Feedback Linearization, Integrator Backstepping and Passivity-Based Controller Designs: A Comparison Example

Abstract

This work is dedicated to loan Landau on his 60th birthday for his continuing support in the battle for world passivation.Summary. The objective of this paper is to compare in a simple example three controller design techniques for stabilization of nonlinear systems which have emerged in the last few years: 1) Feedback linearization, which as the name says aims at achieving a linear system in closed-loop via nonlinearities cancellation, is probably the best well known and easier to understand; 2) Integrator backstepping, which is another widely publicized technique that has proven very succesful for systems with special triangular structures; 3) Passivity-based control, which has traditionally received a wide acceptance among practicioning engineers, achieves system stabilization solving an, apparently more natural, passivation problem. Application of these, seemingly unrelated, methodologies will typically lead to the definition of different control schemes. For some specific examples these differences blurr and some interesting connections and similarities between the controller design techniques emerge. The careful study of such cases will improve our understanding of their common ground fostering cross-fertilization. In this paper we investigate these questions, both analytically and via simulations, for the simple problem of stabilization of a magnetically levitated ball. Our motivation in choosing this particular example stems, not just from the fact that due to its simplicity the connections between the controllers are best revealed, but also that such an equipment is available D. Normand-Cyrot (ed.), Perspectives in Control © Springer-Verlag London Limited 1998 98 M. Torres, R. Ortega in many engineering schools, hence experimental work can be easily carried out to complement our studies.

Immersion and Invariance: A New Tool for Stabilization and Adaptive Control of Nonlinear Systems

“…Adopting the standard modeling assumptions for the electromagnetic coupling, see, e.g., [41], we obtain the model (with domain of validity )…”

“…In this case, it is possible to asymptotically stabilize the aforementioned model at any constant desired ball position via a nonlinear static state feedback derived using, for instance, feedback linearization [11], backstepping [19] or interconnection and damping assignment control [29], see also [41] for a comparative study. In medium-to-high power applications, the voltage is generated using a rectifier that includes a capacitance.…”

A state observer for sensorless control of magnetic levitation systems

“…Remark 1 Full-state feedback stabilizing controllers for Maglev systems, applying various nonlinear control techniques, are available in the literature, cf. [17,21,33]. Therefore, the main task to be solved is the observation of the systems state from the measurement of the currents I.…”

“…Since there are several full-state controllers that achieve the stabilization objective, see e.g., [17,21,33], our main contribution is the solution of the-until now openproblem of state observation that, as shown below, turns out to be significantly involved. In [37] injection of highfrequency sinusoidal probing signals in the voltage is used to generate a virtual output [7] and be able to design a PEBO for a 1-dof MagLev system.…”

Sensorless Control of the Levitated Ball

“…A. Vedyakov. facilities for them. Although many full-state feedback asymptotically stabilizing controllers are available in the literature, see e.g., Bonivento et al (2005); Levine et al (1996); Lindlau and Knospe (2002); Maslen et al (2000); Ortega et al (2013); Torres and Ortega (1998), to the best of our knowledge, no sensorless solution for the full nonlinear model has been reported. A notable exception is Yi et al (2018a) where the signal injection technique proposed in Combes et al (2016); Yi et al (2018b), is used to give a solution to this problem.…”