Técnicas de cálculos de derivadas para identificação de sistemas aplicados em estabilidade de aeronaves

Abstract

The process of building a mathematical model from available data of a dynamic system and being able to infer about the real system is known within the control area as Systems Identification. Systems identification techniques are used extensively to obtain aircraft models from flight tests for the development of simulators and control systems. These same techniques can be applied in other areas, too, such as curve fitting, machine learning, statistics, economics, data mining, and neural networks. Several identification techniques are based on the iterative minimization of cost functions and, for that, use information from derivatives. The calculation of derivatives for models with a large number of parameters, states, and measurements, using a large amount of data, is a challenge that hinders the application of these techniques in problems at the frontier of knowledge. The present work aims to survey the main derivative calculation techniques for system identification, show their application in the cost functions used, and study their consequences in challenging problems. Numerical methods of finite differences by step forward, central and complex are discussed, as well as algorithmic differentiation techniques in direct mode, reverse mode and symbolic differentiation. These techniques are applied in the output error method for identifying longitudinal and lateral-directional models of aircraft, whose mathematical representations will also be described. As expected, derivative methods have a strong influence on execution time, especially when the number of parameters is large.