There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Electronic Control Of Switched Reluctance Machines

This paper investigates the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system (WHS) with Gaussian inputs. The WHS nonlinearity is assumed to be expandable in a series of orthogonal Hermite polynomials. The sequential procedure uses (1) a gradient search for the unknown coefficients of the Hermite polynomials, (2) an LMS adaptive filter to partially identify the input and output linear filters of the WHS, and (3) the higher order terms in the Hermite expansion to identify each of the linear filters. The third step requires the iterative solution of a set of coupled nonlinear equations in the linear filter coefficients. An alternative scheme is presented if the two filters are known a priori to be exponentially shaped. The mean behavior of the various gradient recursions are analyzed using small step-size approximations (slow learning) and yield very good agreement with Monte Carlo simulations. Several examples demonstrate that the scheme provides good estimates of the WHS parameters for the cases studied.

Analysis of Stochastic Gradient Identification of Wiener-Hammerstein Systems for Nonlinearities with Hermite Polynomial Expansions

The paper deals with identification of fractional order nonlinear systems based on Hammerstein–Wiener models. An output error approach is developed using the robust Levenberg–Marquardt algorithm. It presents the difficulty of the parametric sensitivity functions calculation which requires a heavy computational load at each iteration. To overcome this drawback, the fractional nonlinear system is reformulated under a regression form, and the gradient and the Hessian can be obtained in a closed form without using the parametric sensitivity functions. The method’s efficiency is confirmed on numerical simulations, and its feasibility is illustrated with its application to the modeling of an experimental arm robot.

Nonlinear system identification using fractional Hammerstein–Wiener models

This paper deals with the identification of Hammerstein–Wiener models. The novelty lies in the fact that the front nonlinear block is allowed to be the memory of hysteresis type. The latter is any ...

Identification of Hammerstein–Wiener models with hysteresis front nonlinearities

The problem of system identification is addressed for Hammerstein-Wiener systems that involve memory operator of backlash type bordered by straight lines as input nonlinearity. The system identification of this model is investigated by using easily generated excitation signals. Moreover, the prior knowledge of the nonlinearity type, being backlash or backlash-inverse, is not required. The nonlinear dynamics and the unknown structure of the linear subsystem lead to a highly nonlinear identification problem. Presently, the output nonlinearity may be noninvertible and the linear subsystem may be nonparametric. Interestingly, the system nonlinearities are identified first using a piecewise constant signal. In turn, the linear subsystem is identified using a frequency approach.

Frequency Identification of Hammerstein-Wiener Systems with Backlash Input Nonlinearity

Identification of nonlinear system composed of parallel coupling of Wiener and Hammerstein models

Switched reluctance machine (SRM) acts as a suitable choice for electromechanical conversion of wind energy because of its wide range of speed operation, thermal robustness high performances, and reduced cost. This paper presents a numerical modeling of nonlinear inductance and torque for doubly salient switched reluctance machine (DSSRM) with finite element method (FEM) using the femm which considers magnetic saturation. The results obtained have been compared with other study that showed the same nonlinear behavior of phase inductance and phase torque.

Numerical Modeling of a Nonlinear Four-Phase Switched Reluctance Machine

Identification of phase self-inductance is a central step in control and development of Switched Reluctance Machine (SRM) model because the voltage and torque equation are functions of the phase se...

Modelling and identification of switched reluctance machine inductance

Switched reluctance motor (SRM) is gaining more interest in the last decades due to its wide range of speed operation, thermal robustness, high performances and low manufacturing cost. For these reasons, it is investigated as an alternative generator for many applications like wind energy conversion, aircraft actuators and electric vehicles. The SRM is considered highly nonlinear which makes the SRM modeling difficult to achieve. This paper presents a new method for analytical modeling and identification of SRM nonlinearity using standstill tests. It is shown that the electrical model of the SRM machine can be described by block-oriented nonlinear systems. Specifically, this system nonlinearity can be exactly described by a nonlinear block followed by a linear element. The proposed method differs from the existing methods used to estimate the inductance of SRM. Indeed, the parameters estimation algorithm is based only upon the accessible input-output measurement data.

Laila Kadi

Papers

Frequency Identification of Hammerstein-Wiener Systems with Backlash Input Nonlinearity

Identification of nonlinear system composed of parallel coupling of Wiener and Hammerstein models

Numerical Modeling of a Nonlinear Four-Phase Switched Reluctance Machine

Modelling and identification of switched reluctance machine inductance

Modeling and Determination of Switched Reluctance Machine Nonlinearity