This thesis is focused on the dynamics and control of nonlinear engineering systems. A developed approach is applied to three specific problems: suppression of torsional vibrations occurring in a drill-string, lateral vibrations on an unbalanced rotor and vibrational energy extraction from rotating pendulum systems. The first problem deals with drill-string torsional vibrations while drilling, which is conducted in the experimental drilling rig developed at University of Aberdeen. A realistic model of the experimental setup is then constructed, taking into account the dynamics of the drill-string and top motor. Physical parameters of the experimental drilling rig are estimated in order to calibrate the model to ensure the correspondence of the research results to the experimental conditions. Consequently, a control method is introduced to suppress torsional and stick-slip oscillations exhibited in the experimental drilling rig. The experimental and numerical results considering delay of the actuator are shown to be in close agreement, including the success of the controller in significantly reducing the vibrations. In the second problem a soft impact oscillator approach is used to study the dynamics of the asymmetric Jeffcott rotor. A realistic model of the experimental setup is developed, taking into account an asymmetric physical configuration in rotor part as well as snubber rig. Several experimental bifurcation diagrams are conducted with different conditions in range around the grazing point. Experimental and numerical results based on the proposed model are compared and shown to be in close agreement. The last problem relates to initiating and maintaining the rotational motion of a parametric pendulum as an energy harvesting system. Several possible control methods to initiate and maintain the rotational motion of a harmonically-excited pendulum are proposed and then verified experimentally. The time-delayed feedback method is shown to maintain quite well the rotational motion of a sinusoidally excited parametric pendulum, even in the presence of noise. A control method for the wave-excited pendulum system is then suggested and tested in order to increase the probability of its rotational motion. This proposed control method succeeds in significantly raising the probability of rotational motion of the wave-excited pendulum.

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