Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

• Published in: Mechanical systems and signal processing Vol. 99; pp. 930 - 945
• Main Authors: Thenozhi, Suresh, Tang, Yu
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15.01.2018; Elsevier BV
• Subjects: Adaptive control; Adaptive systems; Control systems design; Convergence; Convergence analysis; Cubic damping; Damping; Design engineering; Frequency response function; Frequency response functions; Linear systems; Mechanical systems; Nonlinear response; Nonlinear systems; Nonlinearity; Numerical analysis; Satellites; Studies; Vibration; Vibration control; Cubic damping; Satellites; Vibration control; Adaptive control; Frequency response function; Convergence analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.03.017

•A framework for frequency response based vibration controller design for two types of nonlinear systems is developed.•Uses convergence analysis to prove the existence of nonlinear frequency response function.•Controller gains are tuned adaptively to obtain vibration suppression over a wide magnitude and frequency range.•Numerical studies on a mechanical system with cubic damping and a satellite system has been provided. Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.