• Citer

Optimal Architectures for Mechatronic System Design: A Pole-Zero Distance Approach

par Piron, Dimitri
Président du jury Hendrick, Patrick
Promoteur Deraemaeker, Arnaud ;Collette, Christophe
Publication Non publié, 2025-09-10

Thèse de doctorat

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

The proper positioning of transducers in active damping of structures is fundamentally important. Their placement directly influences several critical aspects: closed-loop stability, overall performance and the robustness of the system with respect to uncertainties (inaccuracies of the model, ageing of the transducers, misplacement). The importance of this placement concern is reflected by the numerous optimal placement criteria developed over the past decades. Depending on the application, the different criteria provide a cost function that determines the most effective transducer locations. However, identifying the optimal positions based on those criteria necessitates the use of search algorithms, as evaluating the cost function across all possible configurations is infeasible. Among the available methods, genetic algorithms (also called evolutionary algorithms) represent an attractive solution as they do not require prior knowledge and are capable of identifying the global optimum even in the presence of numerous local ones. Nonetheless, these algorithms typically require an extensive number of evaluations to converge towards a solution. Because of the possible prohibitive convergence duration, optimization of large and/or complex structures are not commonly implemented.This doctoral thesis investigates the potential of replacing the genetic algorithms by non-evolutionary ones, reducing consequently the computational effort required to obtain the optimal placement of transducers. In this regard, a new pole-zero distance criterion is introduced for single-input-single-output (SISO) systems, as well as for multiple-input-multiple- outputs (MIMO) ones. This criterion is based on the maximization of the pole-zero distance of the mode(s) to be damped, which has a direct link with the maximum achievable damping ratio once in closed-loop. Such well-established link in SISO system is extended and experimentally demonstrated for MIMO ones.It is shown that this pole-zero distance criterion allows the extraction, based on a limited number of evaluations, of a configuration that exhibits high damping and strong robustness. It consequently provides a suitable starting position for a non-evolutionary algorithm, which converges extremely fast compared to the genetic ones. This new method is applied to multiple examples, including industrial structures. Its effectiveness is numerically demonstrated in terms of computational effort required to find the solution, as well as the performance and robustness of the optimal position. Finally, the reliability of numerical models is discussed, and some recommendations are provided to reduce potential inaccuracies.