强流加速器中束晕-混沌的延迟反馈控制

Controlling beam halo-chaos via backstepping design

“…Fang and Chen [9] proposed a set of nonlinear feedback control methods based on the mechanism of control chaos, and the measurability to variables of complex system such as the wavelet-based function feedback, [10] the sample function feedback, [11] variables delayed feedback and variable structure method. [12,13] It will be valuable and realizable in engineering application if some external parameters (for example the exterior field) can be used to control the beam halo-chaos in a high-current accelerator. [14] In this paper, the formation of beam halo-chaos in the PFCs with a raised cosine magnetic field is considered, and a magnetic field backstepping design for controlling the beam halo-chaos in the PFCs is proposed.…”

Control of beam halo-chaos by Gauss function in the triangle periodic-focusing channel

“…Therefore, the study of the beam halo-chaos becomes one of the key issues in current research projects. [7−22] Since the beam halo-chaos is a sensitive and unstable spatio-temporal chaotic motion in essential, many advanced control methods based on the chaos control strategy have been proposed to suppress the halo through many years of efforts, including nonlinear feedback method, [7−12] wavelet function method, [7−13] delay feedback control method, [14] logarithm-function control method, [18] and coupling pinning control based on complex networks. [20] Simulation results have shown that these methods are effective for controlling the halo-chaos complexity.…”

“…At present, study of controlling the beam halochaos through a rectangle periodic-focusing channel or a uniform-focusing channel has been carried out in Refs. [7][8][9][10][11][12][13][14][15][16][17][18][19], but the high intensity beam through a triangle periodic-focusing channel has not been studied. In this paper, we investigate the beam halo-chaos in the triangle periodic-focusing magnetic field, and propose the idea of Gauss function controller of strong nonlinearity and stability for controlling the halo.…”

Control of Beam Halo-Chaos by Fraction Power-Law Function in Hackle Periodic-Focusing Channel

“…If the beam is used, it is necessary to control the halo-chaos. [6−9] Since the beam halo-chaos is a sensitive and unstable spatio-temporal chaotic motion in essential, many advanced control methods based on the chaos control strategy have been proposed to suppress the halo through many years of efforts, including wavelet function method, [7−10] delay feedback control method, [11] exterior magnetic field control [12,13] and logarithm-function control method. [14] At present, study of controlling the beam halochaos through a rectangle periodic-focusing channel or an uniform-focusing channel has been carried out in Refs.…”