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In this note we study the generation of non‐trivial oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, that is, a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model loses its Euler–Lagrange structure after the collocated pre‐feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and the model class identified in the article is characterized via some easily a priori verifiable assumptions on the inertia matrix and the potential energy function. [ABSTRACT FROM AUTHOR]

Summary: This article aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that it is possible to adapt the immersion and invariance technique to design static state‐feedback controllers that solve this problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels. [ABSTRACT FROM AUTHOR]

Summary: In this article we propose an energy pumping‐and‐damping technique to regulate nonholonomic systems described by kinematic models. The controller design follows the widely popular interconnection and damping assignment passivity‐based methodology, with the free matrices partially structured. Two asymptotic regulation objectives are considered: drive to zero the state or drive the systems total energy to a desired constant value. In both cases, the control laws are smooth, time‐invariant, state‐feedbacks. For the nonholonomic integrator we give an almost global solution for both problems, with the objectives ensured for all system initial conditions starting outside a set that has zero Lebesgue measure and is nowhere dense. For the general case of higher order nonholonomic systems in chained form, a local convergence result is given. Simulation results comparing the performance of the proposed controller with other existing designs are also provided. [ABSTRACT FROM AUTHOR]

Several heuristic procedures to estimate the rotor position of interior permanent magnet synchronous motors (IPMSM) via signal injection have been reported in the application literature, and are widely used in practice. These methods, based on the use of linear time-invariant (LTI) high-pass/low-pass filtering, are instrumental for the development of sensorless controllers. To the best of authors' knowledge, no theoretical analysis of these methods has been carried out. The objectives of this note are (i) to invoke some recent work on the application of averaging techniques for injection-based observer design to develop a theoretical framework to analyse the LTI filtering used in sensorless methods and (ii) to propose a new method that on the one hand ensures improved accuracy and on the other hand can be related to the current filtering technique. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments on an IPMSM platform driven by a 521 V DC bus with a 5-kHz pulse-width modulation. [ABSTRACT FROM AUTHOR]

Summary: 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 by means of some classical mechanical engineering and power electronics examples. [ABSTRACT FROM AUTHOR]