LMI-based state feedback controller design for vibration control of a negative imaginary system

This paper presents state feedback control via linear matrix inequality (LMI) for vibration control of a flexible link manipulator (FLM) system. FLM is a negative imaginary (NI) system with high amplitude vibration and oscillation. In this work, pole placement controller (PPC) which is NI controller is used to control the FLM vibration, to achieve a precise hub angle positioning with minimum tip deflection. A decay rate is introduced to improve the speed of the system and investigate the effect on the system performance. LMI optimization technique is used to obtain the optimal and best control gains of PPC using Matlab LMI toolbox with different values of the decay rate. Simulation results show that satisfactory hub angle and tip deflection responses are achieved using the proposed controller. Damping is successfully added into the system and reduces the system vibration at the first two vibration modes by 40 dB. Hub angle positioning is achieved with minimum tip deflection by changing the value of decay rate.