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

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.