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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1358930, 11 pages
Research Article

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

1CIC, Instituto Politécnico Nacional, Ciudad de México, DF, Mexico
2Sección de Mecatrónica, CINVESTAV, Ciudad de México, DF, Mexico
3ESCOM, Instituto Politécnico Nacional, Ciudad de México, DF, Mexico

Received 6 May 2016; Revised 5 September 2016; Accepted 15 September 2016

Academic Editor: Alessio Merola

Copyright © 2016 Carlos Aguilar-Ibanez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction.