实时RK公式稳定域的研究

实时仿真通常要求计算机在一个动态循环中与外部硬件相互作用。外部数据必须从输入信号中采集,并融入到数值积分算法中以计算出状态变量。同样,从积分过程中求得的数据也必须及时被输出。因此,一般希望能选择较大的积分步长,以保证能有足够的计算时间。通过引入稳定域计算比的定义和对一～六阶RTRK公式稳定域的分析,得出了具有最大稳定域的RTRK4公式的实时性最好的结论。为了解决实时仿真中系统特征值集中在实轴附近或虚轴附近的情况,提出了两个特殊形式的RTRK4公式。它们分别具有最大实稳定域和最大虚稳定域。仿真结果表明,它们是有效可行的。

Study on Stability Region of Real-time RK Formulae

Real-time simulation often requires a computer to interact with external hardware in a dynamic loop. Data must be sampled from input signals and incorporated into the numerical integration algorithm to calculate the state variables. Also, data from the integration process must be outputted in time. Thus, the ability for choosing larger integration step-size is often demanded, so as to guarantee enough time for computation. The definition of computation ratio of stability region was introduced, and the analysis of stability region from real-time first-order Runge-Kutta formula to the sixth-order one was carried, and the conclusion of the real-time RK4 formula with maximum stability region having the best character of real-time was gotten. To deal with the circumstances that system eigenvalues gather near real axis or imaginary axis, a real-time RK4 formulae which has maximum real stability region and another one which has maximum imaginary stability region were proposed. The simulation results show that the formulae are feasible and effective.