Dissipativity-based control of nonlinear systems : application to stabilization and power factor compensation of electrical systems

This dissertation is concernedwith the theoretical development of nonlinear controlmethods for physical systems from a power–based perspective, with application to the stabilization of nonlinear physical systems and power factor compensation of electrical systems. In the first part of the thesis, we dealwith the stabilization problemof nonlinear physical systems, putting forth the system’s energy and power properties as a new building block for controller design and stability analysis. We revisit the dissipation obstacle of the widely appreciated method of energy balancing and propose some alternatives to overcome this obstacle, which include the proof of passivity for a class of nonlinear incremental models and an extension to general nonlinear systems, of the power shaping methodology originally introduced for electrical circuits. Concerning electric energy processing systems, themain contribution is the proof that a certain cyclo–dissipativity property of the compensated circuit is necessary and sufficient for PF improvement. This important observation suggests an analysis and compensator design framework based on cyclo–dissipativity, which is a natural alternative candidate to replace (standard) dissipativity for applications where we are interested in inducing periodic orbits, instead of stabilizing equilibria