Skyhook controller design using bilinear matrix inequalities

This paper focuses on the design of the so called sky-hook controller, which is used to isolate vibrations on suspension systems. The design of the sky-hook controller is posed as a single input-single output static output feedback control problem. The design of the sky-hook controller is posed using the generalized plant with the sparse structure of the sky-hook controller. It is shown that, the root-locus plot for visualization and some of the w4ell known stability analysis methods can be utilized to acquire a stability interval for the sky-hook controller. By gridding the stability interval, it has been shown that there may exist convex sub intervals, and posing a BMI problem with the corresponding D region, it is possible to solve the skyhook design problem, with regard to H₂ or H_∞ optimality. The sky-hook design is simulated using two different suspension systems and an experiment is carried out on a system for three different road profiles. It has been sown that using a sky-hook controller instead of an LQR controller is plausible, since the number of required sensors is reduced, therefore the cost is reduced and the performance is almost equal for both controllers.