A look at self-balancing manufacturing lines through theory of hybrid dynamical systems

The "bucket brigades" belong to a particular class of manufacturing lines governed by some typical rules that ensure their self-balancing. Such lines can be configured to be spontaneously and maximally productive and to autonomously maintain their steady optimal production rate. It is said that these lines behave stationary at balancing themselves. Due to this property, the design of such lines avoids the difficulty of solving the classical assembly line balancing problem. In this paper it is presented a systemic approach of the self-balancing manufacturing lines. In a previous work of Bratcu et al. (1999) simulation has shown that their state trajectories are piecewise continuous in between occurrences of certain discrete events. That is why such lines may be modeled as hybrid dynamical systems with autonomous switching and autonomous impulses (jumps). In this frame, an analysis of stability is also proposed. A sufficient condition to reach the stationary periodical behavior is proved.