Modelagem baseada em grafos para sistemas de controle descritos por espaços de estados

Abstract

In this work, a graph-based method is proposed to represent control systems described by state spaces. For this purpose, it is described the study of graph topological structures, which qualify and quantify the relations of several elements of a set, associating with the modern control theory, which models systems in the time domain with multiple variables through the state space method, to finally treat through a proposal for digital modeling the difficulty of representing controlled systems in terms of complexity of implementation, adaptability of the system and also possible constructive problems of equipment and prototypes used. The results present the case study analysis of a control process represented in graph form, and the concepts of modern control over graph representation. Also presented are comparative results of the LQR, Linear Quadratic Regulator, and PI, Proportional Integral controller, compared to the proposed control on the graph representation. The comparisons use metrics for evaluating control variance, absolute and quadratic errors, and determining controllability, observability, and stability. It is concluded that the graph analysis and control method is capable of representing the dynamics of a system described in state space, making it possible to apply modern control concepts. The results obtained using a granularity of 5 subspaces in the phase space showed improvement in the control energy evaluations and worsening in the evaluation of reference follow-ups.