State observation–based control algorithm for dynamic vibration absorbing systems featuring magnetorheological elastomers: Principle and analysis

Based on state observation, a rapid, stable, and effective control algorithm for magnetorheological elastomer (MRE)–based dynamic vibration absorbers (DVAs) applied to automobile powertrain mount systems is proposed and investigated in this article. The state-space model for powertrain mount systems with MRE-based DVAs is established using the rank criterion method for observable systems. According to the principle of system reconfiguration, a full state observation model using an adaptive Kalman filter with Sage–Husa noise estimator is developed. With the state vectors estimated by the Kalman filter, the phase difference between the displacement of the dynamic mass of the MRE-based DVA relative to the powertrain and the absolute displacement of the powertrain is updated continuously based on Simpson’s rule. By adjusting the applied current to the MRE-based DVA with fuzzy logic control corresponding to the cosine value of the phase difference, the natural frequency of the MRE-based DVA could track the excitation frequency of the powertrain well, which results in vibration attenuation of the powertrain mount system. With consideration of excitation noise, time delays, and parametric uncertainties, the simulation experiments of vibration attenuation performance of the MRE-based DVA for the powertrain mount systems when under time-varying excitation are carried out to verify the effectiveness and the stability of the proposed algorithm with fuzzy steps. The simulation results show that when using the proposed algorithm with fuzzy steps, the MRE-based DVA could attenuate the powertrain vibration rapidly and effectively, and the vibration attenuation performance will not be influenced by noise, time delays, and parametric uncertainties.