Fractional Exponential Feedback Control for Finite-Time Stabilization and its Application in a Spin-Exchange Relaxation-Free Comagnetometer

This article is the first work to propose a series of control strategies for the longitudinal electron spin polarization of the spin-exchange relaxation-free comagnetometer system to ensure its ultrastable measurement. Two types of finite-time control strategies are presented for a nonlinear system with affine input. The first control strategy is finite-time fractional exponential feedback control (FEFC), which ensures that the trajectories of an autonomous system converge to an equilibrium state in a finite time that can be specified. The second control strategy is finite-time robust FEFC, which provides a finite-time stability of a nonautonomous system with unknown structures under disturbance and perturbations, and its upper bound of the settling time can be estimated. The theoretical results are supported by numerical simulations.

I. Introduction

The spin-exchange relaxation-free comagnetometer (SERFCM) [1], [2] is widely used in fundamental physics experiments [3], inertial rotation sensing [4], and magnetometry [5], such as searches for long-range spin-dependent forces [6], [7], and tests of CP, CPT [8], and Lorentz symmetries [9], due to its ultrahigh precision [10]. It is also crucial to be ultrastable for practical long-term measurement, and many methods have been applied to SERF systems, for example, amplitude-modulated nonlinear magneto-optical rotation [11], locking electron resonance [12], and low-noise magnetic shielding [13]. These methods can achieve good performance in specific situations, but they also have weaknesses. For example, amplitude-modulated nonlinear magneto-optical rotation is vulnerable to magnetic perturbations. Locking electron resonance is inaccurately manipulated due to the large resonance linewidth. Low-noise magnetic shielding can be used to reduce magnetic perturbations efficiently; however, it is difficult to improve further, limited by volume and material. This article is the first work to propose a series of control strategies for the longitudinal electron spin polarization of the SERFCM system that can ensure its ultrastable measurement, which overcomes the weaknesses of the other methods with the same purpose.