Hybrid systems modelling and control using multiple mixed logical dynamical predictive model control: Application to a three-tank spherical system

Abstract

This study employs the mixed logical dynamical (MLD) framework for modelling, simulating, and controlling hybrid dynamical systems. Hybrid systems, which combine continuous-time dynamics and discrete logical events, pose significant challenges for conventional control strategies, such as proportional-integral-derivative (PID) controllers, particularly under complex operational constraints. To address these challenges, the MLD formalism provides a unified representation that integrates differential equations, logical rules, and inequality constraints. Based on the MLD model, a multivariable hybrid model predictive control (HMPC) approach is designed to optimize control system performance and operational efficiency over a prediction time horizon. At each sampling time step, a mixed quadratic programming (MIQP) optimization problem is solved online to determine the control law. The proposed control approach is applied to a three-spherical tank system, where simulation and experimental results demonstrate its effectiveness in ensuring stability, minimizing tracking errors, and satisfying physical constraints. These results underscore the relevance of MLD-based predictive control approaches for the optimization and advanced control of complex multivariable hybrid dynamical systems in industrial fields.