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Shock and Vibration
Volume 2017, Article ID 8340510, 14 pages
Research Article

SDRE Control Applied to the Wheel Speed of a Compressed Air Engine with Crank-Connecting-Rod Mechanism

1Sao Paulo State University, Bauru, SP, Brazil
2Federal University of Technology-Parana, Ponta Grossa, PR, Brazil
3Aeronautics Technological Institute, São José dos Campos, SP, Brazil

Correspondence should be addressed to Jose Manoel Balthazar; rb.ati@ahtlabmj

Received 6 March 2017; Revised 11 May 2017; Accepted 23 May 2017; Published 15 August 2017

Academic Editor: Mario Terzo

Copyright © 2017 Alexandre de Castro Alves 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.


Renewable energy sources for vehicles have been the motivation of many researches around the world. The reduction of fossil fuels deposits and increase of the pollution in cities bring the need of more efficient and cleaner energy sources. In this way, this work will present the application of a compressed air engine applied to a bicycle. The engine is composed of two pneumatic cylinders connected to the bicycle wheel through a crank-connecting-rod mechanism. In order to control the velocity of the bicycle, a strategy of control composed of two controls was implemented: a feedback and a feedforward control. For feedback control, the State-Dependent Riccati Equation (SDRE) control and also a proportional-derivative (PD) control are considered, considering three cases for velocity bicycle variation: 10 km/h, 20 km/h, and 30 km/h. The equations of motion of the system were obtained through the Lagrangian energy method. Numerical simulations were performed in order to analyze the dynamics of the system and the efficiency of the controllers.