forces/torques, uncertainties in electromagnetic modeling, satellite inertia moments, the effects of Earth's magnetic field on electromagnetic satellites, and the exacting demands for precise control required by space missions with satellite formations. Initial research into the complexities and foundational aspects of EMFF was undertaken by the MIT Space Systems Laboratory and the University of Tokyo. [PERSON] explored an EMFF system comprising two spacecraft, each equipped with three orthogonal electromagnets and reaction wheels [7]. They elucidated the nonlinear dynamics of the EMFF system, delineated its linear dynamics, and devised a linear controller. [PERSON]'s research delved into the nonlinear translational dynamics of EMFF reconfiguration, anchored in in/out-of-plane angles and relative distance [8]. Utilizing analytical mechanics theory, they formulated a nonlinear translational dynamics model and proposed a linear feedback control approach based on optimal control theory and the Gauss pseudospectral method. [PERSON] examined the deployment of adaptive control laws within linear dynamics, proposing a control allocation strategy for angular momentum management [9]. Later studies predominantly focused on decoupling and frequency multiplexing applications. [PERSON] suggested combining frequency multiplexing with an adaptive sliding mode controller, informed by learning algorithms, to manage the relative positioning of satellites [10]. [PERSON] employed sinusoidal and steady electromagnetic fields to regulate the relative positioning and to mitigate the accumulation of angular momentum caused by the Earth's magnetic field [11]. [PERSON] innovated a new frequency multiplexing technique, facilitating simultaneous control of both force and torque [12]. Obviously, prevailing research in the realm of EMFF is predominantly centered on control strategies derived from linear error dynamics, with a notable scarcity of studies directly implementing nonlinear controllers founded on nonlinear dynamics. A variety of modeling strategies are crucial for handling the relative translational dynamics in EMFF, particularly because of the internal force nature attributed to electromagnetic forces. In fact, [PERSON]'s work has substantiated that, for the modeling of complex systems, analyzing the system from the perspectives of energy and constraints offers substantial advantages [7]. Additionally, given the system's strong coupling and nonlinearity, the complexity of the model and the control challenges notably escalate when formations include more than two satellites. Consequently, researchers typically commence with studies on electromagnetic force control in two-satellite systems. In this research, a unique input-state-output port-Hamiltonian (pH) system technique is utilized to construct an accurate nonlinear dynamic model for a two-satellite EMFF and to directly develop a corresponding control law. The pH system, an extension of Hamiltonian systems, accommodates inputs and dissipation, referred to as 'ports.' This methodology facilitates the modeling and analysis of intricate physical systems and their interconnections, thereby harmonizing the processes of modeling and control [13]. Owing to its reliance on energy methods, the pH dynamic model effectively preserves nonlinearities without enforcing specific distance constraints between satellites, enhancing model accuracy. External disturbances, uncertainty in the inertia matrices, and coupled nonlinear elements represent the uncertain factors in the satellite attitude and orbit control systems [14]. Moreover, it is crucial to address uncertainties in the electromagnetic modeling and actuator saturation within EMFF studies. Attaining high-precision formation control performance amidst these complexities presents a significant challenge. Various scholars have delved into control methodologies for EMFF, exploring adaptive control [9; 15], sliding mode control [8; 16], linear quadratic regulation (LQR) control [17; 18], and robust suboptimal control [19].