Nonlinear Stochastic Optimal Control Of Automobile Suspension System Using MR Damper

According to the nonlinear stochastic optimal control theory, this thesisdesigned a new smart car semi-active suspension control system which was based ona magnetorheological damper device. The simulation showed that this newsuspension control system can not only greatly attenuated the structural vibrationwhich caused by the ground roughness and uneven tire, but also significantlyimproved the vehicle’s riding comfort and safety.Firstly, this Thesis analyzed the magnetorheological fluids inherent stronglynonlinear output characteristics and the principle of magneto-rheological damper.Based on the Bouc-Wen magnetorheological damper mathematical correction model,which had fewer parameters and higher accuracy, was widely recognized all over theworld, the decomposition of the hysteretic force potential energy and dissipationenergy were accomplished. The final expression of the potential energy of thedamper was obtained, which provided a basis for the establishment of the Hamiltonenergy equation below.Then based on the consideration of the harmful effect bought by the roadroughness and the uneven tire, a model of the vehicle suspension system wasestablished. This system regarded the external incentive as a Gauss white noise,and used the dissipation quasi-Hamilton system with the stochastic parametricexcitation to approximate describe the random vibration of the suspension dynamics.The averaging stochastic differential equation which dominated the randomvibration process was worked out by applying the stochastic averaging principle.The thesis was further based on the average stochastic differential equationfrom the top of that, the probability of uncontrolled system’s local asymptoticstability constraints by solving the largest Lyapunov exponent was obtained; and byanalyzing the features of the dynamics average diffusion process’s boundary classesof the random vibration of suspension, two necessary conditions for the widelyrange of asymptotic stability of the system were worked out. In addition, based onthe non-linear stochastic bifurcation theory, the critical point of the Hopf bifurcationoccurs of the stochastic dynamic system which was followed by the tire stiffnesschanges was calculated.Finally, based on the nonlinear stochastic dynamic programming theory,through the integration of control methods, by regarding the anti-random interference of the car seat as the objective function to be determined bycost-function traversal, the suspension system of nonlinear stochastic optimalcontrol law was designed. The following simulation study was conducted.Comparing with the classical optimal linear quadratic control strategies, the resultsshowed that the two control strategies can both decay the random vibrationamplitude and frequency attenuation ground roughness to the car seat to some extent,improve the car’s driving comfort and ride comfort, but the stochastic optimalcontrol strategy based on the principle of energy dissipation in terms of efficiency orcontrol of the control effect is better than the linear-quadratic classical optimalcontrol.