PI‐based implementation for modeling and simulation of the continuous‐time LTI system and its Matlab‐Simulink‐based application

Abstract

The continuous‐time “linear time‐invariant” (LTI) system supplies a wide variety of process solutions in science and engineering. It is one of the most fundamental concepts in scientific and engineering education. This article addresses the so‐called PI‐based implementation for modeling and simulation of the continuous‐time LTI system. The PI‐based implementation refers to using “proportional and integral” (PI) elements as well as other basic elements to build and simulate one circuit for the LTI system. In the classical teaching, its simulation implementation usually employs the signal‐flow‐graph approach which is somewhat complicated due to its complex mathematical derivations or other methods in the S‐transform domain. From the perspective of time‐domain analysis, this article introduces one principle of superposition in the time domain for equivalently describing the LTI system. Then by applying the principle, this article presents a straightforward implementation method in the time domain for the PI‐based modeling and simulation of the LTI system. Moreover, compared to its physical implementation, the computer‐based simulation (CBS) provides an extended flexible and graphical approach. Finally, the PI‐based straightforward implementation method in the time domain for modeling and simulation of the LTI system is applied in the Matlab‐Simulink environment. Simulation results and extended applications show workability and potentiality of the presented PI‐based implement method for teaching and study on analysis of the LTI system. The proposed methodology is integrated into a basic course of “signals and systems” for undergraduate students at Hunan University of Science and Technology, China. It may be useful for electronic and electrical engineering studies.

Simulink‐based teaching design for multipath‐effect elimination utilizing convolution analysis and pade approximation

“…For instance, reflections from buildings, mountains, and water bodies, atmospheric ducting, ionospheric reflection, and refraction will result in the multipath effect. This phenomenon may be also called “echo” , which is illustrated in Figure .…”

“…Given h ( t ), how to design the inverse system h i ( t ) to get , it is called the deconvolution . However, the analytic solution of the deconvolution for the continuous‐time system is always unavailable.…”

“…Normally, put , one circuit simulation diagram [12,15] for modeling the LTI system (Equations and 14) is shown in Figure , where, x ( t ) and y ( t ) denote the input and the output, respectively, and Y ( s ) = H ( s ) X ( s ).…”

“…Convolution is one important mathematical integral method in the theory of signals and systems, which is also one of important teaching contents in the basic professional course of “signals and systems” for the electrical and electronic specialty [8,15]. Generalizations of convolution have been employed in a wide range of applications in science and engineering.…”

“…Along with the rapid development of digital computational technology, CAI ("computer aided instruction") as one powerful tool has been widely applied in teaching and study [2,7,5,9,10,11,14]. The Simulink offers a graphical programming environment for modeling, simulation and analysis of multi-domain systems.…”