基于FPGA的射频腔体系统数学模型在线辨识算法

Online Identification Algorithm for Mathematical Model of RF Cavity System Based on FPGA

射频系统的数学模型包含了射频腔体的关键特征参数(如腔体半带宽、谐振频率和洛伦兹力失谐系数等),数学模型对腔体性能检测、控制系统仿真及低电平控制算法优化具有重要意义。网络分析仪通常用于测量射频系统的散射参数,进而构建射频系统的数学模型,但其测量步骤繁琐且无法实现系统模型的在线自动辨识。本文通过模拟网络分析仪的工作原理,在数字低电平系统内部构建了基于数控振荡器的扫频算法,实现了射频腔体系统的在线辨识。该算法的有效性已在加速器驱动嬗变研究装置前端示范样机的超导腔上验证,其测量结果与网络分析仪测量结果吻合。此外,本文利用该辨识算法还成功测得了由洛伦兹力失谐引起的超导腔频率响应畸变曲线,并讨论了洛伦兹力失谐量的大小对腔体关键特征参数测量的影响。

The mathematical model of a radio frequency(RF)system incorporates crucial characteristic parameters of an RF cavity,including the cavity bandwidth,the resonant frequency,and Lorentz force detuning factors,which is very important for the cavity performance evaluation,the control system simulation,and the optimization of low-level control algorithms.A network analyzer is usually used to measure scattering parameters and subsequently construct mathematical models of a RF system.However,the measurement steps are tedious and fail to identify the system model online.Therefore,an advanced online identification algorithm was described for RF cavity systems in this paper,which simulated the operational principles of a network analyzer.This algorithm was integrated within a digital low-level RF(LLRF)system and consisted of a high-precision numerically controlled oscillator,a frequency control word generator module,an amplitude-phase calculation module,and a sweep frequency amplitude-phase processing module.With the assistance of the Matlab/Simulink platform,which provides an ideal environment for simulation and analysis,the deployment of this algorithm was ultimately realized on the field-programmable gate array(FPGA)chip of the low-level system,accomplishing the online identification of RF systems.Then,the sweeping algorithm was verified on a superconducting cavity of the China Accelerator Driven System Front-end Demo Linac at the Institute of Modern Physics.During the verification process,the half-bandwidth of all cavities in CM1 was accurately measured using an online identification algorithm,and the half-bandwidth of all cavities corresponding to CM1 was also measured utilizing a network analyzer.The results of half-bandwidth measured by the two methods are in good agreement,strongly supporting the validity of the online identification algorithm for cavity system models proposed in this paper.Furthermore,we successfully measured the distortion curve of cavity frequency response caused by Lorentz force detuning.Finally,the influence of Lorentz force detuning variation on the measurement of the critical cavity parameters was discussed in this paper.As the RF peak electric field increases,the radiation pressure within the cavity rises proportionately,leading to a corresponding increase in Lorenz force detuning.This article demonstrates that when the RF peak electric field of the cavity operating is less than 16 MV/m,Lorenz force detuning has a relatively limited impact on the bandwidth measurement of the cavity.Conversely,once the peak acceleration electric field surpasses this threshold,Lorenz force detuning exerts an unnegligible effect on the measurement of the half-bandwidth of the cavity.The specific mechanisms of the Lorenz force detuning’s influence on the half-bandwidth of the cavity will be further studied in future research.