Operator-based non-linear vibration control system design of a flexible arm with piezoelectric actuator

Abstract

Most real plants must deal with some non-linear characteristics. For the non-linear plants, design of non-linear control system using operator-based robust right coprime factorisation is considered. The considered non-linear control system applications show the desired results. In this paper, operator-based non-linear vibration control of a flexible arm experimental system with uncertainties using robust right coprime factorisation is considered. In general, the vibrations by the characteristic vibration mode include from one to infinite order vibration modes and appear on the arm vibration. It is difficult to consider all vibration modes. Consequently, based on the concept of Lipschitz operators and robust right coprime factorisation condition, robust stability of the closed-loop system with unconsidered vibration modes as uncertainties is guaranteed, and desired vibration control performance actuated by piezoelectric element is ensured. Finally, simulation and experimental results are presented to support the effectiveness of the proposed design.