Understanding Of Transfer Function Research Articles

Teaching transfer functions without the Laplace transform

ABSTRACT Transfer functions are convenient representations to analyse cause-and-effect relationships of linear time-invariant dynamic systems. Traditionally, transfer functions are introduced using the Laplace transform. In this paper, we argue that the Laplace transform method is not a necessary prerequisite to understanding the topic ‘transfer functions’. We offer an inquiry-based learning method to represent transfer functions without formally using the full machinery of Laplace transforms. The method is used in an introductory engineering course on system modelling and simulation at Aalborg University, Denmark. The paper also presents an initial assessment of the students' understanding of transfer functions without knowledge of Laplace transforms and the experiences gained from implementing inquiry-based learning in the course. Finally, we conclude with a discussion of the impact of CAS tools on mathematics and engineering science teaching and learning.

Discuss about Linear System Transfer Function and Optical Transfer Function

Transfer function (TF) for linear time invariant system and optical transfer function (OTF) for linear space shaft invariant system are compared and contrasted. TF is the unilateral Laplace transform of system’s one-dimensional unit impulse response, dimensions of the input and output may be same or different, TF can be used to describe a variety of filter or to express solution of linear differential equations accurately. But OTF is the Fourier transform of system’s two-dimensional impulse response, dimensions of the input and output must be same, OTF can be used only to describe a low-pass filter or to express solution of the linear univariate partial differential equations approximately. Their eigenfunctions are similar complex exponential functions. OTF has stricter requirements and application conditions than TF. It is helpful to the readers’ understanding of TF and OTF.

The Popov criterion and the inverse Nyquist method†

Kosonbrock's inverse Nyquist array (I.N.A.) theory for linear multivariable control Bystema with constant feedback elements is extended, to include systems lip to m nonlinear feedback elements, where the system has m inputs and m outputs. This extension is achieved by considering the Popov criterion for the most general case and through two further theorems. It shows that, as in the ease of Rosenbrock's I.N.A. theory, when certain auxiliary conditions are met with the help of suitable controllers, the design of multivariable controllers containing many non-linear feedbacks, can be based on the m frequency response loci corresponding to the diagonal entries of the open-loop inverse transfer function matrix. This leads to a simple design technique identical to the I.N.A. design method, suitable for use with a computer-aided design facility which permits a designer to use his intuitive understanding of transfer functions based on classical theory. The I.N.A. theory has been extended by Rosenbrock to cover sy...