The magnetorheological elastomer (MRE) is a kind of smart material, which is often processed as vibration isolation and\nmitigation devices to realize the vibration control of the controlled system. The key to the effective isolation of vibration and shock\nabsorption is how to accurately and in real time determine the magnitude of the applied magnetic field according to the motion\nstate of the controlled system. In this paper, an optimal fuzzy fractional-order PID (OFFO-PID) algorithm is proposed to realize\nthe vibration isolation and mitigation control of the precision platform with MRE devices. In the algorithm, the particle swarm\noptimization algorithm is used to optimize initial values of the fractional-order PID controller, and the fuzzy algorithm is used to\nupdate parameters of the fractional-order PID controller in real time, and the fractional-order PID controller is used to produce\nthe control currents of the MRE devices. Numerical analysis for a platform with the MRE device is carried out to validate the\neffectiveness of the algorithm. Results show that the OFFO-PID algorithm can effectively reduce the dynamic responses of the\nprecision platform system. Also, compared with the fuzzy fractional-order PID algorithm and the traditional PID algorithm, the\nOFFO-PID algorithm is better.
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