Fractional Critical Damping Theory and Its Application in Active Suspension Control

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.

[1]  S. Sakakibara.  Properties of Vibration with Fractional Derivative Damping of Order 1/2. , 1997 .

[2]  Laiq Khan,et al.  Comparative Analysis of Adaptive NeuroFuzzy Control Techniques for Full Car Active Suspension System , 2014 .

[3]  Ronald L. Bagley,et al.  Power law and fractional calculus model of viscoelasticity , 1989 .

[4]  Moonyong Lee,et al.  Attitude control of full vehicle using variable stiffness suspension control , 2015 .

[5]  R. M. Bulatovic,et al.  On the critical damping in multi-degree-of-freedom systems , 2002 .

[6]  R. Lewandowski,et al.  Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model , 2015 .

[7]  M. Shitikova,et al.  Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results , 2010 .

[8]  A. Shkel,et al.  Nonresonant micromachined gyroscopes with structural mode-decoupling , 2003 .

[9]  Frank L. Lewis,et al.  Active suspension control of ground vehicle based on a full-vehicle model , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[10]  Yang Ying,et al.  Critical damping of the second-order pendulum-like systems , 2005 .

[11]  R. Bagley,et al.  On the Appearance of the Fractional Derivative in the Behavior of Real Materials , 1984 .

[12]  Peter J. Torvik,et al.  Fractional calculus in the transient analysis of viscoelastically damped structures , 1983 .

[13]  J. M. Vogel,et al.  A Review of Active Suspension Control for On and Off-Highway Vehicles , 1989 .

[14]  H. Eric Tseng,et al.  State of the art survey: active and semi-active suspension control , 2015 .

[15]  T. Caughey,et al.  Classical Normal Modes in Damped Linear Dynamic Systems , 1960 .

[16]  Sajib Roy,et al.  A modified skyhook control system (SKDT) to improve suspension control strategy of vehicles , 2014, 2014 International Conference on Informatics, Electronics & Vision (ICIEV).

[17]  Critical Damping in Certain Linear Continuous Dynamic Systems. , 1981 .

[18]  Dean Karnopp,et al.  Vibration Control Using Semi-Active Force Generators , 1974 .

[19]  Zaihua Wang,et al.  Stability of a linear oscillator with damping force of the fractional-order derivative , 2010 .

[20]  Li Yu-ling.  Full Vehicle Semi-Active Suspension Modularize Parallel Fuzzy Control , 2013 .

[21]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[22]  Pankaj Wahi,et al.  Averaging Oscillations with Small Fractional Damping and Delayed Terms , 2004 .

[23]  H. Eric Tseng,et al.  Optimisation of active suspension control inputs for improved vehicle ride performance , 2016 .

[24]  C.-M. Lee,et al.  WAVELET ANALYSIS OF VEHICLE NONSTATIONARY VIBRATION UNDER CORRELATED FOUR-WHEEL RANDOM EXCITATION , 2004 .

[25]  Dean Karnopp,et al.  Design Principles for Vibration Control Systems Using Semi-Active Dampers , 1990 .