基于增量谐波平衡法的流量调节器非线性频率特性

Research of the Flow Regulator Nonlinear Frequency Characteristics by Incremental Harmonic Balance Method

关键词:  流量调节器  增量谐波平衡法  周期解  非线性频率特性

Key words:  Flow regulator  IHB method  Periodic solution  Nonlinear frequency characteristics

摘要:

针对多个状态变量、非线性关系复杂、方程刚性强的流量调节器系统,应用增量谐波平衡法研究了调节器在入口压力扰动下的强迫振荡问题,得到了系统周期解的解析表达式。通过与龙格库塔数值仿真结果相比较,验证了增量谐波平衡法应用于该系统的有效性,且计算量相对较小。进而在频域内探讨了流量调节器系统的非线性频响特性,结果表明,随着扰动振幅的增大,幅频响应在整个频率范围上都有所增大。计算结果可以用于评估线性化方法的误差范围。通过分析周期解的时均值与稳态值的差别,揭示了调节器受上游压力周期扰动时,其出口流量的时均值略低于稳态值的非线性特性。 

Abstract:

For a flow regulator system with many state variables, complicated nonlinear relationship and strong stiffness of the model equations, the incremental harmonic balance method was applied to study the forced oscillation of such a regulator under inlet pressure disturbance, and the analytical expressions of periodic solutions were derived. The accuracy, validity and less calculation cost of the methodology employed for this system were confirmed by comparing the analytical solutions with results from Runge-Kutta numerical integration. Then the nonlinear frequency response characteristics of the system were discussed in frequency domain, and the results indicate that the amplitude-frequency response of the flow regulator increases with enlarging the amplitude of pressure perturbation within the whole frequency range. The error range of linearized method could be evaluated by the results. By comparing the time-averaged value of periodic solutions with steady state value, a nonlinear property reveales that the time-averaged value of the regulator outlet flow rate is slightly below the steady state value under periodic disturbance of inlet pressure.