Optimal control and parameters design for the fractional-order vehicle suspension system

In this paper the optimal control and parameters design of fractional-order vehicle suspension system are researched, where the system is described by fractional-order differential equation. The linear quadratic optimal state regulator is designed based on optimal control theory, which is applied to get the optimal control force of the active fractional-order suspension system. A stiffness-damping system is added to the passive fractional-order suspension system. Based on the criteria, i.e. the force arising from the accessional stiffness-damping system should be as close as possible to the optimal control force of the active fractional-order suspension system, the parameters of the optimized passive fractional-order suspension system are obtained by least square algorithm. An Oustaloup filter algorithm is adopted to simulate the fractional-order derivatives. Then, the simulation models of the three kinds of fractional-order suspension systems are developed respectively. The simulation results indicate that the active and optimized passive fractional-order suspension systems both reduce the value of vehicle body vertical acceleration and improve the ride comfort compared with the passive fractional-order suspension system, whenever the vehicle is running on a sinusoidal surface or random surface.

[1]  Xavier Moreau,et al.  Principles and Synthesis of Hydractive CRONE Suspension , 2004 .

[2]  F. Mainardi,et al.  Recent history of fractional calculus , 2011 .

[3]  Bingsan Chen,et al.  Fractional modeling and analysis of coupled MR damping system , 2016, IEEE/CAA Journal of Automatica Sinica.

[4]  Shaopu Yang,et al.  Primary resonance of Duffing oscillator with fractional-order derivative , 2012 .

[5]  Xavier Moreau,et al.  Study of the effects of structural uncertainties on a fractional system of the first kind – application in vibration isolation with the CRONE suspension , 2012, Signal, Image and Video Processing.

[6]  O. Sename,et al.  Survey and performance evaluation on some automotive semi-active suspension control methods: A comparative study on a single-corner model , 2012, Annu. Rev. Control..

[7]  Weiqiu Zhu,et al.  Stochastic dynamics and fractional optimal control of quasi integrable Hamiltonian systems with fractional derivative damping , 2012 .

[8]  Xavier Moreau,et al.  The CRONE Suspension: Management of the Dilemma Comfort-Road Holding , 2004 .

[9]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[10]  Hao You,et al.  Optimal design for fractional-order active isolation system , 2015 .

[11]  Delfim F. M. Torres,et al.  Numerical approximations of fractional derivatives with applications , 2012, 1208.2588.

[12]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[13]  Clovis Francis,et al.  Study of the inertial effect and the nonlinearities of the CRONE suspension based on the hydropneumatic technology , 2011 .

[14]  Michael C. Constantinou,et al.  Fractional‐Derivative Maxwell Model for Viscous Dampers , 1991 .

[15]  Teodor M. Atanackovic,et al.  On a numerical scheme for solving differential equations of fractional order , 2008 .

[16]  Shen Yongjun,et al.  Research on the Application of Optimal Control Theory on Parameters Optimization of Vehicle Suspension , 2003 .

[17]  B. Onaral,et al.  Fractal system as represented by singularity function , 1992 .

[18]  Xavier Moreau,et al.  The CRONE Suspension , 1996 .

[19]  A. Gemant,et al.  A Method of Analyzing Experimental Results Obtained from Elasto‐Viscous Bodies , 1936 .

[20]  Xavier Moreau,et al.  Effect of Hydropneumatic Components Nonlinearities on the CRONE Suspension , 2012, IEEE Transactions on Vehicular Technology.