Robust finite-time stabilizers for five-degree-of-freedom active magnetic bearing system

• Published in: Journal of the Franklin Institute 2019-01, Vol.356 (1), p.80-102
• Main Authors: Abooee, Ali, Arefi, Mohammad Mehdi
• Format: Article
• Language: English
• Subjects: Air gaps; Bearings; Computer simulation; Control theory; Degrees of freedom; Finite element analysis; Inequalities; Magnetic bearings; Magnetic fields; Nonlinear control; Robustness (mathematics); Settling; Sliding friction; Sliding mode control; Systems stability
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2018.08.026

In this paper, the robust finite-time stabilization problem for a fully suspended five-degree-of-freedom active magnetic bearing system is addressed in the presence of external disturbances and additive uncertainties. By developing the nonsingular terminal sliding mode control and defining new nonlinear sliding surfaces, three separate classes of stabilizers are proposed to regulate and place the suspended rotor in the desired positions of air gaps within adjustable finite times. The suggested nonlinear sliding surfaces and designed control inputs for each class of stabilizers are two major differences between these stabilizers. It is mathematically proven that five control voltages of this system, designed by each class of the suggested stabilizers, are able to locate the suspended rotor at the centers of air gaps in the adjustable finite time which is summation of two reaching and settling finite times. Moreover, several new inequalities are extracted for determining the reaching and settling finite times related to the three classes of stabilizers. These inequalities reveal the dependencies between optional parameters of the proposed stabilizers and the mentioned finite times. Finally, numerical simulations are provided to illustrate the efficiency and good performance of each class of the designed stabilizers.