An optimal control method is provided to mitigate the cubic strongly nonlinear vibration of vehicle suspension with velocity and displacement feedback controllers. The forced vibration of the vehicle suspension is studied utilizing the methods of modified Lindstedt-Poincaré and multiple scales. Ranges of feedback gains that can keep the vibration system stable are worked out by the stability conditions of eigenvalue equation. Taking the decay rate and the energy function as the objective functions and the ranges of stable vibration feedback gains as constrained conditions, the optimal feedback gains of velocity and displacement are calculated by the method of minimum method. The simulation results show that the control method can have optimal control results.
GuoD. L.HuH. Y.YiJ. Q.Neural network control for a semi-active vehicle suspension with a magnetorheological damper. Journal of Vibration and Control, Vol. 10, 2004, p. 461–471.
2.
LiuH.NonamiK.HagiwaraT.Semi-active fuzzy sliding mode control of full vehicle and suspensions. Journal of Vibration and Control, Vol. 11, 2005, p. 1025–1042.
3.
LauwerysC.SweversJ.SasP.Robust linear control of an active suspension on a quarter car test-rig. Control Engineering Practice, Vol. 13, Issue 5, 2005, p. 577–586.
4.
LiS. H.YangS. P.GuoW. W.Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations. Mechanics Research Communications, Vol. 31, Issue 2, 2004, p. 229–36.
5.
ZhuQ.MitsuakiI.Chaotic vibration of a nonlinear full-vehicle model. International Journal of Solids and Structures, Vol. 43, Issue 3–4, 2005, p. 747–759.
6.
LitakG.BorowiecM.FriswellM.SzabelskiK.Chaotic vibration of a quarter-car model excited by the road surface profile. Communications in Nonlinear Science and Numerical Simulation, Vol. 13, Issue 7, 2008, p. 1373–1383.
7.
SieweSiewe M.Resonance, stability and period-doubling bifurcation of a quarter-car model excited by the road surface profile. Physics Letters A, Vol. 374, Issue 13–14, 2010, p. 1469–1476.
8.
JiJ. C.ZhangN.Suppression of the primary resonance vibrations of a forced nonlinear system using a dynamic vibration absorber. Journal of Sound and Vibration, Vol. 329, Issue 11, 2010, p. 2044–2056.
9.
NaikR. D.SingruP. M.Resonance, stability and chaotic vibration of a quarter-car vehicle model with time-delay feedback. Communications in Nonlinear Science and Numerical Simulation, Vol. 16, Issue 8, 2010, p. 3397–3410.
10.
El-GoharyH. A.El-GanainiW.A.A. Vibration suppression of a dynamical system to multi-parametric excitations via time-delay absorber. Applied Mathematical Modelling, Vol. 36, Issue 1, 2012, p. 35–45.
11.
LitakG.BorowiecM.FriswellM. I.Chaotic response of a quarter car model forced by a road profile with a stochastic component. Chaos, Solitons & Fractals, Vol. 39, Issue 5, 2009, p. 2448–2456.
12.
LiuC.H.QiuJ.H.SunH.Y.Nonlinear vibrations of beams with spring and damping delayed feedback control. Journal of vibroengineering, Vol. 15(1), 2013, p. 340–354.
13.
LiuC.RenC.LiuL.LiL.Optimal time delay control for nonlinear vibration of single walled carbon nano-tube on elastic medium. Journal of vibroengineering, Vol. 15(3), 2013, p. 1409–1418.
14.
El-LatifAbd G. M.On a problem of modified Lindstedt-Poincaer for certain strongly non-linear oscillators. Applied Mathematics and Computation, Vol. 152, 2004, p. 821–836.
15.
NayfehA. H.Perturbation Methods, Wiley, New York, 1973.
16.
LiX. Y.JiJ. C. and HansenC. H.The response of a Duffing-van der Pol oscillator under delayed feedback control. Journal of Sound and Vibration, Vol. 291, 2006, p. 644–655.
17.
JiJ.C. and LeungA.Y.T.Responses of a non-linear sdof system with two time-delays in linear feedback control. Journal of Sound and Vibration, Vol. 253, 2002, p. 985–1000.
