In this work, exact closed-form solutions are derived for optimizing the resonant shunt circuits of electromagnetic shunt dampers (EMSDs), which use an electromagnetic transducer, and piezoelectric shunt dampers (PZSDs), which use a piezoelectric element, shunted with an electric circuit. Modeling of the EMSD and PZSD is unified by nondimensional parameters. The optimization criteria selected for the EMSD and PZSD are H∞-norm minimization, H2-norm minimization, and exponential time-decay rate maximization. The aim of this study is to derive for the first time the exact solutions that have not previously been investigated, including cases that consider the inherent damping of the primary system. This paper comprehensively summarizes the exact solutions based on the optimization criteria together with approximated solutions obtained by the fixed-point method, which is commonly used to optimize the dynamic vibration absorber (DVA).

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Electromagnetic shunt damping is a sensor-less passive damping technique using an electromagnetic actuator. The accurate values of the parameters of the system are essentially required for designing a controller in the damping technique. This paper proposes a parameter estimation method of an electromagnetic actuator attached to a mechanical structure in order to use for electromagnetic shunt damping. The electromagnetic actuator attached to the structure is modeled as the system including the mechanical and electrical systems which are connected by the electromechanical coupling coefficient. This paper points out a remark on the estimation: The frequency response of the electrical admittance especially neighborhood the natural frequency of the mechanical structure shows an electro-mechanically resonant feature, which does not appear in the pure electrical system without the electromechanical coupling. By applying least squares method to the frequency response data of the electrical admittance neighborhood the natural frequency, the parameters of the mechanical system and the electromechanical coupling coefficient as well as the electrical parameters can be estimated. The proposed estimation method requires only measurements of the frequency response of the electrical admittance across the terminals of the electromagnetic actuator. Therefore, both the parameter estimation and the electromagnetic shunt damping are possible to perform without any displacement or velocity sensors, or any additional actuators. In order to verify the effectiveness of the proposed method, the experiments of parameter estimation and of electromagnetic shunt damping are performed. The experimental results show that the proposed method is effective to estimate the parameters of the electromagnetic actuator without use of any other sensors.

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This paper presents a method of estimating the parameters of an electromagnetic transducer without sensors. The proposed method utilizes the measured admittance of the electromagnetic transducer, and therefore position, velocity, and/or acceleration sensors are not necessary in this framework. Novel impedance models are proposed based on the basic physical principles of electromagnetics; in particular, the effect of eddy currents has been included in these proposed models. The validity of the proposed estimation method and models was experimentally demonstrated by comparing the parameter estimation and vibration control capabilities of the proposed models with three conventional models.