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中国科学院近代物理研究所在兰州重离子研究装置(HIRFL)上新建了一台CW直线加速器SSC-LINAC,作为分离扇回旋加速器(SSC)的注入器[1],提高了整个HIRFL系统的运行效率。SSC-LINAC由1个RFQ加速器[2]和4个DTL(Drift Tube Linac)组成[3]。SSC-LINAC RFQ谐振腔主要参数见表1[4]。
参数 数值 工作频率/MHz 53.667 设计粒子 238U34+ 输入能量/(keV/u) 3.728 输出能量/(keV/u) 143 腔体电压/kV 70 传输效率/% 94.1 结构长度/cm 250.846 功率消耗/kW 30 馈入功率会引起腔体温度升高,引发腔体受热形变,导致腔体谐振频率变化[5]。SSC-LINAC RFQ腔体调谐通过其侧面安装的四根直径为55 mm的调谐杆完成,如图1所示。调谐杆位置与腔体谐振频率改变量关系见图2[6]。
四根调谐杆同步移动,移动范围为0~350 mm。移动调谐杆可以使得腔体谐振频率发生改变,由图2可见,最大改变量为125 kHz。通过调整调谐杆位置,可以使腔体处于谐振状态。
高频谐振腔失谐会导致高频电压降低和功率源系统的损坏[7]。为了保证腔体时刻处于调谐状态需要为腔体设计自动调谐系统[8]。调谐系统的作用是令腔体在选定频率上谐振,可以使腔体与功率源阻抗匹配,保证功率源向腔体馈入功率的效率[9]。高频谐振腔的调谐方法主要分为基于相位差与基于反射信号的调谐方法[10]。基于相位差的调谐方法缺点为启动时间较长,需要经常性的人为干预且准确性易受环境温度影响。结合Lyapunov稳定性理论[11],对滑模极值搜索算法进行改进。将改进后的算法应用在基于反射信号的调谐系统设计中,可以减小腔体调谐过程受环境温度变化的影响程度,提高调谐过程准确性,缩短启动时间,实现腔体功率的自动加载且满足调谐过程的频率稳定度[12]要求。
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在MATLAB 2018b软件中进行仿真,利用滑模极值搜索算法改变控制参数u,记录腔体反射电压信号幅度和控制参数随时间的变化。设定仿真参数如表2所列,结合式(7),进行当输入为连续信号时,基于滑模极值搜索算法的仿真。
参数 数值 Ωic/MHz 53.667 Ω0/MHz 53.55 Z0C 1.418 4×10-4 γ(1/RC + 1/Z0C) 14 100 k 1×1012 Vf/kV 70 u/(kHz)2 495 ε 2 ρ 10 g(0) 0 ku 0.000 01 设腔体初始谐振频率为53.55 MHz。进行仿真,得到仿真结果如图4所示。
由仿真结果可见,随着迭代次数增加,腔体反射电压信号幅度趋于极小值。控制参数u的变化量收敛于极小值,代表调谐杆趋于目标位置。Δu趋于极小值,代表调谐杆速率趋于零。三种情况的频率稳定度仿真结果如图5所示。
腔体反射电压信号幅度在算法滑动段的收敛速度由
$ |\dot {g(t)} | $ 决定,增大β会导致$ |\dot {g(t)} | $ 减小。由图4和图5可见,增大β会降低腔体反射电压信号幅度的收敛速度。结合图5,计算在迭代次数超过60次后三种情况的频率稳定度,当β=10,ku=0.000 05时,频率稳定度保持在3.435 7×10–9以内。当β=10.164,ku=0.000 05时,频率稳定度保持在3.559 4×10–9以内。当β=10,ku=0.000 03时,频率稳定度保持在1.879 9×10–9以内。可见降低ku会导致收敛速度变慢,但调谐精度明显提高。在不触发高频发射机保护机制的前提下,选择较小的β和较小的ku可以使得收敛过程较快且调谐精度较高。
Design and Testing of SSC-LINAC RFQ Tuning System Based on Extremum Seeking Algorithm with Sliding Mode
doi: 10.11804/NuclPhysRev.38.2021034
- Received Date: 2021-04-20
- Rev Recd Date: 2021-05-08
- Publish Date: 2021-12-20
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Key words:
- RF cavity /
- RFQ /
- extremum seeking with sliding mode /
- SSC-LINAC
Abstract: Extremum seeking algorithm with sliding mode is presented for design of automatic tuning control system of SSC-LINAC RFQ(Radio Frequency Quadrupole) based on the cavity reflected signal. Combined with the Lyapunov stability theory and the characteristics of SSC-LINAC RFQ radio frequency system, the control gain and reference signal of the sliding mode algorithm are improved. By solving the differential equation, the functions of the cavity reflected signal with respect to time and the position of the tuning rod are obtained. Through software simulation and hardware system design, the tuning process based on extremum seeking algorithm with slidig mode is simulated and tested. The results show that the designed frequency stabilization system can realize the automatic power feeding process of SSC-LINAC RFQ cavity in a short time, and the frequency stability meets the design index requirements, and has passed the long-time stability test. The feasibility of applying the extremum seeking algorithm with sliding mode to the tuning of high frequency resonator is proved.
Citation: | Xinyu WANG, Yan CONG, Zhe XU, Ruihuai ZHOU, Shilong LI, Xiaodong HAN. Design and Testing of SSC-LINAC RFQ Tuning System Based on Extremum Seeking Algorithm with Sliding Mode[J]. Nuclear Physics Review, 2021, 38(4): 389-395. doi: 10.11804/NuclPhysRev.38.2021034 |