Efficient Numerical Integration and Table Lookup Techniques for Real Time Flight Simulation

Abstract

Table look-up and numerical integration techniques that are suitable for the real-time implementation in flight simulators are the subject of study in this paper. A typical flight simulator consists of models of various elements such as the flight dynamic model, filters and actuators, which have fast and slow eigen values in the overall system. This results into an electromechanical control system of stiff ordinary differential equations. It may be possible to solve these equations with small step size, but this would affect the speed of computation. The concept of multi-rate integration scheme is recommended for real time flight simulation where it is possible to use a step size for the actuator simulation that is sufficiently small to ensure an accurate and stable numerical solution and a larger step size for simulating the slower dynamics of the airframe. Similarly, accessing huge aerodynamic and engine database in table look-up format at high speed is an essential requirement for high fidelity real time flight simulation. A study is carried out by implementing the numerical integration and table lookup techniques in a real time flight simulator facility designed and developed in house. Table lookup techniques such as linear search and index computation methodology using novel Virtual Equi-Spacing concept are studied. From the results, it is found that the multi-rate integration technique and the table look up using Virtual Equi-Spacing concept perform better.