使用高阶无条件稳定显式算法的实时混合模拟稳定性

Stability of Real-Time Hybrid Simulation Using High-Order Unconditionally Stable and Explicit Algorithms

摘要:

为了提高实时混合模拟（RTHS）计算效率、计算精度和稳定性，基于具有二阶精度的无条件稳定显式Chen?Ricles（CR）和Chang积分算法，提出具有高阶精度的无条件稳定新型双显式（NDE）和新型半显式（NSE）积分算法。基于离散控制理论，推导出使用两种高阶算法的RTHS系统的闭环离散传递函数，分析了时滞、阻尼比、刚度比例系数、积分算法等对RTHS系统稳定性的影响，并以时滞微分方程推导出的近似解和精确解作为参照。分析结果表明，时滞会降低RTHS系统的稳定性；增大刚度比例系数会降低不同分析结果间的差异；增大阻尼比会提升RTHS系统的稳定性，同时会增大考虑积分算法与不考虑积分算法的稳定性差异，也会增大使用不同积分算法的稳定性差异；使用两种高阶算法的RTHS系统稳定性优于使用两种二阶算法的RTHS系统稳定性。

关键词:实时混合模拟;积分算法;稳定性;离散控制理论

Abstract:

To provide high computational efficiency， accuracy and stability integration algorithms for real-time hybrid simulation （RTHS）， the high order accurate， unconditionally stable new dual-explicit （NDE）， and new semi-explicit （NSE） algorithms were developed based on the second-order accurate unconditionally stable and explicit Chen-Ricles （CR） and Chang algorithms. Based on the discrete control theory， the closed-loop discrete transfer function of the RTHS system using the two new algorithms were derived. The influences of time delay， damping ratio， stiffness proportional ratio， and integration algorithm on the stability of the RTHS system were investigated. Additionally， the approximation solution and accurate solution derived from the delay differential equation were also adopted for reference. The analytical results show that the time delay decreases the stability of the RTHS system. Increasing the stiffness proportional ratio reduces the difference between different analysis results. Increasing the damping ratio improves the stability of the RTHS system， enlarges the difference between the stability with and without considering the integration algorithm， and magnifies the difference between the stability using different integration algorithms. The stability of the RTHS system using the two high-order accurate integration algorithms is superior to that of the two second-order accurate integration algorithms.

Key words:real-time hybrid simulation (RTHS);integration algorithm;stability;discrete control theory