Control laws synthesis for timed event graphs subject to generalised marking constraints by Min-Plus algebra: application to cluster tools

Abstract

This paper discusses the problem of control laws for Discrete Event Dynamic Systems (DEDSs) represented by Timed Event Graphs (TEGs) under Generalized Marking Constraints (GMCs). The behaviour of TEGs is described using linear equations while GMCs are expressed by weighted inequalities in Min-Plus algebra. We formulate the problem in terms of control linear Min-Plus models. Hence, an algebraic method to calculate control laws ensuring the respect of GMCs is suggested. And once sufficient conditions are satisfied, we propose casual feedbacks to guarantee these marking specifications. Besides, the proposed control strategy is applied to a dual-armed cluster tool, a well-known industrial application.

KEYWORDS:

• Discrete event dynamic systems
• timed event graphs
• Min-Plus algebra
• generalized marking constraints
• control laws

Disclosure statement

No potential conflict of interest was reported by the author(s).