Robust Rejection of Periodic and Almost Periodic Disturbances

Abstract

We present algorithms to exponentially reject periodic and almost periodic disturbances, the motivating application being a rejection of reel eccentricity induced disturbances in tape-drive systems. The prevalent periodic disturbance rejection algorithms rely on a constant gain approximation of the system at a particular frequency. These are inadequate for this application because a tape-drive system has parametric uncertainties and because the disturbance is time-varying. We present a robust extension of an existing technique derived by Bodson et al. and further use quadratic and parameter-dependent Lyapunov functions to synthesize gain-scheduled feedback compensators. Copyright c 2005 IFAC

Robust generalized asymptotic regulation against non‐stationary sinusoidal disturbances with uncertain frequencies

“…When the frequency of the sinusoidal disturbance is measurable (or reliably estimable) online, as is the case—for instance—in systems with rotational machinery, linear parameter‐varying (LPV) controller synthesis techniques can also be applied for robust and adaptive non‐stationary sinusoidal disturbance attenuation 3, 22–29. The exact asymptotic regulation problem was in fact considered recently for linear time‐varying systems by Zhang and Serrani 30, Ichikawa and Katayama 31 and the solvability condition was obtained as the existence of two bounded matrix‐valued functions that satisfy a differential matrix equation as well as an equality constraint.…”

LPV Control for Robust Attenuation of Non-stationary Sinusoidal Disturbances with Measurable Frequencies

“…sinusoidal disturbance rejection. When the frequency is measurable or estimable online, as is the case -for instancein systems with rotational machinery, linear parametervarying (LPV) controller synthesis techniques can also be applied for robust and adaptive non-stationary sinusoidal disturbance attenuation, Dettori [2001], Du et al [2003], Hüttner et al [2005], Kulkarni et al [2005], Gruenbacher et al [2007]. Within the LPV control framework, it even becomes possible to systematically handle other performance objectives as well, Köroglu and Scherer [2007].…”

Robust Controller Synthesis for the Attenuation of Non-stationary Sinusoidal Disturbances with Uncertain Frequencies

“…This can be realized either by robust controller synthesis techniques, Lee and Chung [1998], Tsao et al [2000], Li and Tsao [2001], Steinbuch [2002], Osburn and Franchek [2004], Kim and Tsao [2004], Steinbuch et al [2007], Dietz et al [2007], or by adaptive methods, Bodson and Douglas [1997], Bodson [2001], Guo and Bodson [2005], Serrani et al [2001] as specialized to sinusoidal disturbance rejection. When the frequency is measurable or estimable online, as is the case -for instance-in systems with rotational machinery, linear parametervarying (LPV) controller synthesis techniques can also be applied for robust and adaptive non-stationary sinusoidal disturbance attenuation, Dettori [2001], Du et al [2003], Hüttner et al [2005], Kulkarni et al [2005], Gruenbacher et al [2007]. Within the LPV control framework, it even becomes possible to systematically and simultaneously handle other performance objectives, as has been illustrated by .…”