Energy shaping control methods for mechanical and electromechanical systems

This thesis proposes control approaches addressing both set-point regulation and trajectory-tracking problems for physical systems while tackling specific implementation and design-oriented issues. These approaches are rooted in energy-shaping techniques developed within the port-Hamiltonian (pH) framework. The pH systems theory provides an energy-based framework for modeling, analysis, and control design for nonlinear dynamical systems belonging to
different physical domains, such as mechanical, electrical, and electromechanical. This framework offers a systematic and unified approach for modeling and control while preserving the physical interpretation of the system. Using the pH framework, this thesis employs the notions of contractive systems and dynamic extensions to develop energy-shaping control approaches for mechanical, electromechanical, and networked systems.

In Chapter ref{chapter:RWmethods}, we
provide trajectory tracking and regulation control approaches for classes of fully and underactuated mechanical systems formulated within the pH systems. These methods are designed to avoid
implementation-oriented issues, such as the lack of velocity sensors and the
presence of constant disturbances. They ensure exponential stability properties without employing coordinate transformations.

Chapter ref{chapter:SEM methods} studies tracking and set-point regulation problems for strongly coupled electromechanical systems, such as motor applications, modeled within the pH framework. Employing a contraction-based control method, we propose a control approach without the need to solve PDEs or employ any change of coordinates.

Chapter ref{chapter:EMW method} suggests a unified pH framework for controlling weakly coupled electromechanical systems. According to this model, constructive control design strategies are proposed to solve the set-point stabilization problems for specific classes of weakly coupled electromechanical systems. These methods are static and
do not require solving PDEs or changing the coordinates, thereby easing their implementation. Moreover, the weak coupling between subsystems can be considered a design-oriented issue in weakly-coupled electromechanical systems. To solve this problem,
we introduce the concept of coupled damping in electromechanical systems
and discuss its potential to enhance the performance of the transient response and convergence rate.

In Chapter ref{chapter:formation}, we propose a distributed controller that simultaneously solves the formation stabilization and trajectory-tracking problems for large-scale networks of mechanical systems. To this end, the agents are modeled as pH systems to develop a distributed tracking
formation law through a leader-follower architecture. Moreover, we introduce the concept of scalable asymptotic stability (SAS) for networked systems, which ensures the scalability of the network with respect to
the network size. By providing a 2-dimensional perspective of the network through the PDE
approximate model of the closed-loop system, we investigate the SAS property of the networked system.
Hence, the approaches presented in this thesis provide more realistic controllers by integrating energy-shaping methods and addressing both implementation and design-oriented challenges using pH systems.