4 research outputs found
Tracking control for an ellipsoidal submarine driven by Kirchhoff's laws
International audienceIn this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid. The dynamics of the uncontrolled body are given by Kirchhoff's laws. By adopting a backstepping viewpoint, we prove that the position and the attitude of the solid can be forced to approximatively follow any given path, using three controls (two controls for the direction and one control for the velocity). Moreover, we prove that the controlled mechanical system (which includes the momenta) is completely controllable in arbitrary small time
Constructive interconnection and damping assignment passivity-based control with applications
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.Open Acces