Reduction of Time Delays in Runge-Kutta Integration Methods

摘要

A fourth order accurate Runge-Kutta (RK4) method for real time system simulation is proposed, where data must be sampled from input signals and incorporated into the numerical integration algorithms in order to evaluate the derivatives of the state variables. The method is compared to a standard RK4 for a flight simulation. Simulation of a one DOF-system with varying damping ratios shows that the accuracy of the proposed routine is equal (in the case of constant input function) or slightly superior (in the case of sinusoidal input) to the RK4 standard method. The results are for a system requiring no extrapolation. Simulation of a complex real time system (approach and touchdown of aircraft) shows that the proposed routine provides an increase in accuracy over the RK4 standard method even beyond decreasing the size of steps in output signals. This is particularly important when system variables change with high frequency and large increments.