Control of Chaos in Rate-Dependent Friction-Induced Vibration Using Adaptive Sliding Mode Control and Impulse Damper

Abstract

Two different control methods, namely, adaptive sliding mode control and impulse damper, are used to control the chaotic vibration of a block on a belt system due to the rate-dependent friction. In the first method, using the sliding mode control technique and based on the Lyapunov stability theory, a sliding surface is determined, and an adaptive control law is established which stabilizes the chaotic response of the system. In the second control method, the vibration of this system is controlled by an impulse damper. In this method, an impulsive force is applied to the system by expanding and contracting the PZT stack according to efficient control law. Numerical simulations demonstrate the effectiveness of both methods in controlling the chaotic vibration of the system. It is shown that the settling time of the controlled system using impulse damper is less than that one controlled by adaptive sliding mode control; however, it needs more control effort.

Control of dry friction oscillator using semi-active magneto-rheological tuned liquid column damper

“…There exist numerous works on the theory of oscillations with self-excitation in the literature, for example: influence of the belt speed on the system response, 1 dynamics of three-block mechanical with dry friction, 2 investigation on the geometry of chaotic attractors for dry friction oscillators, 3,4 investigation on the dynamic friction induced vibration with weak and high nonlinearity, 5 dynamic analysis of frictiondriven vibro-impact system, 6 stability analysis of a sliding oscillator subjected to nonlinear friction force, 7 the dynamic behavior of friction driven oscillator with impact damper, 8 and chaotic vibration of a block on a belt system due to the rate-dependent friction. 9 In all of them, an energy source such as electric motor is used to excite the system, but in many real systems, the forcing system has a limited energy source and thus its dynamics is influenced by the oscillating system. 10,11 Dynamics of friction-driven oscillator with limited power supply was investigated and it was shown that the system has a nonperiodic and chaotic vibration.…”