Ignacio Villalobos Aguilera - Academia.edu (original) (raw)

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Papers by Ignacio Villalobos Aguilera

Irreversible Hamiltonian Port Systems (IPHS) are an extension of the classic Port Hamiltonian Sys... more Irreversible Hamiltonian Port Systems (IPHS) are an extension of the classic Port Hamiltonian System (PHS) Formulation. Like PHS systems, this form of modeling allows the representation of a large number of multiphysical systems, with the ability to represent each physical system as a block capable of connecting with the others through energy functions. Unlike a PHS system, IPHS represent in their structure not only the first principle of thermodynamics (energy conservation) but also the second thermodynamic principle (the irreversible creation of entropy). Therefore, this representation allows not only the modeling of electromechanical systems but also allows to represent thermodynamic systems and, in general, systems with irreversible processes. This formalism provides. as in the case of PHS, a theoretical framework for the control of multiphysical systems. Passive and non-linear control techniques have proven to be useful in controlling PHS systems. These techniques aim to modify the energy function of the system such that the resulting energy function is a candidate for a Lyapunov function, and has a strict minimum energy at a desired equilibrium point. This form of control ensures stabilization of the system at a desired equilibrium point, along with asymptotic stability of the system. Within these passive control techniques, control by interconnection and energy shaping have been used to change the natural equilibrium point of a Lyapunov candidate energy function in PHS; the existence and use of the Casimir functions are, therefore, fundamental for this purpose since these functions are structural invariants of the system. Although the stability of the system is guaranteed by the energy-Casimir control, the additional incorporation of damping, through the passive input of the system, ensures that the system is asymptotically stable at the desired point. The main objective of this thesis is to extend the passive and non-linear control techniques used for PHS to the control of IPHS. Precisely, a systematic design method control for IPHS is proposed, based on control by interconnection techniques and damping injection. For this, an IPHS controller structure is proposed as an interconnection with the system, and conditions are derived for the existence of structural invariants that allow changing the equilibrium point. In the design process, the concept of availability function is of great importance for the design of the energy function. This function turns out to be a candidate for a Lyapunov function for irreversible systems. The result is a systematic design method, using classical passive control techniques such as control by interconnection and energy shaping, along with Casimir structural invariants, and energy availability functions to synthesize a controller that stabilizes the IPHS system in a specified dynamic equilibrium, and that is asymptotically stable. Finally, simulations are performed using systems with irreversible-reversible processes.

Irreversible Hamiltonian Port Systems (IPHS) are an extension of the classic Port Hamiltonian Sys... more Irreversible Hamiltonian Port Systems (IPHS) are an extension of the classic Port Hamiltonian System (PHS) Formulation. Like PHS systems, this form of modeling allows the representation of a large number of multiphysical systems, with the ability to represent each physical system as a block capable of connecting with the others through energy functions. Unlike a PHS system, IPHS represent in their structure not only the first principle of thermodynamics (energy conservation) but also the second thermodynamic principle (the irreversible creation of entropy). Therefore, this representation allows not only the modeling of electromechanical systems but also allows to represent thermodynamic systems and, in general, systems with irreversible processes. This formalism provides. as in the case of PHS, a theoretical framework for the control of multiphysical systems. Passive and non-linear control techniques have proven to be useful in controlling PHS systems. These techniques aim to modify the energy function of the system such that the resulting energy function is a candidate for a Lyapunov function, and has a strict minimum energy at a desired equilibrium point. This form of control ensures stabilization of the system at a desired equilibrium point, along with asymptotic stability of the system. Within these passive control techniques, control by interconnection and energy shaping have been used to change the natural equilibrium point of a Lyapunov candidate energy function in PHS; the existence and use of the Casimir functions are, therefore, fundamental for this purpose since these functions are structural invariants of the system. Although the stability of the system is guaranteed by the energy-Casimir control, the additional incorporation of damping, through the passive input of the system, ensures that the system is asymptotically stable at the desired point. The main objective of this thesis is to extend the passive and non-linear control techniques used for PHS to the control of IPHS. Precisely, a systematic design method control for IPHS is proposed, based on control by interconnection techniques and damping injection. For this, an IPHS controller structure is proposed as an interconnection with the system, and conditions are derived for the existence of structural invariants that allow changing the equilibrium point. In the design process, the concept of availability function is of great importance for the design of the energy function. This function turns out to be a candidate for a Lyapunov function for irreversible systems. The result is a systematic design method, using classical passive control techniques such as control by interconnection and energy shaping, along with Casimir structural invariants, and energy availability functions to synthesize a controller that stabilizes the IPHS system in a specified dynamic equilibrium, and that is asymptotically stable. Finally, simulations are performed using systems with irreversible-reversible processes.