Accurate nonlinear force modeling and compensation control in hybrid active-passive zero-stiffness system

Full-physics ground testing has become an indispensable component of spacecraft development. A critical technical bottleneck lies in simulating zero-gravity conditions for vertical translational motion, which limits the effectiveness of full-degree-of-freedom ground testing systems. Current passive methods exhibit limited accuracy, while active control strategies face substantial time-delay challenges. A hybrid active-passive zero-stiffness system based on a zero-stiffness spring mechanism is proposed, which augments the conventional spring configuration by integrating a parallel linear force-compensation motor. The spring mechanism provides the primary load-bearing force, while the motor dynamically compensates for residual forces. The presence of strongly nonlinear complex error forces in this system makes precise dynamic modeling with traditional methods particularly challenging, thereby imposing significant limitations on achieving high-precision, rapid-response control. To address this, an interpretable differential neural network framework is proposed to model the system’s dynamics and identify its nonlinear complex error forces. Building on this model, a hybrid controller incorporating a nominal model feedforward term, a PID feedback term, and a learning-based feedforward component is designed. Finally, through comparative experiments, it is validated that the hybrid controller outperforms the PID-Feedforward control law, achieving improvements of at least 60.47%, 31.14%, and 82.76% in position tracking accuracy, force output accuracy, and response speed.