Dissertação
Técnicas de cálculos de derivadas para identificação de sistemas aplicados em estabilidade de aeronaves
Fecha
2022-12-20Autor
Christian Prado dos Santos Machado
Institución
Resumen
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.