Adaptive disturbance rejection for unknown stable linear systems. (June 2016)

• Record Type: Journal Article
• Authors: Marino, Riccardo; Tomei, Patrizio
• Other Names: Yang Jun guest-editor.; Chen Wen-Hua guest-editor.; Ding Zhengtao guest-editor.
• Is Part Of: Transactions of the Institute of Measurement and Control. Volume 38:Number 6(2016)
• Page Start: 640
• Page End: 647
• Publication Date: 2016-06
• Subjects: Disturbance rejection -- frequency estimation -- notch filter -- linear stable systems -- unknown linear systems; Automatic control -- Periodicals; Measuring instruments -- Periodicals; Commande automatique -- Périodiques; Mesure -- Instruments -- Périodiques; 681.2
• DOI: 10.1177/0142331215625769
• Languages: English
• ISSNs: 0142-3312

Abstract

The design of an adaptive output feedback compensator is addressed to reject biased multi-sinusoidal disturbances of unknown amplitudes, phases and frequencies, acting on unknown stable single-input single-output linear systems of unknown order and relative degree. A single biased sinusoidal disturbance is first considered. It is shown that the knowledge of the sign of the real part (or the imaginary part) of its transfer function at zero and at the disturbance frequency is sufficient for the explicit design of an adaptive compensator which guarantees local exponential convergence to zero of the system output and of the frequency estimation error. This result is generalized to the case of biased multi-sinusoidal disturbances. As a special case, an adaptive notch filter which provides the unknown frequencies contained in the disturbance is obtained.