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Selective model inversion and adaptive disturbance observer for rejection of time-varying vibrations on an active suspension

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This paper presents an adaptive control scheme for identifying and rejecting unknown and/or time-varying narrow-band vibrations. We discuss an idea of safely and adaptively inverting a (possibly non-minimum phase) plant dynamics at selected frequency regions, so that structured disturbances (especially vibrations) can be estimated and canceled from the control perspective. By taking advantage of the disturbance model in the design of special infinite-impulse-response (IIR) filters, we can reduce the adaptation to identify the minimum amount of parameters, achieve accurate parameter estimation under noisy environments, and flexibly reject the narrow-band disturbances with clear tuning intuitions. Evaluation of the algorithm is performed via simulation and experiments on an active-suspension benchmark.
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... To satisfy this requirement, enhanced control at selected frequencies has been adopted by many researchers. Based on the location of servo enhancement, enhanced control can be categorized into three groups to deal with (1) independent disturbance frequencies by, for instance, peak filters, 5,6 adaptive feedforward cancellation, 7,8 disturbance observers, [9][10][11] and Youla-Kucera (YK) parameterization; [12][13][14][15] (2) a fundamental frequency and its integer multiples by means of RC and its variants; 16,17 and (3) broadband frequencies through adaptive disturbance rejection, 18 adaptive noise cancellation, 19 and so on. This article discusses recent results in enhanced control to reach the desired servo goals. ...
... For example, candidate Q-filter designs can be found using a linear combination of some basis transfer functions (e.g., P k Q i = 0 u i z Ài in discrete-time schemes), and adaptive/H ' control can be applied to find the scaling coefficients for the combination. 11 Regardless of what tools are used, to achieve good disturbance attenuation,S in (4) is required to be small, and hence PQ should be close to 1 at the desired frequencies. Consider a block diagram realization in Figure 3. ...
... When there is (stable and bounded) model uncertainty D(z) such thatP(z) = P(z)(1 + D(z)), standard robust stability analysis 11 gives that the closed-loop system of the add-on design is stable if and only if both of the following hold: Table 1 is satisfied, that is, the closed loop is stable when ...
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... A narrow notch in the error-rejection function can no longer provide sufficient attenuation; yet a wide notch tends to cause undesired amplification at other frequencies due to the fundamental waterbed limitation of feedback control [16]- [18]. In view of such challenges, the authors proposed an infinite-impulseresponse (IIR) filter design in DOB to control the waterbed effect manually [15], [19] and optimally [20]; such a design also benefits narrow-band disturbance rejection, and underpins first-tier results [21], [22] in an international benchmark on adaptive regulation [12]. [23] provides additional comparison of the DOB framework with peak filter algorithms. ...
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... In contrast, both the magnitude and phase compensations are taken into consideration in (4). Compared with other loop-shaping algorithms, the proposed scheme inherits the advantages of flexible intuitive design and high performance of the DOB [12], [21]. It also shares the capability of easy adaptation [21], [23] (Section VIII-A). ...
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... We take for example the active suspension system in [29] that serves as a benchmark on adaptive regulation. The control goal there is to attenuate the vibrations transmitted to the base frame, and model inversion is critical for the best results achieved in the benchmark [30]. Although the system is open-loop stable, the existence of the NMP zeros challenges model inversion in general feedback and feedforward control. ...
... In the active suspension benchmark discussed in [30], the minimum-phase model (red dashed line in Fig. 11) is obtained by applying the proposed H ∞ -based optimal inversion. The model is then used to build an adaptive disturbance observer with an infinite impulse response structure to reject unknown or time-varying narrow-band vibrations. ...
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... We take for example the active suspension system in [29] that serves as a benchmark on adaptive regulation. The control goal there is to attenuate the vibrations transmitted to the base frame, and model inversion is critical for the best results achieved in the benchmark [30]. Although the system is open-loop stable, the existence of the NMP zeros challenges model inversion in general feedback and feedforward control. ...
... In the active suspension benchmark discussed in [30], the minimum-phase model (red dashed line in Fig. 11) is obtained by applying the proposed H ∞ -based optimal inversion. The model is then used to build an adaptive disturbance observer with an infinite impulse response structure to reject unknown or time-varying narrow-band vibrations. ...
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... While an adaptation algorithm can be derived (see (I. ) there is not enough richness in the signal to adjust the parameters of both B Q and A Q . A solution has been proposed and successfully tested in Castellanos-Silva, Landau, Dugard, and Chen (2016) where a direct adaptation of the parameters of B Q is done and the parameters of the A Q are cleverly computed from the estimation of the parameters of the disturbance (see also Chen and Tomizuka (2013)). ...
... There are many papers reporting results in using Youla Kucera parametrization for rejection of narrow band disturbances in active vibration control and in adaptive active To validate comparatively the various approaches to adaptive rejection of multiple narrow band disturbances in active vibration control, a benchmark is available. The synthesis of the results of the benchmarking can be found in I. as well as in the references of the contributors: Aranovskiy and Freidovich (2013), Airimitoaie, Castellanos Silva, and Landau (2013),Castellanos-Silva, , Castellanos-Silva et al. (2016),de Callafon andFang (2013), Chen and Tomizuka (2013), Karimi and Emedi (2013), Wu and Ben Amara (2013). A recent application paper using adpative Youla Kucera feedback compensation is Wu, Zhang, Chen, and Wang (2018) ...
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... While in (3), both the magnitude and the phase compensation are taken into consideration. On the other hand, compared with other narrowband algorithms, the proposed scheme inherits the advantages of conventional DOB of intuitive design and good performance [22,23]. It also shares the benefits of capability of easy adaptation and extension to rejecting broad-band disturbances [24]. ...
... It needs to be tuned based on the characteristics of w(k). For more discussion on the application of the PAA for identifying time-varying disturbance, we refer readers to [22]. ...
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