Sky-hook control of nonlinear quarter car model traversing rough road matching performance of LQR control

The control of the stationary random response of a two degree of freedom (dof) quarter car vehicle model with nonlinear passive elements traversing a homogenous rough road with sky-hook damper control strategy is considered. The sky-hook damper control strategy is realized through a feedback control scheme. The parameters of the sky-hook damper are optimally determined by equating the control force of the feedback system to that obtained by linear quadratic regulator (LQR) control in a mean square equivalence sense. The nonlinear suspension is of hysteretic type and modeled by the Bouc–Wen model. The equivalent linearization method is used to linearize the system and the stochastic optimal control LQR theory is applied to the equivalent linear system. Results show the enhanced performance of feedback control based on sky-hook to levels of performance of LQR control which are also verified by Monte Carlo simulation.