A Robust Design Method of Active Controller for Uncertain Vibration Systems

Abstract

This paper presents a robust design method of active controller for parameter uncertain vibration systems subjected to external unmeasurable disturbances. Based on the combination of complex modal theory, parameter optimization, linear matrix inequality approach, and robust eigenvalue assignment, the control law is reconstructed by adjusting the variable parameter r for robust active vibration control. The design is simple and easy to be implemented in real-time control.

RETRACTED: Applications of the fuzzy Lyapunov linear matrix inequality criterion to a chaotic structural system

“…In LMI-based design approaches, a numerical solution is obtained by convex optimization methods, such as the interior-point method. Li and Yam (2001) presented a robust design method for the active control of uncertain parameter vibration systems subjected to external unmeasurable disturbances. Based on the combination of complex modal theory, parameter optimization, the LMI approach and robust eigenvalue assignment, they reconstructed control laws by adjusting the variable parameters for robust active vibration control.…”

Active Structural Vibration Control: A Review

“…The transfer function matrix of the generalized plant can be partitioned according to the input-output variables: H ¥ theory has been applied to the active vibration control of a number of civil and mechanical engineering structures (Seto, 1998). Application of the H ¥ controller in the vibration control of flexible structures can be found in Bayard and Chiang (1998), Zhang et al (2001), Li and Yam (2001a), Moreira et al (2001), Chang et al (2002), Seto and Kar (2000), and Kar et al (2000). Rijanto et al (2000) utilized an H ¥ controller to design an active mass damper (AMD) for the attenuation of floor vibrations.…”

Hybrid under-actuated control for autonomous dynamic balance of a running electrical bicycle including motor dynamics and in the presence of huge uncertainty

“…However, it needs a trial-and-error method to obtain an acceptable tracking performance. In thispaper, the combination of sliding-mode control, decentralized control, and fuzzy control, which is so-called fuzzy decentralized sliding-mode control (FDSMC), provides a robust controller for the nonlinear systems (Banavar and Dominic, 1999; Li and Yam, 2001; Khaled and Chalhoub, 2010). Moreover, this paper introduces an FDSMC scheme with the number of outputs larger than that of the control inputs (Hwang et al, 2009).…”