Time-Optimal Motion Planning and Anti-Sloshing Control for a Container Under Disturbances

Sloshing is the term for the liquid’s internal movement, which is often undesirable in technological processes. This paper aims to provide a solution for suppressing sloshing liquid in a moving cylindrical container. To prevent the negative impact of the sloshing problem, our approach is a combination of generating a desired path, robust control, and output constraints. To begin with, this research introduces a discrete model derived from a nonlinear equivalent mass-spring-damper system. Subsequently, after establishing the flatness of the approximate nonlinear model, we introduce rest-to-rest and time-optimal trajectory planning. We overcome the unmeasurable state variable and disturbance with the Linear Extended State Observer (LESO) algorithm. In addition, to address the challenge of tracking the orbital path, we suggest a control technique Terminal Sliding Mode Control (TSMC), which is well-known for its fast convergence while ensuring global stability. Moreover, to meet the constraints of a practical system, the control barrier function is applied. Lastly, the effectiveness of this control methodology is validated by comprehensive numerical simulations.