Motion Control of a Container With Slosh: Constrained Sliding Mode Approach

A constrained sliding mode control methodology developed by the author is applied to the motion control of an open container filled with liquid. The objective is to control the position of the container to meet the performance and robustness requirements, and to specify a safe operating set, i.e., the set of initial conditions from which the system can be operated without exceeding a prescribed liquid level and additional constraints. A conventional sliding mode regulator is designed first to address nominal performance in the sliding mode. Then, a robustly invariant cylinder formed as the Cartesian product of an ellipsoid, and a closed interval is constructed using linear matrix inequalities. A set of constraint qualification conditions are evaluated to ensure that the intersection of the cylinder and the state constraints is robustly positively invariant, constituting the required operating set. Simulations and experimental results corresponding to a high-speed transfer validate the methodology.