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In order to break the bottleneck of the integer-order transfer function in vehicle ISD (inerter-spring-damper) suspension design, a positive real synthesis design method of vehicle mechatronic ISD suspension based on the fractional-order biquadratic transfer function is proposed. The emergence of the fractional-order components disrupts the equivalence relationship between the passivity of components and the positive realness of integer-order transfer functions in traditional networks. In this paper, the positive real condition of the fractional-order biquadratic transfer function is given. Then, a quarter dynamic model of the vehicle mechatronic ISD suspension is established, and the parameters of the fractional-order biquadratic transfer function and vehicle suspension are obtained by an NSGA-II multi-objective genetic algorithm. Moreover, the structure of the external circuit and the parameters of the electrical components are obtained by the fractional-order passive network synthesis theory. The simulation results show that under the condition of random road input and vehicle speed of 20 m/s, the root-mean-square (RMS) value of the vehicle body acceleration and the dynamic tire load of the fractional-order ISD suspension are reduced by 7.98% and 18.75% compared with the traditional passive suspension, while under the same condition, the integer-order ISD suspension can only reduce by 5.34% and 16.07%, respectively. The results show that employing a fractional-order biquadratic electrical network in the vehicle mechatronic ISD suspension enhances vibration isolation performance compared with the suspension using an integer-order biquadratic electrical network.
Shen et al. (2025) studied this question.