Kamal A. F. Moustafa

Electromechanical modelling of overhead cranes

A non-linear electromechanical model describing the dynamical behaviour of overhead cranes is presented. The model takes into consideration the non-linear dependence of the load sway on transients of driving motors during voltage disturbances and start-ups. This is extremely useful in practice since load sway control schemes normally utilize input voltages as control variables. The mechanical subsystem within the model is that of the load sway and has the swing angles and their derivatives as state variables. Each of the two driving motors, namely, the girder motor and the trolley motor, is represented by the classical fifth-order model of induction machines where electrical transients as well as mechanical transients are considered. The model is linearized using Taylor series expansion around a normal operating point. A numerical example is presented to illustrate the usefulness of the results.

On identification of parallel block-cascade nonlinear models

The class of nonlinear systems studied in this paper is assumed to be modelled by parallel block-cascades. Such models are composed of parallel branches where each branch has a linear block in cascade with a zero-memory nonlinear block followed by another linear block. These types of models are extensively used to represent nonlinear dynamic systems and are known in the literature as Wiener-Hammerstein models. Using a zero-mean stationary white gaussian sequence as an input to such models, a structure identification criterion is developed, utilizing the bispectrum estimate of the output sequence only. The application of this criterion is shown by several simulation examples. Also, impulse response estimation of an example of such a model is considered to show the effectiveness of the proposed identification technique.

Characterization of dynamic system nonlinearities via probabilistic approach

The problem of nonlinearity detection in system identification is treated. A probabilistic approach is taken which facilitates the analysis and enables the treatment of both strong and weak nonlinearities. The analysis shows that third- and fourth-order cumulants of the system output can be used to detect the existence of system nonlinearities, and to characterize their type

Non-linearity detection of weakly non-linear dynamic systems using cumulants

Non-linearity detection in dynamic systems is a fundamental issue in non-linear system identification. This problem is treated with the aid of the perturbation technique. A criterion for the detection of even non-linearities is developed in terms of the third-order cumulants of vector stochastic processes.

Time-domain structural identification using free response measurements

The problem of determining linear time-invariant models of flexible structures is considered. The approach is first to identify the modal parameters by using free response measurement records that could be contaminated with noise. The stiffness and damping matrices are then extracted from the identified modal parameters. The identification technique, which is developed in the time-domain is based on least square linear regression theory and is organized as a systematic and easy to implement scheme. The estimates are produced without the need of solving an eigenvalue problem or singular value decomposition of a data matrix. The effect of measurement noise on estimation accuracy is discussed. A numerical example is presented to illustrate the results.

Non-parametric identification of generalized Hammerstein models

The Hammerstein model is considered in a generalized form, where its nonlinear element can have multi-inputs and a finite memory. The identification of the multi-input finite memory nonimearity and the impulse response sequence of the model is treated using a non-parametric approach. A numerical example is given. The identification results of the example illustrate the effectiveness of the developed technique.

Dynamic Modelling and Accuracy Control of Flexible Arm Manipulators

Abstract In this work, a mathematical model is developed to represent the behavior of flexible arm manipulators, and an inverse dynamics technique is proposed to achieve the prescribed motion trajectory and geometrical constraints, accurately. The present technique has the same number of actuators as needed by the corresponding rigid manipulator. A method based on a lagrangian formulation is presented to investigate the dynamics of the above mentioned multi-link manipulators. A finite element model is developed to study the structural behavior of the anns, using the displacements superimposed on the configuration of the rigid body motion as degrees of freedom. The finite element model is combined with the matrix dynamic fonnulation. Regarding the singularities associated with the elastic degrees of freedom, additional states has been utilized such that the dynamical equations can be solved. Hence, an inverse dynamics technique is proposed to calculate the control forces, which are necessary to achieve the prescribed motions, taking into account the flexibility of the arms. A flexible manipulator is then simulated to illustrate the importance of the present analysis. The results illustrate that the rigidity assumption, of the considered manipulator, leads to considerable errors, and the implementation of the proposed approach, on the basis of the present analysis, can realize the desired motions precisely.

A Statistical Test for Detecting System Nonlinearity & Distinguishing Its Type

Abstract In this paper the problem of nonlinearity detection in dynamic system identification is addressed. The detection problem is formulated in a statistical framework where statistical hypotheses are tested. The test employs two statistics that are functions of third and fourth order cumulants of the system output. The cumulants are estimated from the available noisy data and the statistics are shown to be asymptotically chi-squared distributed. No assumptions are made concerning the functional form of the nonlinearity. It is shown that even and/or odd nonlinearities can be detected by comparing the values of test statistics to their critical values for a given level of significance.

Asymptotic analysis of almost periodic weakly non-linear systems

Asymptotic solutions of weakly non-linear oscillatory systems are considered in this paper. An algorithm is given for constructing an Nth order asymptotic solution for a class of such systems. The asymptotic solution is almost periodic and has a two-time scale property. Fourier like projections are introduced and used in this paper together with perturbation techniques to arrive at the sought asymptotic solution. The results in this paper extend the results by Hoogstraten and Kaper (1975).