In this paper, a model-based control algorithm is developed for a solenoid-valve system. The electric-driven machinery system and its sophisticated control give high levels of automation on huge systems such as ships and submarines. It is known that the characteristics between the force versus displacement and fluid dynamics are strongly nonlinear. The system has uncertainties in multiple parameters in the model, which make the system difficult to adjust to the environment and consequently require adaptation for sustainability and capability. The novelty of this research is that the uncertain nonlinear dynamics of the solenoid-valve system is simplified by formulating in dimensionless form. The non-dimensional control approach of the unknown bounded parameters which is approximately twenty parameter groups used in general adaptive control of the solenoid-butterfly valve system dramatically reduced to just four lumped parameter groups. The control objective is to the set-point of the solenoid-valve and accordingly control the angle position of the butterfly valve in spite of the complications presented by the uncertainties in the dynamic model. The estimated parameters are updated by the adaptation laws using the projection algorithm. After combining the translational and rotational dynamic models, the control input is designed by substituting the electric signal such as current from the model of electromagnetic force. Error signals of the trajectory tracking are developed for the solenoid-valve system. A closed-loop stable controller is designed based on the above error dynamics of the nonlinear solenoid-valve system utilizing Lyapunov-type stability which yields a stable result while obtaining the set-point objective.