Jose Guadalupe Romero

Romeo Ortega, Bowen Yi, Jose Guadalupe Romero et al.

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.

Jose Guadalupe Romero, Romeo Ortega

A globally exponentially stable speed observer for mechanical systems was recently reported in the literature, under the assumptions of known (or no) Coulomb friction and no disturbances. In this note we propose and adaptive version of this observer, which is robust vis--a--vis constant disturbances. Moreover, we propose a new globally convergent speed observer that, besides rejecting the disturbances, estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples.

Alexey Bobtsov, Jose Guadalupe Romero, Romeo Ortega et al.

In this paper we present a radically new approach to design state observers for nonlinear systems, with particular emphasis on physical ones. Our objective is to obtain an algebraic relation between the unmeasurable part of the state and filtered versions of the systems inputs and outputs, which holds true for all $t \geq 0$. The latter qualifier should be contrasted with the usual asymptotic (or fixed/finite time) objective. The standing assumption for our design is the availability -- or possibility of constructing, via coordinate change -- state components with measurable derivatives. In the physical systems studied in the paper this condition is naturally satisfied. The next step in the design is the application of the Swapping Lemma to pull out from the dynamics the derivative of one of these signals. The design is completed replacing the latter by the measurable signals and arranging the remaining terms. The algebraic observer constitutes a refreshing major departure from classical asymptotic observer designs, even in the case of electrical motors and mechanical systems that have been exhaustively studied. Particularly notable is the fact that no observability or excitation condition is imposed for the construction of the algebraic observer.

Alejandro Donaire, Romeo Ortega, Jose Guadalupe Romero

To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to [1], it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by [2], we propose to consider the inclusion of generalised forces, going beyond the gyroscopic ones used in standard IDA-PBC. It is shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.