Finite Frequency $H_{\infty }$ Control for Vehicle Active Suspension Systems

This brief addresses the problem of control for active vehicle suspension systems in finite frequency domain. The performance is used to measure ride comfort so that more general road disturbances can be considered. By using the generalized Kalman-Yakubovich-Popov (KYP) lemma, the norm from the disturbance to the controlled output is decreased in specific frequency band to improve the ride comfort. Compared with the entire frequency approach, the finite frequency approach suppresses the vibration more effectively for the concerned frequency range. In addition, the time-domain constraints, which represent performance requirements for vehicle suspensions, are guaranteed in the controller design. A state feedback controller is designed in the framework of linear matrix inequality (LMI) optimization. A quarter-car model with active suspension system is considered in this brief and a numerical example is employed to illustrate the effectiveness of the proposed approach.