Biased Sinusoidal Disturbance Compensation With Unknown Frequency

Output Regulation for Unknown Stable Linear Systems

“…Theorem 3.1 determines special cases in which the regulator has the modular structure of q + 1 parallel simple regulators, each one designed for a single sinusoid or bias. As special cases, known results (see [6], [14]) on exosystems generating constant or sinusoidal signals are reobtained in Corollaries 3.1 and 3.2. Finally, Theorem 3.2 establishes that for the special class of stable plants P (s) for which Re[P (jω)] > 0 for any ω ∈ R, then the fixed universal regulator (8)solves the regulator problem without restrictions on the gain: this implies that very robust regulators exist for such a special class of stable systems.…”

“…This technical note presents three results in the design of a minimal order regulator of order 2q + 1 for unknown stable systems P (s) of unknown order and linear exosystems (2) of order 2q + 1: (i) Sufficient conditions on P (0) and P (jω i ), 1 ≤ i ≤ q, are obtained which generalizes those in [6] when q = 0 and agree with those in [14], [15] when the exosystem is of order two. Those conditions require the knowledge of sign[P (0)] and either sign{Re[P (…”

“…If the exosystem has order one, that is it generates constant disturbances and/or references, [6] establishes that if P (s) is stable and sign[P (0)] is known, the regulator problem is solved by an integral control provided that its gain is sufficiently small. If the exosystem has order two, that is it generates sinusoidal disturbances and/or references with frequency ω, [14] and [15] establish that if P (s) is stable and the phase of P (jω) has an uncertainty less than 180 degrees, then a possibly fractional regulator can be designed provided that its gain is sufficiently small. In particular, if Re[P (jω)] > 0 then a second order regulator can be designed.…”

A parallel prefiltering approach for the identification of a biased sinusoidal signal: Theory and experiments

“…Methodologies for the on-line identification of a sinusoidal signal from uncertain measurements are widely employed in many engineering applications such as active noise cancellation, vibrations monitoring in mechanical system and periodic disturbance rejection (see [1,2,3,4,5] and the references cited therein), to mention a few. A variety of techniques has been presented in the literature for estimating the unknown sinusoids in terms of estimating the amplitude, the frequency and the phase (AFP), such as phase-lock-loop (PLL), adaptive notch filter (ANF) and state variable filtering (see, for instance [6,7,8,9,10]).…”

Torque ripple suppression control for permanent magnet motors

“…The method here proposed makes use of an adaptive frequency-locked loop system, namely AFLL (see [19], [20]), to identify the input frequency even in presence of noisy measurement data. In [19], an averaging analysis was used to prove the stability of such a scheme while in [20] a similar filter has been presented to cancel the effects of a biased multi-sinusoidal signal acting on an unknown plant. An original feature is that the disturbance cancellation scheme uses the internal signals produced by the AFLL.…”