Constructive interconnection and damping assignment passivity-based control with applications

Abstract

Energy-based modeling and control of dynamical systems is crucial since energy is a fundamental concept in Science and Engineering theory and practice. While Interconnection and Damping Assignment Passivity-based Control (IDA-PBC) is a powerful theoretical tool to control port-controlled Hamiltonian (PCH) systems that arise from energy balancing principles, sensorless operation of energy harvesters is a promising practical solution for low-power energy generation. The thesis addresses these two problems of energy-based control and efficient energy generation. The design via IDA-PBC hinges on the solution of the so-called matching equation which is the stumbling block in making this method widely applicable. In the first part of the thesis, a constructive approach for IDA-PBC for PCH systems that circumvents the solution of the matching equation is presented. A new notion of solution for the matching equation, called algebraic solution, is introduced. This notion is instrumental for the construction of an energy function defined on an extended state-space. This yields, differently from the classical solution, a dynamic state-feedback that stabilizes a desired equilibrium point. In addition, conditions that preserve the PCH structure in the extended closed-loop system have been provided. The theory is validated on four examples: a two-dimensional nonlinear system, a magnetic levitated ball, an electrostatic microactuator and a third order food-chain system. For these systems damping structures that cannot be imposed with the standard approach are assigned. In the second part of the thesis, the design of a nonlinear observer and of an energy-based controller for sensorless operation of a rotational energy harvester is presented. A mathematical model of the harvester with its power electronic interface is developed. This model is used to design an observer that estimates the mechanical quantities from the measured electrical quantities. The gains of the observer depend on the solution of a modified Riccati equation. The estimated mechanical quantities are used in a feedback control law that sustains energy generation across a range of source rotation speeds. The proposed observer-controller scheme is assessed through simulations and experiments.