In this paper, a homogenized finite element method for transient analysis of electric apparatus including a multi-turn coil with elliptic cross-section. The tensor-type complex permeability of the multi-turn coil is expanded into partial fractions, which can then be transformed into time-domain. The convolution integral is effectively evaluated using the RC method which does not need large memory storage. It is shown that the power computed by the proposed method is in good agreement with that computed by the conventional finite element method without homogenization.

To obtain an optimum acoustic device with excellent performance in some frequency range (target band), we define the objective function as the squared effective sound pressure integrated over the target band in the topology optimization. To efficiently evaluate the objective function, the frequency response of the sound pressure is, first, estimated by the Pade approximation. Then, the rational polynomial approximation for the response of the´ integrand is derived from the Pade approximation. Finally, the closed-form approximation of the objective function´ is obtained after some manipulations on the integral of the rational polynomial approximation. The topological derivative of the objective function is derived from that of the sound pressure by the chain rule. It is confirmed that the approximation of the response is valid, and the intent of the objective function is achieved in the optimization.

Authors previously proposed a closed loop identification method based on Laguerre functions for an industrial controller with non-linear procedures. In this method, the controlled and manipulated variable are presented in the frequency domain using the orthonormality of the Laguerre functions. The estimated process model is described as their ratio. However, the estimated model has the relative order of 0, which is not suitable for simulation. This paper proposes a method to correct the estimated model to strictly proper model by partial fraction decomposition. The effectiveness of the proposed method is confirmed by PID control simulations for the corrected model and actual model.