Analysis and Control of Chaos in Nonlinear Gear System using Predictive Sliding Mode Control

Subject Areas : vibration and control

Nima  Valadbeigi ¹ (Department of Mechanical Engineering, Industrial and Mechanics Faculty, Qazvin Islamic Azad University, Iran)
Seyed Mahdi  Abtahi ² (Department of Mechanical Engineering, Industrial and Mechanics Faculty, Qazvin Islamic Azad University, Iran)

Received: 2022-01-13 Accepted : 2022-04-15 Published : 2022-06-01

Keywords: Chaos analysis, Chaotic vibration, Gearbox system, Bifurcation diagram, Predictive Sliding Mode Control,

Abstract :

This paper presents a control system for elimination of chaotic behaviors in spur gear system. To this end, at first different aspects of chaos are investigated by means of numerical tools including time series response, phase plane trajectories, bifurcation diagram, Poincare’ section, Lyapunov exponent and power spectrum density. The nonlinear dynamic model encompasses constant mesh stiffness and damping along the line of action, static transmission error and backlash. In order to suppress the chaotic oscillations, a novel controller on the basis of the Predictive Sliding Mode Control (PSMC) is proposed in which the sliding surface is predicted by the use of model predictive control theory and the control input is obtained. Consequently, the control system takes advantage of the both approaches in developing a robust controller. The simulation results of the feedback system depict the effectiveness of the controller in elimination of the chaotic vibrations along with reduction of settling time, overshoots, and energy consumption. Furthermore, stability and robustness of the system are guaranteed.

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