order control

中图分类号:

V215

张家旋, 李斌, 牛文超, 李凯翔. 基于自适应分数阶正位置反馈的垂尾振动主动控制[J]. 兵工学报, 2024, 45(8): 2542-2553.

ZHANG Jiaxuan, LI Bin, NIU Wenchao, LI Kaixiang. Adaptive Fractional Order Positive Position Feedback for Vibration Control of Vertical Tail[J]. Acta Armamentarii, 2024, 45(8): 2542-2553.

图/表 17

图1 不同变量下FOPPF控制器Bode图

Fig.1 Bode diagram of FOPPF controller with different variables

图2 闭环FOAPPF控制系统的结构框图

Fig.2 Block diagram of closed-loop FOAPPF control system

图3 FOAPPF控制器框图

Fig.3 Block diagram of FOAPPF controller

图4 试验系统

Fig.4 Experimental system

图5 摄动模型构建方案

Fig.5 Construction schemes of perturbation model

表1 垂尾的摄动模型

Table 1 Perturbation model of vertical tail

模型描述	固有频率/Hz	摄动模型
无质量块	13.50	标称模型
1个质量块	12.00	-11%摄动模型
2个质量块	10.75	-20%摄动模型
实时增加铁砂	13.50~10.75	-20%缓变模型

图6 方案1 FOPPF控制器的Bode图

Fig.6 Bode diagram of FOPPF controller in Scheme 1

图7 方案2 FOPPF控制器的Bode图

Fig.7 Bode diagram of FOPPF controller in Scheme 2

图8 方案3 FOPPF控制器的Bode图

Fig.8 Bode diagram of FOPPF controller in Scheme 3

图9 仿真框图

Fig.9 Simulation block diagram

图10 控制系统的极点分布

Fig.10 Pole distribution of control systems

图11 FOAPPF控制器与APPF控制器的bode图对比

Fig.11 Contrast of Bode diagrams of FOAPPF and APPF controllers

图12 1阶弯曲模态定频正弦响应抑制性能

Fig.12 First order bending mode suppression performance of fixed frequency sinusoidal response

表2 1阶弯曲模态随机响应RMS值降低比与PSD谱峰值降低值

Table 2 RMS reduction ratio and PSD peak reduction value for random response near the 1st order bending mode

控制器	标称模型		-11% 摄动模型		-20% 摄动模型
控制器	RMS/%	PSD/dB	RMS/%	PSD/dB	RMS/%	PSD/dB
APPF	53.30	9.29	57.10	10.55	39.50	6.65
FOPPF	66.72	16.27	54.13	13.58	36.53	5.59
FOAPPF	59.50	12.65	66.80	19.47	55.00	12.38

图13 垂尾模型1阶弯曲模态随机响应的PSD谱

Fig.13 PSD spectrum of random response of vertical tail near the 1st order bending mode

图14 垂尾模型在线摄动随机响应的PSD谱

Fig.14 PSD spectrum of online perturbation random response ofvertical tail model

表3 垂尾模型在线摄动随机响应RMS值降低比与PSD谱峰值降低值

Table 3 RMS reduction ratio and PSD peak reduction value of online perturbation random response of vertical tail model

控制器	RMS/%	PSD峰值/dB
APPF	43.01	11.71
FOAPPF	57.83	13.40

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