Structure Flexibility Impacts on Robust Active Vibration Isolation Using Mixed Sensitivity Optimization

Active vibration isolation from an arbitrarily, structurally complex receiver is considered with respect to the impacts of structure flexibility on the open- and closed-loop system characteristics. Specifically, the generally weak influence of flexibility on the open-loop transfer function in the case of total force feedback, in contrast to acceleration feedback, is investigated. The open-loop system characteristics are analyzed based on open-loop transfer function expressions obtained using modal expansion and on modal model order reduction techniques. To closely demonstrate and illustrate the impacts of flexibility on the closed-loop system performance and stability, a problem of automotive engine vibration isolation from a flexible subframe is presented where the neglected dynamics are represented as an output multiplicative model perturbation. A physical explanation as to why the contribution of flexibility to the open-loop transfer function could be neglected in the case of total force feedback in contrast to acceleration feedback is given. Factors for an individual eigenmode to not significantly contribute to the total force output are presented where the deviation of the mode direction relative to the actuator force direction is pointed out as a key one in addition to modal mass and damping coefficient. In this context, the inherent differences between model order reduction by modal and by balanced truncation are being stressed. For the specific automotive vibration isolation application considered, the degradation of robust performance and stability is shown to be insignificant when obtaining a low-order controller by using total force feedback and neglecting flexibility in the design phase.