Abstract
The magnetorheological elastomer (MRE) is a kind of smart material, which is often processed as vibration isolation and mitigation devices to realize the vibration control of the controlled system. The key to the effective isolation of vibration and shock absorption is how to accurately and in real time determine the magnitude of the applied magnetic field according to the motion state of the controlled system. In this paper, an optimal fuzzy fractional-order PID (OFFO-PID) algorithm is proposed to realize the vibration isolation and mitigation control of the precision platform with MRE devices. In the algorithm, the particle swarm optimization algorithm is used to optimize initial values of the fractional-order PID controller, and the fuzzy algorithm is used to update parameters of the fractional-order PID controller in real time, and the fractional-order PID controller is used to produce the control currents of the MRE devices. Numerical analysis for a platform with the MRE device is carried out to validate the effectiveness of the algorithm. Results show that the OFFO-PID algorithm can effectively reduce the dynamic responses of the precision platform system. Also, compared with the fuzzy fractional-order PID algorithm and the traditional PID algorithm, the OFFO-PID algorithm is better.
Highlights
Mathematical Model of the Controlled SystemAccording to equation (1), it can be seen that the responses of the precision platform are affected by the adjustable stiffness of the magnetorheological elastomer (MRE) device
An optimization fuzzy fractional-order PID control algorithm (OFFO-PID) is proposed to control the isolation and vibration reduction system of the precision platform based on magnetorheological elastomer (MRE), and the algorithm is composed of the fuzzy control algorithm and the fractional PID algorithm based on particle swarm optimization (PSO), which significantly improve the control accuracy of the system
Using SIMULINK simulation platform, the mathematical model of the precise platform structure and the OFFO-PID control algorithm were simulated and analyzed. e simulation results of OFFO-PID are compared with the simulation results of unoptimized fuzzy fractional PID, no control condition, and traditional PID. e analysis results show that the OFFO-PID can effectively suppress the vibration response of the precision platform under certain vibration disturbance, and the simulation results show that it is obviously superior to the no control condition, unoptimized condition, and traditional PID control
Summary
According to equation (1), it can be seen that the responses of the precision platform are affected by the adjustable stiffness of the MRE device. From equation (3), it can be seen that ΔGm can be adjusted by changing the intensity of the external magnetic field. The intensity of the external magnetic field can be adjusted by changing the control currents. According to the formula of magnetic field strength, H0 IcN/Le. So, the functional relationship between ΔGm and the control current Ic can be obtained as
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