Document Type : Research

Authors

• Mehrasa Ayatollahi ¹
• Maryam Rouzbehi ²

¹ Department of mathematics. Payame noor university, Tehran. Iran.

² Department of physics Payame noor university Tehran Iran

Abstract

A B S T R A C T

In this research, we investigate the stability of harmonic oscillator systems. To achieve this, we transform the differential equation describing the oscillator into a state-space model using appropriate variables, enabling the application of matrix algebraic relationships to design a stabilizing controller for the system under study. Within the state-space framework, by utilizing state matrices and eigenvalue assignment techniques, we can develop a state feedback control law. The parameters of this controller are tuned such that the closed-loop system eigenvalues (which determine stability) are positioned in favorable locations within the complex plane, thereby ensuring system stability.

Keywords

• Harmonic Oscillator
• Stability
• State-Space Model
• Eigenvalue Assignment