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In control mechanical systems design, the velocity signal is not always available and may be corrupted by noise. It is therefore necessary to estimate it in order to construct the control law. This paper proposes a new sliding mode observer for nonlinear mechanical systems subject to non smooth impacts. The estimation of the velocity signal is derived from only position measurements. The proposed observer ensures an asymptotic velocity observation also in presence of non-smooth impacts. Excellent simulation results are included to show the effectiveness of the proposed approach.

This paper presents a new method of controlling chaos in the nonlinear Van Der Pol oscillator with uncertainties. The proposed method is based on a nonlinear observer to estimate unmeasured velocity signal coupled to a control law. The observer ensures, firstly, an asymptotic convergence of the velocity estimation error. Then, the control law, which is based on the estimated variables, forces the output system to track a desired trajectory despite presence of uncertainties (external forces) on the system dynamics. Simulation results are provided to show the effectiveness of the proposed control strategy.

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