Blockwise Subspace Identification for Active Noise Control

In this paper, a subspace identification solution is provided for active noise control (ANC) problems. The solution is related to so-called block updating methods, where instead of updating the (feedforward) controller on a sample by sample base, it is updated each time based on a block of N samples. The use of the subspace identification based ANC methods enables non-iterative derivation and updating of MIMO compact state space models for the controller. The robustness property of subspace identification methods forms the basis of an accurate model updating mechanism, using small size data batches. The design of a feedforward controller via the proposed approach is illustrated for an acoustic duct benchmark problem, supplied by TNO Institute of Applied Physics (TNO-TPD), the Netherlands. We also show how to cope with intrinsic feedback. A comparison study with various ANC schemes, such as block filtered-U, demonstrates the increased robustness of a subspace derived controlle

From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples

Sparse Nonlinear MIMO Filtering and Identification

In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation

Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Analytical study of the frequency response function of a nonlinear spring damper system

A spring damper system with a nonlinear damping element is investigated using the Volterra series method to study the system frequency response function (FRF) characteristics. The relationship between the FRF and the characteristic parameters of the nonlinear damper is determined to produce an analytical description for the system FRF. Simulation studies are used to verify the theoretical analysis. These results provide an important basis for the FRF based analysis and design of nonlinear spring damper systems in the frequency domain