The Inertial Electromagnetic Actuator
Actuators are the main element in active vibration control to provide secondary forces acting on the structure to damp out the unwanted vibration brought on by impulsive disturbances . It familiarly can be classified into two types; electromechanical actuator which is normally implementing magnetic field to accelerate the proof mass and fluid mechanical actuator that uses fluid power from hydraulic and pneumatic to move its cylinders, as illustrated in Figure 1 and Figure 2, respectively.
Figure 1: Inertial actuator for Figure 2: Hydraulic actuator 
electromechanical purpose 
Generally, electromagnetic mechanism is preferred as an inertial actuator mechanism because it has a long lifespan compared to piezoelectric and electrostatic devices so as to suffer from degradation and leakage effect, respectively. In additional, for huge application for example in controlling cutting or grinding tool and aircraft fuselages & wings, inertial electromagnetic actuator more practical in producing secondary force to control the structures. Moreover, it is widely studied due to established theories and progress in integration of permanent magnets with MEMS devices .
Usually, inertial actuator and sensor (i.e. accelerometer) are designed separately for the research purpose and embedded unit are more efficient for the commercialization purpose. By focusing on an inertial actuator or proof mass actuator, the most widespread concept is an electromagnetic mechanism [5-7] and seconded by piezoelectric as studied by [8, 9]. Winberg  has introduced the concept of analogy mobility to verify how the proof mass actuator and the spring constant of the suspension affect the natural frequency and output of the actuator. By taking lightly-damped panels as a vibrating structure, Paulitsch uses Finite Element Analysis to optimize the characterization of the inertial actuator resulting maximum force of 3N by 20g weight . In addition, the natural frequencies of actuator suspension are also designed to be laid outside the desired control bandwidth. The saturation of the stroke length issue or nonlinear behavior of the proof-mass was investigated by Scruggs . He proposed two indicators for nonlinear behavior; the linear region radius and the operating region radius. By concerning the similar issue, Lindner  in his work found that when the actuator sized such that the saturation break frequency matches the natural frequency of the structure, the actuator is optimally utilized. Still in the same issue, a time domain model of a plate structure with multiple inertial actuators has been proposed  to optimize the decentralized controller in the AVC system. Furthermore, to overcome the instability of the velocity feedback controller that subject to stroke saturation , a simple nonlinear, time domain model of an inertial actuator mounted on a single degree of freedom is presented. Seeing to the importance of active vibration control mechanism, development of inertial actuator with considering a lot of aspect i.e. size of mass, frequency bandwidth, stroke limitation in nonlinear issue; has driven the researchers to produce more reliable, effective and robust inertial actuator. From the above studies, the nonlinear behavior that affects the stability of the inertial actuator becomes the most ongoing topic to be explored.
- J. Scruggs and D. K. Lindner, "Optimal Sizing of a Proof-Mass Actuator," in Proceedings of the AIAA/ASME/ASCE/AHS/ASC 40th Structures, Structural Dynamics, and Materials Conference, St. Louis, CA, 1999, pp. 876 - 886.
- G. Priyandoko, et al., "Vehicle active suspension system using skyhook adaptive neuro active force control," Mechanical Systems and Signal Processing, vol. 23, pp. 855-868, 2009.
- "Active Damping Devices and Inertial Actuators," Micromega-Dynamics, Ed., ed. Angleur, Belgium.
- Y. Jiang, et al., "Fabrication and evaluation of NdFeb microstructure for electromagnetic energy harvesting," presented at the PowerMEMS 2009, Washington DC, USA, 2009.
- A. Behrens, et al., "Electromagnetic shunt damping," in 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003), 2003, pp. 1145-1150.
- D. Niederberger, et al., "Adaptive electromagnetic shunt damping," in IEEE/ASME Transactions on Mechatronics, 2006, pp. 103-108.
- C. Paulitsch, et al., "Design of a lightweight, electrodynamic, inertial actuator with integrated velocity sensor for active vibration control of a thin lightly-damped panel," in Proceding of International of Noise and Vibration Engineering, Leuven, Belgium, 2004.
- M. S. Weinberg, "Working equations for piezoelectric actuators and sensors," Journal of Microelectromechanical Systems, vol. 8, pp. 529-533, 1999.
- G. Lesieutre, "Modelling and characterization of a piezoceramic inertial actuator," Journal of Sound and Vibration, vol. 261, pp. 93-107, 2003.
- M. Winberg, et al., "Inertial mass actuators, understanding and tuning," presented at the 11th International Congress on Sound and Vibration (ICSV11), St Petersburg, Russia, 2004.
- D. K. Lindner, et al., "Performnance and control of proof-masss actuators accounting for stroke saturation," AIAA Journal of Guidance, Control, and Dynamics, vol. 17, pp. 1103 - 1108, 1994.
- O. N. Baumann and S. J. Elliott, "The stability of decentralized multichannel velocity feedback controllers using inertial actuators," The Journal of the Acoustical Society of America, vol. 121, p. 188, 2007.
- O. N. Baumann and S. J. Elliott, "Destabilization of velocity feedback controllers with stroke limited inertial actuators," The Journal of the Acoustical Society of America, vol. 121, p. EL211, 2007.