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. 1. Introduction There exist a lot of works on the theory of friction-driven oscillations in the literature, for example, influence of the belt speed on the system response [1], dynamics of three-block mechanical system with dry friction [2], investigation on the geometry of chaotic attractors for dry friction oscillators [3, 4], influence of parametric and external excitations on a dry friction oscillator dynamics [5], and the dynamic behavior of friction-driven oscillator with an impact damper [6]. The characteristics of the friction force between two surfaces are quite complex and depend on many parameters such as, normal pressure, slip velocity, surface, and material properties [7]. The friction-actuated oscillation is strongly nonlinear, and discontinuous and has nonsmooth process, which is a source of instabilities generating stick-slip, chatter, squeal, and chaos [8, 9]. LuGre friction law is one of the most widely used friction laws which models rate dependency of the friction force by one additional inner variable [10]. In [11], LuGre friction model is applied to the single degree of freedom friction-induced oscillator, and it is shown that the oscillations of this system turned out to be chaotic for most parameter combinations. Many active control methods have been presented for control of chaotic systems such as nonlinear feedback control [12], drive-response synchronization method [13], adaptive control method [14, 15], variable structure (or sliding mode) control method [16–19], back stepping control method [20, 21], fractional control [22], impulsive control [23], and adaptive sliding
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