Adaptive control of vibration for systems with non-stochastic uncertainty measure and bounded disturbances

The application of feedback control with adaptive approach in vibration systems is considered. This research field is considered now as significant and not investigated. The elaborated method allows designing of controllers which provide adaptive control of oscillations with improved performance for the systems with complex behavior and unknown parameters. A direct adaptive pole-placement controller (APPC) is designed based on the bicriteria optimization and ellipsoid bounded estimation of the controller parameters. In contrast to the well-known direct APPC, based on the certainty equivalence (CE) assumption, the accuracy of the controller parameter estimation, the size of the ellipsoid for bounded estimation, and necessity of an optimal excitation signal are taken into account in the presented controller design. The new adaptive control algorithm is simple and allows improving the performance of the adaptive pole-placement control especially at the beginning of the adaptation. The elaborated method can be suggested for software development and applications to laboratory and industrial equipment. Increased precision of the control, improved practical acceptance of the systems as well as extension of their application field are expected as advantages of the suggested adaptive systems for vibration control.