Adaptive Fractional Order Positive Position Feedback for Vibration Control of Vertical Tail

doi:10.12382/bgxb.2023.0570

Abstract

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

CLC Number:

V215

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.

Figures/Tables 17

Fig.1 Bode diagram of FOPPF controller with different variables

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

Fig.3 Block diagram of FOAPPF controller

Fig.4 Experimental system

Fig.5 Construction schemes of perturbation model

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

Fig.6 Bode diagram of FOPPF controller in Scheme 1

Fig.7 Bode diagram of FOPPF controller in Scheme 2

Fig.8 Bode diagram of FOPPF controller in Scheme 3

Fig.9 Simulation block diagram

Fig.10 Pole distribution of control systems

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

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

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

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

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

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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