Hybrid dynamical system approaches for power converter systems and electric drives

The modeling and control of dynamical systems are fundamental objectives in the field of control engineering. When approaching the problem of controlling physical or digital systems, dynamical models have historically been categorized into two types: continuous-time models, which are modeled by differential equations, and discrete-time models, which are modeled by difference equations. However, many real-world systems involve both continuous evolution and discrete events, requiring a more general framework. In recent years, a new class of models, known as hybrid dynamical systems, has gained significant attention in the control field thanks to its versatile modeling framework, which combines continuous-time dynamics with discrete-time evolution. This hybrid framework allows for the description of a broader class of systems and enables the development of more flexible and effective control strategies compared to traditional continuous-time approaches. This thesis explores both the theoretical foundations and practical implementations of hybrid control strategies, with a specific focus on power electronic and electrical drives. The thesis is organized into three main parts. The first part of the work develops the theoretical background and is divided into two sections. The first section introduces the modeling framework of hybrid dynamical systems, discussing solution concepts, stability analysis, and relevant applications. The second section focuses on switched systems, presenting their classification, stability properties, and interconnections with hybrid systems. Moreover, the concept of dynamic allocation is introduced as a flexible control principle that enables adaptive distribution of control inputs or energy resources among multiple subsystems, enhancing performance and robustness in hybrid architectures. In contrast to a static allocation scheme, where the control inputs or energy resources are distributed according to predefined rules, dynamic allocation represents an adaptive mechanism capable of continuously reallocating the control effort in response to variations in system states, external perturbations, and performance objectives. This mechanism enables the controller to leverage structural redundancies and inherent system flexibilities, enhancing system robustness, stability, and overall performance under time-varying operating conditions. Within the framework of hybrid dynamical systems, dynamic allocation can be interpreted as a hierarchical coordination mechanism that integrates continuous control actions with discrete switching events, ensuring a consistent interaction among interconnected subsystems. Its application to power electronic architectures, such as multi-input converters and multi-phase electrical drives, provides a rigorous framework for optimal energy management, loss minimization, and fault-tolerant operation, thus improving overall system efficiency and reliability. The second part of the thesis is application-oriented, focusing on power electronic converters. This part is structured into three main sections, reflecting the energy flow in a typical power conversion system. The first section addresses the hybrid control of a DC-DC boost converter using a min-type strategy, aiming at efficient voltage regulation and robust dynamic performance. The second section focuses on multi-input converters and their role in microgrid integration, where a dynamic input allocation strategy is developed to manage multiple power sources while ensuring robust voltage control and decoupled current regulation without degrading overall system performance. The third section is dedicated to the DC/AC conversion stage, where an advanced nonlinear hybrid controller is designed for a differential boost inverter, integrating active disturbance compensation and a sliding mode component to enhance robustness and power quality. The third part of the thesis extends the proposed methodologies to electrical drives, highlighting their role as key end-users of power electronic conversion. This part is also structured into three main sections. The first section investigates robust nonlinear control for induction motors with adaptive disturbance compensation. The second section focuses on harmonic losses minimization in dual three-phase induction motors through dynamic input allocation. The third section presents sensorless control of a permanent magnet synchronous motor for energy recovery in automotive applications, comparing Kalman filters and MRAS observer approaches. The proposed control strategies are validated through rigorous mathematical analysis and robust Lyapunov-based stability proofs. The application problem is examined from a theoretical perspective, with the study concluding through numerical results obtained from simulations or experiments.