Decoupled Online Q-Learning Design for MIMO Active Magnetic Compensation Systems

The inherent cross-coupling phenomenon in three-input three-output active magnetic compensation (AMC) systems employing multi-axial coil configurations hinders precise system characterization and complicates decoupling control strategies, ultimately leading to a reduction in overall compensation performance. To solve this problem, this paper presents a decoupled online Q-learning linear quadratic regulator (LQR) framework for AMC systems. Initially, Q-learning-based online optimization of LQR parameters is employed to achieve model-free control that adapts to environmental variations. Secondly, the proposed framework innovatively extends conventional Q-learning through two principal technical contributions specifically targeting coupling challenges: a novel coupling-aware interaction matrix that effectively characterizes multi-axis dynamic interactions through a priori coupling channel perception, and a decoupling-oriented policy optimization module that adaptively coordinates multi-input control efforts through gradient-based temporal difference updates. Finally, the stability of the proposed decoupled Q-learning algorithm, derived from the aforementioned innovations, is rigorously demonstrated through Lyapunov stability analysis, thereby ensuring theoretical convergence guarantees for the decoupled control system. Experimental results demonstrate that this algorithm achieves three-axis control without requiring precise system models. Compared to the conventional Q-learning and the feedforward decoupling control scheme integrated with proportional-integral-derivative (PID) controllers, it demonstrates significant attenuation of magnetic field variations, yielding a stabilized remnant field configuration.