Rejection of periodic disturbances of unknown and time‐varying frequency

Abstract

The paper reviews available methods for the rejection of periodic disturbances. Such disturbances are often encountered in active noise and vibration control, due to rotating machinery. The emphasis of the paper is on feedback control problems where reference sensors are not available. The case where the frequency of the disturbance is known is considered first. Two sets of algorithms are discussed: one based on the internal model principle of feedback control theory, and the second based on adaptive feedforward cancellation. An interesting observation is that algorithms originating from both approaches can be shown to be equivalent under certain conditions. When the frequency of the disturbance is unknown, an intuitive approach consists in combining a method for the rejection of disturbances of known frequency with a frequency estimator. Alternatively, one may seek to develop a stable adaptation mechanism so that the disturbance is cancelled asymptotically. While algorithms can be designed to adapt to plant and disturbance parameters, the most successful approaches use some limited plant information to adapt the magnitude, frequency, and phase parameters of the control signal. Applications are discussed throughout the paper.

Robust hybrid estimation and rejection of multi‐frequency signals

“…. , 1] ∈ R q such that y ω is scalar and it contains all the frequencies of w. Once the correct value 2n = m of eigenvalues related to the sinusoidal components is obtained, an estimatê ω is provided by (14) with initial conditionsω i (0), i = 1, . .…”

“…When the exosystem, on the other hand, is not perfectly known, the problem becomes much more complicated since it is necessary either to directly adapt the internal model of the exosystem contained in the regulator (see for instance [6,7,8], often considering the case of nonlinear system), or to identify the frequency characteristics of the exogenous signals entering the plant and then either redesign the regulator according to the obtained information or directly cancel the exogenous disturbances using the estimated signal (see for instance [9,10,11,12,13,14,15]). The latter approach is pursued here.…”

Asymptotic rejection of sinusoidal disturbances based voltage balance control in back-to-back power converters

“…Both the case when the disturbance frequency is known as well as the case when it is an unknown parameter have been studied. Even the varying frequency disturbance scenario, typical in applications such as rolling machines and magnetic tape drives, has been also discussed [34,35]. Thus, methods related to adaptive control [36,37], repetitive control [38,39], backstepping [40], among others, have been used providing solid results.…”

Robust stability and performance of adaptive jitter supression in laser beam pointing

“…The efficacy of the proposed scheme and performance improvement in jitter reduction are demonstrated by experiment. The problem of unknown time-varying periodic disturbance rejection is investigated in some other references such as [21], [22]; however, no robustness analysis is provided in the presence of unmodeled dynamics. It is known that adaptive techniques such as these may fail in some circumstances [23].…”