تشدید تاخیر با بازخورد سرعت - طراحی و تجزیه و تحلیل عملکرد

In this work a tunable torsional vibration absorption mechanism, the delayed resonator (DR) is studied. The tuning feedback used is time delayed proportional control on the angular velocity of the absorber. Dynamic analysis of the absorber and its tuning features are presented. Single- and dual-frequency resonance characteristics are introduced, both of which are achieved owing to the added delay in control. Combined system stability, for such time delayed dynamics and relevant topics of relative stability and dominant pole placement are discussed. A design tool is suggested based on the property called, the degree-of-stability. Experimental results are also presented, using a torsional vibration setup involving electric motor drives. They support the theoretical findings strongly.

The paper elaborates on a recently introduced real-time tunable vibration absorption strategy, the delayed resonator (DR) [1], [2] and [3]. The underlying control strategy is a partial state feedback with time delay. It has been shown that this control structure can convert the absorber into a resonator, with a tunable resonance frequency. This resonator functions as a perfect vibration absorber against a tonal excitation even when its frequency is varying with time. The DR absorber is studied for transverse vibration cases in the earlier efforts [1], [2], [3], [4], [7] and [12]. Its usage for torsional oscillations was first introduced by Filipović and Olgac [3]. This paper presents two contributions. First is on the analysis of single- and dual-frequency resonances for delayed speed feedback. It is shown that the torsional DR can be tuned to resonate at not only one but two distinct frequencies. At these settings the DR can absorb bi-tonal oscillations. These two frequencies, however, are not tunable, i.e., they are fixed for a given passive absorber. Both the direct problem (i.e., the analysis) and the indirect problem (i.e., the synthesis) of the absorber for a given pair of frequencies are presented. Second contribution is on the stability measure of the operation. When the DR is effectively suppressing the tonal vibrations, the combined system (the primary system and the DR absorber) should remain asymptotically stable. This feature is studied from various points-of-view. The characteristic equation representing the combined system exhibits the form of a quasi-polynomial, i.e. a polynomial with exponential, e−τs delay terms where τ represents the time delay. This class of systems are not easy to analyze [5], [6], [8] and [9]. They possess infinitely many finite characteristic roots due to the transcendentality of the equation. The dominant (i.e., the rightmost) root dictates the system behavior. The stability, tuning speed (i.e., settling) characteristics are studied using this information to impart a better design of the absorber. Three different approaches can be found in the literature for the analysis of such time delayed systems: (i) root locus analysis [2] and [7], (ii) modified Nyquist method [2], (iii) stability chart method [2] and [7]. This text revisits (iii) with the aim of introducing a new interpretation for the degree-of-stability. It is organized as follows: In Section 2 single frequency DR with speed feedback is presented. Section 3 contains direct and indirect problem of dual frequency fixed DR (DFFDR). Section 4 addresses the stability issues including new results of degree-of-stability analysis for determining the limitations of the methodology. In Section 5 the description of the laboratory set-up for torsional DR is given. Experimental results are presented in Section 6.

This work presents further elaboration on DR vibration absorption methodology in particular for torsional vibration cases. Electric drives are taken as the application objectives; both theoretical and experimental results are discussed. Following contributions are presented. Delayed speed feedback is considered as opposed to position or acceleration. This natural proposition for electric drive applications is also shown to offer some simpler analytical steps for the DFFDR. As a design tool for selecting the structural parameters of the DR, a DFFDR linked approach is suggested. It is based on the observation that, for a given frequency range a DR can be simply formed by setting these frequency limits as the dual frequencies of DFFDR and using this absorber as the basis for DR implementation. On another front, using the DOS concept it is proved analytically that the stability margin decreases exponentially for increasing feedback delays. Several experimental observations are presented in the text. They show better than 20 dB absorption over the passive absorber, although the absorber mechanism at hand and its operating properties (friction etc.) are far from ideal.