非线性机电换能器混沌系统的分数阶控制及其电路仿真

摘要

Anstract: The chaos feature of the bifurcation and the largest Lyapunov exponent for a self-sustained electro-mechanical transducer coupled system are obtained by numerical analysis in this paper.According to the theo-ries of fractional order calculus and the Gershgorin cycle theorem,two fractional order feedback controllers of this system are designed.The circuit implementation is simulated using Multisim for electromechanical control system by the proposed methods.And the simulation results demonstrate the effectiveness of the proposed fractional order controller for the chaos control of electromechanical transducer.Meanwhile,the circuit design is feasible and can be realized.%通过数值分析计算一类自激机电换能器耦合系统的分叉、最大Lyapunov 指数等混沌特性，并运用分数阶稳定性理论及Gershgorin圆定理证明并构造两个反馈控制器。采用所提方法，运用 Multisim软件对机电控制系统进行电路实验仿真验证。实验结果表明：所设计的分数阶控制器对机电换能器的混沌控制是有效的，同时，电路设计具有可行性和可实现性。