Optimization of linear acceltrator parameters taken into account of radial vibrations and requirements of sensitivity
DOI:
https://doi.org/10.31548/energiya2019.05.170Abstract
Abstract. The problems of optimization of the motion of charged particles with consideration of radial vibrations and sensitivity requirements for the case of relay control are considered. In the case of constraints on the control function, the initial minimization optimization problem is reduced to the problems of optimal choice of switching points (points at which the control function changes its value). For its numerical solution, an iterative gradient descent procedure is proposed. In this case, the region of the initial conditions in the phase coordinates of the particles is pre-presented in a discrete form, and the gradient of the function of the target at the switching points is determined by the sensitivity functions that characterize the rate of change of the perturbed motion relative to the calculated value of the parameter vector. For the problem of focusing particles by energy, spatial coordinate, and their velocity at the end of the accelerator, linear constraints on the sensitivity functions are considered. The algorithms of practical stability of parametric systems in the space of sensitivity functions were applied to account for the sensitivity requirements. To this end, at each iteration of the gradient descent, the set of initial conditions for the sensitivity functions is given in structural form. To solve the dimensionality problem and reduce the computation time of the sensitivity functions, we replaced the independent variable in the corresponding Cauchy problem. In this approach, the calculation of the optimal control parameters is made taking into account the possible deviations of the calculated trajectories on the real modes of operation of the studied system. An analysis of the proposed computational scheme and directions of further research on the design of low-sensitivity acceleration-focusing systems by jointly solving the problem of trajectory optimization and the problem of minimizing the maximum sensitivity over the entire range of motion of charged particles are presented.
Key words: parameters, structural-parametric optimization, practical stability, relay control, switching points, gradient, sensitivity functions
References
Muryn, B.P., Bondarev, B.Y., Fedotov, A.P. (1978). Lyneinye uskorytely yonov. – T.1: Problemy y teoryia [Linear ion accelerators. – T.1: Problems and theory]. Moscow: Atomрubl, 260.
Bublyk, B.N., Harashchenko, F.H., Kyrychenko, N.F. (1985). Strukturno-parametrycheskaia optymyzatsyia y ustoichyvost dynamyky puchkov [Structural-parametric optimization and stability of beam dynamics]. Kyiv: Scientific thought, 304.
Rosenwasser, E.N., Yusupov, R.M. (1981). Chuvstvytelnost system upravlenyia [Sensitivity of control systems]. Moscow: Science, 464.
Harashchenko, F.H., Pantalienko, L.A. (1995). Analiz ta otsinka parametrychnykh system [Analysis and evaluation of parametric systems]. Kyiv: 140.
Harashchenko, F.H., Pichkur, V.V. (2014) Prykladni zadachi teorii stiikosti [Applied problems of stability theory]. Kyiv: Kyiv University,125.
Pantaliienko, L.A. (2015). Nedyferentsiiovni zadachi optymizatsii chutlyvosti dynamichnykh system [Undifferentiated problems of optimization the sensitivity of dynamical systems]. Scientific Journal NUBaN Ukraine. A series of «Technology and Energy AIC», 224, 239−243.
Pantaliienko, L.A. (2014). Doslidzhennya zadach obmezhenoyi chutlyvosti metodamy praktychnoyi stiykosti [Investigation of the problems of limited sensitivity by methods of practical stability]. Scientific Journal NUBaN Ukraine. A series of «Technology and Energy AIC», 194(2), 243−248.
Downloads
Published
Issue
Section
License
Relationship between right holders and users shall be governed by the terms of the license Creative Commons Attribution – non-commercial – Distribution On Same Conditions 4.0 international (CC BY-NC-SA 4.0):https://creativecommons.org/licenses/by-nc-sa/4.0/deed.uk
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
