Minimum-time feedforward control of an open liquid container

The paper considers a minimum-time feedforward motion control problem for an open container carrying a liquid. The proposed solution is a time-continuous acceleration planning that avoids liquid spilling and satisfies amplitude constraints on jerk, acceleration, and velocity of the container moving on a linear guide of an automation line. This solution is based on linear programming and can provide rest-to-rest liquid motion planning or, alternatively, a rest-to-disequilibrium planning with bounded post-motion liquid oscillations. Experimental results on a test bench prototype show the effectiveness of the presented approach.