From the Preface:
In chapter 1 the main theory regarding the nonlinear output regulation is briefly recalled. The design of a suitable control law to impose a prescribed steady state response to every external command in a prescribed family is investigated. Both the problem of having the output of a controlled plant asymptotically rejecting any undesired disturbance in a certain class (regulation and disturbance suppression problem) either the problem of having the output of a controlled plant asymptotically tracking any prescribed reference signal in a given family (tracking problem) are taken into account and the main result stating necessary and sufficient conditions in order to solve these problems is presented. Furthermore the extension of the well known internal model principle for nonlinear systems is introduced.
In chapter 2 some results dealing with the robust regulation for magnetic levitation systems are presented. Main characteristic of this kind of systems are presented and in the following a robust regulation problem is stated: positioning a levitating mass moving subject to the force of gravity, to a magnetic force and to an external disturbance force to be rejected.
The design procedure is developed for two different set-up: firstly the case in which only one magnetic force generated by a coil circuit is available in order to control the movement of the mass and, later, the design procedure just introduced is extended considering the presence of two active magnetic forces to move the controlled object within the magnetic coil. The request of sophisticated control techniques due to the highly nonlinear force/current/airgap relationship characteristic of magnetic suspensions is considered and, as the problem is cast as a nonlinear regulation problem, an internal model based regulator able to offset the external disturbance force in spite of the presence of unknown parameters affecting the model of the system is designed. The controller is moreover designed using nested saturation functions and is able to provide a global region of attraction.
In chapter 3 the port-Hamiltonian formalism is briefly introduced and it is pointed out how it is possible to take high advantage of the stabilization design concepts and powerful properties characteristic of these class of systems in order to elegantly solve some nonlinear regulation and tracking problems. The main idea presented is in fact to extend the "classical" nonlinear output regulation theory in the port-Hamiltonian framework: we will show how to design a port-Hamiltonian internal model unit and how the powerful passivity based energy shaping stabilization methodology could be used in order to design the stabilization unit which, coupled with the internal model unit, will be used to solve regulation and tracking problems. In particular some different problems are considered: firstly an output regulation problem for a particular class of port- Hamiltonian system is taken into account and solved globally, introducing in the meantime the concept of port-Hamiltonian internal model. Some different problems of input disturbance suppression for electromechanical and mechanical systems (e.g. permanent magnet synchronous motor, n-dof robotic manipulator) are in the following investigated, and, finally, an exogenous trajectory tracking problem for a mechanical system is considered and a nice and elegant solution based on port-Hamiltonian internal model approach is pointed out.
In appendix A all main definitions and results regarding the basic stability analysis of dynamical nonlinear systems, largely used during the mathematical development of this thesis, are briefly presented.