Abstract
— Linear time invariant (LTI) systems are widely used for modeling of dynamics systems in science and engineering problems. Harmonic oscillation of LTI systems is an outstanding case of LTI system behavior and it is employed for modeling of many periodic physical phenomenon in nature. This study investigates sufficient conditions to obtain harmonic oscillation by using high-order LTI systems. A design procedure for controlling harmonic oscillation of single-input single-output high-order LTI systems is presented. LTI system coefficients are calculated by solving equation sets, which imposes a stable sinusoidal oscillation solution for the characteristic polynomials of LTI systems. Moreover, these analyses are extended to fractional order LTI systems. Simulation examples are demonstrated for high-order LTI systems and the control of harmonic oscillations are discussed by using Hilbert transform and spectrogram of oscillation signals
Highlights
IntroductionL INEAR Time Invariant (LTI) system modeling methods have been played an important role in development of science and technology for a century
We consider stability boundary as the oscillation locus andL INEAR Time Invariant (LTI) system modeling methods have been played an important role in development of science and technology for a century
Behaviors of dynamic systems can be well characterized by Linear time invariant (LTI) system models and consistency of LTI system analyses with real systems has been proven for numerous applied science and engineering problems
Summary
L INEAR Time Invariant (LTI) system modeling methods have been played an important role in development of science and technology for a century. LTI models have found a widespread utilization in theoretical and numerical analyses of linear dynamic systems. Behaviors of dynamic systems can be well characterized by LTI system models and consistency of LTI system analyses with real systems has been proven for numerous applied science and engineering problems. It is obvious that analyses on the base of LTI systems still play a central role in system science, today. Deepened investigation on behaviors of LTI systems promises further contributions in term of modeling and comprehension of physical and electrical system behaviors. The characteristic polynomial of the LTI systems provides a valuable tool for the analysis of the character of LTI system extend our investigation for the harmonic oscillation of LTI systems
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