Identification of Nonlinear Systems Structured by Wiener-Hammerstein Model

Wiener-Hammerstein systems consist of a series connection including a nonlinear static element sandwiched with two linear subsystems. The problem of identifying Wiener-Hammerstein models is addressed in the presence of hard nonlinearity and two linear subsystems of structure entirely unknown (asymptotically stable). Furthermore, the static nonlinearity is not required to be invertible. Given the system nonparametric nature, the identification problem is presently dealt with by developing a two-stage frequency identification method, involving simple inputs

Some Interesting Effects of High-Frequency Non-Resonant Harmonic Excitations on the Slow Response of Duffing Oscillators

This dissertation investigates the response of Duffing oscillators to bi-harmonic ex-citations consisting of a soft resonant component and a hard high-frequency non-resonant component. To this end, the dissertation uses approximate analytical solutions, numerical simulations, and an especially-designed experimental module to detail the influence of non-resonant excitation on the resonant response for oscillators with symmetric/asymmetric, mono and bi-stable potential energy functions. For mono-stable Duffing oscillators, we demonstrate that the high-frequency excitation has a substantial influence on the shape of the potential energy function associated with the slow dynamics. In specific, we show that the hard excitation stiffens the slow response for oscillators with a symmetric potential energy function. For asymmetric potential energy functions, we clearly illustrate that the high-frequency excitation tends to symmetrize the potential function, therewith reducing the softening nonlinear behaviour of the system. In such case, we also demonstrate that the high-frequency excitation can be the effectively utilized to change the effective nonlinearity of the slow dynamics from the softening to the hardening type. Therefore, by choosing the proper parameters, the hard excitation can be used to locally linearize the resonant dynamics of an asymmetric mono-stable Duffing oscillator. We also demonstrate that by reducing the depth of the potential wells and bringing them closer together, a high-frequency hard excitation can influence the effective properties of the slow dynamics of a bi-stable Duffing oscillator. This has the effect of amplifying the intra-well response. The reduction of the depth of the potential wells also causes the wells to become more asymmetric which increases the softening nonlinearity of the slow dynamics. Furthermore, once the magnitude of the non-resonant excitation exceeds a certain threshold, the potential function loses its bi-stable properties and becomes mono-stable. In summary, this dissertation highlights many interesting effects of the hard excitation on the qualitative properties of the slow resonant response. Such effects can be utilized as an effective open-loop tool to alter the resonant behaviour of the system, which, in turn, can be useful in various application problems including, but limited to, vibration mitigation, sensor sensitivity enhancement, and system identification. Here, we present one illustration where we exploit the hard excitation for parametric system identification of a nonlinear mono-stable oscillator. We present the proposed methodology and apply it successfully to identify the nonlinear parameters of several experimental systems

Evaluation of output frequency responses of nonlinear systems under multiple inputs

In this paper, a new method for evaluating output frequency responses of nonlinear systems under multiple inputs, defined as a sum of sinusoids of different frequencies, is developed. The method circumvents difficulties associated with the existing “frequency-mix vector” based approaches and can easily be applied to investigate nonlinear behaviors of practical systems, including electronic circuits, at the system simulation and design stages. Application of the method to the analysis of nonlinear interference and distortion effects in communication receivers is studied, and specific procedures are proposed which can be directly used in practice for this analysi

Robust H2/H∞-state estimation for discrete-time systems with error variance constraints

Copyright [1997] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper studies the problem of an H∞-norm and variance-constrained state estimator design for uncertain linear discrete-time systems. The system under consideration is subjected to time-invariant norm-bounded parameter uncertainties in both the state and measurement matrices. The problem addressed is the design of a gain-scheduled linear state estimator such that, for all admissible measurable uncertainties, the variance of the estimation error of each state is not more than the individual prespecified value, and the transfer function from disturbances to error state outputs satisfies the prespecified H∞-norm upper bound constraint, simultaneously. The conditions for the existence of desired estimators are obtained in terms of matrix inequalities, and the explicit expression of these estimators is also derived. A numerical example is provided to demonstrate various aspects of theoretical results