Exponential Fourier Series

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H. Rahmani - One of the best experts on this subject based on the ideXlab platform.

  • Parameter identification of time-delay systems via Exponential Fourier Series
    International Journal of Systems Science, 1991
    Co-Authors: Babak A. Ardekani, M. Samavat, H. Rahmani
    Abstract:

    A delay matrix D is derived and used along with the Exponential Fourier operational matrix of integration in a new algorithm for parameter identification of LTI delayed systems. The main advantage of this method over similar algorithms is that Fast Fourier Transform (FFT) can be employed for determining expansion coefficients. Therefore, it reduces the computing time considerably. A second advantage is that the Fourier delay and integration matrices are simpler than their counterparts associated with other orthogonal functions. This further reduces compulations. An example is given which shows that the algorithm gives accurate parameter estimates.

M. Samavat - One of the best experts on this subject based on the ideXlab platform.

  • Analysis and Parameter Identification of Scaled Systems via Exponential Fourier Series
    1992
    Co-Authors: M. Samavat, M.a. Vali
    Abstract:

    A scaled matrix S is derived and used along with the Exponential Fourier operational matrix of integration in a new algorithm for analysis and parameter identification of scaled systems. As illustrated in the examples the Fourier Exponential approach has a good accuracy in analysis and parameter identification of scaled systems. Also this method enables us to use the Fast Fourier Transform (FFT) to obtain the Fourier coefficients which reduces the computing time considerally [1].

  • Parameter identification of time-delay systems via Exponential Fourier Series
    International Journal of Systems Science, 1991
    Co-Authors: Babak A. Ardekani, M. Samavat, H. Rahmani
    Abstract:

    A delay matrix D is derived and used along with the Exponential Fourier operational matrix of integration in a new algorithm for parameter identification of LTI delayed systems. The main advantage of this method over similar algorithms is that Fast Fourier Transform (FFT) can be employed for determining expansion coefficients. Therefore, it reduces the computing time considerably. A second advantage is that the Fourier delay and integration matrices are simpler than their counterparts associated with other orthogonal functions. This further reduces compulations. An example is given which shows that the algorithm gives accurate parameter estimates.

Babak A. Ardekani - One of the best experts on this subject based on the ideXlab platform.

  • Parameter identification of time-delay systems via Exponential Fourier Series
    International Journal of Systems Science, 1991
    Co-Authors: Babak A. Ardekani, M. Samavat, H. Rahmani
    Abstract:

    A delay matrix D is derived and used along with the Exponential Fourier operational matrix of integration in a new algorithm for parameter identification of LTI delayed systems. The main advantage of this method over similar algorithms is that Fast Fourier Transform (FFT) can be employed for determining expansion coefficients. Therefore, it reduces the computing time considerably. A second advantage is that the Fourier delay and integration matrices are simpler than their counterparts associated with other orthogonal functions. This further reduces compulations. An example is given which shows that the algorithm gives accurate parameter estimates.

John Y Hung - One of the best experts on this subject based on the ideXlab platform.

  • Design of the most efficient excitation for a class of electric motor
    IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1994
    Co-Authors: John Y Hung
    Abstract:

    Three basic concepts often used in circuit and system theory are innovatively combined to design the minimum power excitation that produces smooth torque in a popular class of electric motor. First, the Exponential Fourier Series is used to represent currents and voltages in three-phase permanent magnet motors. Second, the developed torque is modeled by convolutions of current and voltage harmonics. The torque model can be compactly written as a set of linear equations, in which the currents must be solved to yield smooth torque. However, the set of linear equations is underdetermined, so there is an infinite number of solutions. Hence, the solution that is chosen is the "minimum norm" solution. In practical terms, the resulting current waveforms are optimal in the sense of minimum average power. An example calculation for an actual motor is presented, and theoretical efficiency and torque ripple performance results are compared to that achieved by the popular rectangular current excitation. >

