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Mathematical Problems in Engineering
Volume 2013, Article ID 173051, 9 pages
Research Article

Proportional Derivative Control with Inverse Dead-Zone for Pendulum Systems

Sección de Estudios de Posgrado e Investigación, ESIME Azcapotzalco, Instituto Politécnico Nacional, Avenida de las Granjas No. 682, Colonia Santa Catarina, 02250 México, DF, Mexico

Received 11 July 2013; Revised 30 August 2013; Accepted 2 September 2013

Academic Editor: Zidong Wang

Copyright © 2013 José de Jesús Rubio 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.


A proportional derivative controller with inverse dead-zone is proposed for the control of pendulum systems. The proposed method has the characteristic that the inverse dead-zone is cancelled with the pendulum dead-zone. Asymptotic stability of the proposed technique is guaranteed by the Lyapunov analysis. Simulations of two pendulum systems show the effectiveness of the proposed technique.