In this paper, a control strategy is applied to a nonlinear ideal and nonideal vibrating system coupled to a magneto-rheological damping structure, exhibiting chaotic behavior. In order to suppress the chaotic oscillations and to improve the transient response, a combination of passive (energy pumping) and active (state feedback) control strategies. The chaotic vibrations are suppressed, bringing the system to a desired periodic orbit. Additionally, the control damping force is transformed into the electrical control signal variable.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)