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Many engineering systems undergo undesirable vibrations. Vibration control in mechanical systems is an important problem by means of which vibrations are suppressed or at least attenuated. In this direction, the dynamic vibration absorbers have been widely applied in many practical situations because of their low cost/maintenance, efficiency, accuracy and easy installation (Braun et al., 2001; Preumont, 1993). Some of their applications can be found in buildings, bridges, civil structures, aircrafts, machine tools and many other engineering systems (Caetano et al., 2010; Korenev & Reznikov, 1993; Sun et al., 1995; Taniguchi et al., 2008; Weber & Feltrin, 2010; Yang, 2010). There are three fundamental control design methodologies for vibration absorbers described as passive, semi-active and active vibration control. Passive vibration control relies on the addition of stiffness and damping to the primary system in order to reduce its dynamic response, and serves for specific excitation frequencies and stable operating conditions, but is not recommended for variable excitation frequencies and/or parametric uncertainty. Semiactive vibration control deals with adaptive spring or damper characteristics, which are tuned according to the operating conditions. Active vibration control achieves better dynamic performance by adding degrees of freedom to the system and/or controlling actuator forces depending on feedback and feedforward real-time information of the system, obtained from sensors. For more details about passive, semiactive and active vibration control we refer to the books (Braun et al., 2001; Den Hartog, 1934; Fuller et al, 1997; Preumont, 1993). On the other hand, many dynamical systems exhibit a structural property called differential flatness. This property is equivalent to the existence of a set of independent outputs, called flat outputs and equal in number to the control inputs, which completely parameterizes every state variable and control input (Fliess et al., 1993; Sira-Ramirez & Agrawal, 2004). By means of differential flatness techniques the analysis and design of a controller is greatly Design of Active Vibration Absorbers Using On-Line Estimation of Parameters and Signals 2