Stabilization of State-derivative Feedback Control with Time Delay

Witchupong Wiboonjaroen ； Sarawut Sujitjorn

《Research Journal of Applied Sciences, Engineering and Technology》 4卷18期 (2012/09) Pp. 3201-3208

並列摘要

This study considers the problem of state-derivative feedback controller design via eigenvalue assignment for LTI systems of linear Delay Differential Equations (DDEs) with a single delay. Unlike simple LTI systems, the systems described by DDEs have an infinite eigenspectrum and it is not feasible to assign all closed-loop eigenvalues. The paper proposes a method to assign a critical subset of them using an approach of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE. With the proposed method, one can extend a conventional eigenvalue assignment method for a feedback controller to a delayed LTI system. A scheme including filtered state-derivative feedback is proposed to overcome the destabilizing effect of feedback delays. Proofs of the proposed method and numerical examples are presented.

並列關鍵字

Delay differential equation ； eigenvalue assignment ； feedback controller ； lambert W function ； neutral system ； state-derivative feed back