Discrete‐time adaptive control for nonlinear systems with periodic parameters: A lifting approach

Huang, Deqing; Xu, Jian‐Xin

doi:10.1002/asjc.335

Cited by 20 publications

(21 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…wherês ,̂and̂are the steps sizes of the adaptive algorithms and should be suitably chosen to ensure the stability of the adaptive algorithm [25,26].…”

Section: Modeling Of the Nonlinear Secondary Path Using Thfmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

Ghasemi¹,

Kamil²,

Marhaban³

2015

Asian Journal of Control

View full text Add to dashboard Cite

Adaptive algorithms are prevalently applied in the design of nonlinear active noise control (ANC) systems. The most important nonlinearity in ANC is the saturation effect produced by the electro‐acoustical sensors and transducers. The dominant saturation nonlinearity is in the transducers, which can be represented by a Wiener model. An effective solution to mitigate such nonlinear distortion is to employ the Nonlinear Filtered‐X Least Mean Square (NLFXLMS) algorithm. The controller compensates the nonlinearity using a model of the saturation effect represented by the scaled error function (SEF). However, the NLFXLMS is limited by two practical issues such that the degree of nonlinearity has to be known in advance and the SEF cannot be evaluated in real time. In this work, the NLFXLMS algorithm is modified by incorporating the tangential hyperbolic function (THF) to model the saturation effect of the loudspeaker. The proposed THF‐NLFXLMS algorithm, models the nonlinear secondary path and applies the estimated degree of nonlinearity in the control algorithm design. The results show that the Wiener secondary path, with saturation nonlinearity represented by SEF, can be modelled by THF with a certain degree of accuracy and can yield a reasonable estimate of the degree of nonlinearity. The performance of the proposed algorithm is comparable with the benchmark NLFXLMS and is superior to the conventional FXLMS as well as the second order Volterra algorithm of similar computational complexity with the proposed algorithm.

show abstract

“…wherês ,̂and̂are the steps sizes of the adaptive algorithms and should be suitably chosen to ensure the stability of the adaptive algorithm [25,26].…”

Section: Modeling Of the Nonlinear Secondary Path Using Thfmentioning

confidence: 99%

“…• Case 3. The true nonlinear secondary path is represented with SEF and modelled using THF without updatinĝusing (26) and (27).…”

Section: Modelling Of the Nonlinear Secondary Pathmentioning

confidence: 99%

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

Ghasemi¹,

Kamil²,

Marhaban³

2015

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…The concept of PAC arises in [17], [18], [19] due to the observation that the unknown periodic parameter remains a "constant" after a given period. Thus, the PAC approach updates the parameter estimate after the period interval, instead of carrying out the updating law continuously.…”

Section: Zjuyumiao@gmailcommentioning

confidence: 99%

Discrete-time adaptive learning control for parametric uncertainties with unknown periods

Huang

2013

52nd IEEE Conference on Decision and Control

View full text Add to dashboard Cite

All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org) Discrete-Time Adaptive Learning Control for Parametric Uncertainties with Unknown Periods Miao Yu and Deqing HuangAbstract-In this paper, we approach the problem of unknown periods for a class of discrete-time parametric nonlinear systems with nonlinearities which do not necessarily satisfy the sector-bounded condition. The unknown periods hide in the parametric uncertainties, which is difficult to estimate. By incorporating a logic-based switching mechanism, we estimate the period and bound of unknown parameter simultaneously under Lyapunov-based analysis. Rigorous proof is given to demonstrate that a finite number of switchings can guarantee the asymptotic regulation of the nonlinear system considered. The simulation result also shows the efficacy of the proposed switching periodic adaptive control method.

show abstract

“…Thus, the residual noise e ( k ) can be expressed as

e (k) = x (k) P (z) S (z) + y (k) S (z)

where y ( k ) = W ( k ) T X ( k ), the weighting parameter is W ( k ) = [ w 0 ( k ), w 1 ( k ), … , w N −1 ( k )] T and the input noise is X ( k ) = [ x ( k ), x ( k − 1), … , x ( k − N + 1)] T . The corresponding gradient estimation and adaptations of the weights are formulated as

\nabla_{k} = \frac{\partial e^{2} (k)}{\partial W (k)} = 2 e (k) [X (k) S (z)] .

We have the adaptation as

W (k + 1) = W (k) - μ \nabla_{k} = W (k) - 2 μ e (k) [X (k) S (z)],

where μ is the learning rate . The FXLMS algorithm in has a correction term of X ( k ) S ( z ), unlike that in the conventional least mean squares (LMS) algorithm in ,

W (k + 1) = W (k) - 2 μ e (k) X (k) .

So, in order to realize the ANC system, the reference signal X ( k ) must be filtered by the

\hat{S} (z)

, which is obtained by identifying S ( z ).…”

Section: Anc System Configurationmentioning

confidence: 99%

Active Noise Control and its Application to Snore Noise Cancellation

Chang¹,

Pan²,

Liao³

2012

Asian Journal of Control

View full text Add to dashboard Cite

An active noise control (ANC) system with a digital signal processor (DSP) is proposed for snoring noise cancellation. The ANC system applies the filtered‐X least mean square (FXLMS) method to generate anti‐snoring noise by estimating the secondary path and then adaptively tuning the weights of the finite‐length impulse response (FIR) filter. By interfering with noise, the anti‐snoring noise signals help to create a silent zone around the snorer. Several experiments confirm the effectiveness of the proposed method.

show abstract

Discrete‐time adaptive control for nonlinear systems with periodic parameters: A lifting approach

Cited by 20 publications

References 19 publications

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

Nonlinear Thf‐Fxlms Algorithm For Active Noise Control With Loudspeaker Nonlinearity

Discrete-time adaptive learning control for parametric uncertainties with unknown periods

Active Noise Control and its Application to Snore Noise Cancellation

Contact Info

Product

Resources

About