Nonlinear Aircraft Trim Using Interval Analysis
Erik-Jan Van Kampen, Q. P. Chu, Jan Albert Mulder, M. H. van Emden · AIAA Guidance, Navigation, and Control Conference and Exhibit · 2007
A new method, based on interval analysis, is proposed for finding the equilibrium or trim conditions of an aircraft, which is an important tool in flight control system design and flight simulation. Interval analysis deals with computations on intervals of numbers as opposed to computations on crisp numbers in ordinary arithmetic. Interval analysis generates lower and upper bounds for the result of a computation and is an excellent tool for global nonlinear optimization problems. The advantage of interval analysis over classical optimization algorithms is that it will detect all minima and maxima within a search space, compared to the classical algorithms that only find a local optimum closest to some initial point. In this paper we show how interval analysis can be used to find all solutions to the steady state equations of motion for any type of aircraft model to any desired accuracy. Important concepts in interval analysis such as box consistency and box splitting methods are applied in the trim algorithm. Simulation results for trimming in horizontal flight of a six degrees of freedom fighter aircraft model show that the interval analysis trim algorithm can find all the trim points with any specified accuracy. Trimming for fixed thrust in horizontal and level flight results in multiple equilibrium points that are all found by the algorithm. Application to a nonlinear model with multiple simultaneous equilibrium points demonstrates the advantages of the algorithm over classical algorithms.