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Based on the analysis of a double-layer vibration suppression bilinear system, the limitation of the classic passive vibration suppression technology was solved in case of relatively complex input force mixed signals. Using the maximum value principle and the constrained gradient method, the optimal damping semi-active control (ODSAC) curve of this system model was obtained. Due to the strong nonlinear characteristics of the controlling curve and even a non-derivable problem being existed, a pulse function was introduced, and a theoretic deduction was performed. The defects, that a curve with non-derivable points could not be solved, were overcome so that the proposed method was applicable to a bilinear system model. The stability of the controller was discussed in detail. Finally, the effects of the vibration suppression of the ODSAC method were compared with that of the passive damping system and that of the semi-active skyhook damping system under the excitation of the mix signal of single-frequency sine and pulse input signal, the mix signal of random and sine signal, the mix signal of random and impact input signal. The experiments of electro-rheological fluid (ERF) damper with single damping duct and simulation results show that the ODSAC strategy of a double-layer vibration suppression bilinear system is the best of the five kinds of vibration suppression effect of control strategies, and the vibration reduction effect with respect to the random and shock input mixed signal is remarkable, the vibration suppression effect of the new method is satisfactory.

Double-layer vibration suppression bilinear system featuring electro-rheological damper with optimal damping and semi-active control