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Shock and Vibration
Volume 2017, Article ID 2738976, 8 pages
Research Article

Fractional Critical Damping Theory and Its Application in Active Suspension Control

1College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing 210037, China
2College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China

Correspondence should be addressed to Ning Chen; nc.moc.ufjn@gninnehc

Received 9 June 2017; Revised 8 October 2017; Accepted 23 October 2017; Published 19 November 2017

Academic Editor: Evgeny Petrov

Copyright © 2017 Peng Wang 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.


In this paper, the existence condition of critical damping in 1 DOF systems with fractional damping is presented, and the relationship between critical damping coefficient and the order of the fractional derivative is derived. It shows only when the order of fractional damping and its coefficient meet certain conditions, the system is in the critical damping case. Then the vibration characteristics of the systems with different orders located in the critical damping set are discussed. Based on the results, the classical skyhook damping control strategy is extended to the fractional one, where a switching control law is designed to obtain a more ideal control effect. Based on the principle of modal coordinate transformation, a new design method of fractional skyhook damping control for full-car suspension is given. The simulation results show that the proposed control method has a good control effect, even in some special cases, such as roads bumps.