Frequency-Domain Analysis and Design of Linear Feedback of Nonlinear Systems and Applications in Vehicle Suspensions

Nonlinear vibration control systems (both passive and active) always involve parameter design and performance optimization tasks. A systematic and novel frequency-domain method is established to this aim in this study based on a newly developed concept - nonlinear characteristic output spectrum (nCOS). The nCOS function can be any system output function or multiobjective performance function to be optimized. It is shown for the first time that the nCOS function can be expressed into an explicit and analytical polynomial function of any model parameters which define underlying linear dynamics of the system. A simple least square algorithm is provided for the determination of this nonlinear parametric relationship. This novel nCOS function can obviously facilitate parameter analysis and design of nonlinear vibration control systems and provide a useful tool for a simple linear control design, while simultaneously considering inherent nonlinear dynamics of a system. A case study in vehicle suspension control demonstrates these new results.