  • design of currents to reduce torque ripple in brushless permanent magnet motors
    IEE Proceedings B Electric Power Applications, 1993
    Co-Authors: John Y Hung, Z Ding
    Abstract:

    A method to design an improved motor excitation for three-phase brushless permanent magnet motors is presented. The unique motor excitation reduces ripple in the developed torque, reduces the effects of cogging or detent torque, and is also a minimum average power excitation. Practical benefits are reduced vibration and acoustic noise in speed control applications, and improved accuracy in position control applications. First, an analysis of torque ripple is presented using the Exponential Fourier Series in the torque model. The analysis is simple, yet extends some well known results by predicting the presence of additional harmonic components. Next, the design of an optimal weighting of stator current harmonics is cast as a type of constrained minimisation problem. In contrast to iterative approaches that have been reported in the past, the new design method determines the current harmonic weights in closed form. Steps in the design procedure are demonstrated using measured back EMF data from a 2 hp brushless DC motor.< >

  • minimization of torque ripple in permanent magnet motors a closed form solution
    International Conference on Industrial Electronics Control and Instrumentation, 1992
    Co-Authors: John Y Hung, Z Ding
    Abstract:

    A closed-form solution for minimizing torque pulsations or ripple in three-phase permanent magnet motors by the appropriate weighting of input current harmonics is presented. First, an analysis of torque ripple is presented by using the complex Exponential Fourier Series. In addition, a method to design the optimal weighting of current harmonics is developed by using constrained optimization techniques. In contrast to iterative approaches, the proposed design method determines the current harmonic weights in closed form; the procedure is especially easy to perform. Steps in the design procedure are demonstrated by a numerical example. Application of the optimal current should reduce torque-induced motor vibration and noise, as well as improve accuracy in servo applications. >

George G. Adams - One of the best experts on this subject based on the ideXlab platform.

  • The Point-Load Solution and Simulation of a Flexible Spinning Disk Using Various Disk-to-Baseplate Air-Flow Models
    Tribology Transactions, 1993
    Co-Authors: George G. Adams
    Abstract:

    In magnetic and/or optical recording on flexible media, an elastic disk rotates at a constant angular velocity in close proximity to a stationary baseplate. Such a configuration can be used to stabilize the transverse motion of the flexible disk, whose natural frequencies and critical speeds would otherwise be too low for stability of the flexible-disk-to-head interface. In this investigation, the air-flow between the disk and the baseplate is accounted for by two foundation parameters, stiffness and damping, for each Fourier mode. The effect of using this new model and three other models on the point-load solution and on the simulation of the disk-to-head interface is investigated. Steady-state solutions are obtained by using an Exponential Fourier Series expansion in the circumferential direction and a finite difference approximation radially. The simulation solution also accounts for the effect of disk-to-head contact in an approximate manner. It is further shown that the use of a Fejer sum for the Fou...

  • The Point-Load Solution Using Linearized von Kármán Plate Theory for a Spinning Flexible Disk Near a Baseplate
    Tribology Transactions, 1992
    Co-Authors: J. F. Maher, George G. Adams
    Abstract:

    In magnetic and/or optical recording on flexible media, an elastic disk rotates at constant angular velocity in close proximity to a stationary baseplate. Such a configuration is used to stabilize the transverse motion of the flexible disk whose natural frequencies and critical speeds would otherwise be too low for stability of the flexible-disk-to-head interface. The influences of coupling between the in-plane displacements and transverse deflections (von Karman plate theory) and of the air flow between the disk and the baseplate are investigated. Steady-state solutions, for this nonaxisymmetric problem, are obtained by linearizing the partial differential equations about the axisymmetric configuration due to the baseplate alone. These equations are solved using an Exponential Fourier Series expansion in the circumferential direction and a finite difference approximation radially. The results are the transverse and in-plane deflections of the disk and the air film pressure. Comparisons are made with othe...