Data-driven system identification of nonlinear dynamics for a 6-DOF aircraft model using SINDYc
Thibodeaux IV, Thomas W.
Steck, James E.
This work employs a data-driven, system identification technique to determine the governing dynamic equations of a nonlinear, 6-DOF aircraft model. A generalized aircraft model is developed, and nonlinearities are introduced in the gravity model, the aerodynamic force and moment models, and the coupled dynamic and kinematic models. As a case study, the constant parameters within the generalized model are chosen to closely match those of the SIAI Marchetti S-211, an Italian jet trainer. The model is trimmed and, to establish confidence, the dynamics are excited using both nonzero initial conditions and control inputs. The nonlinear system identification technique, SINDYc (Sparse Identification of Nonlinear Dynamics with Control), is formally introduced, a thorough explanation is provided, and a simple example is conducted. SINDYc is a sparse regression technique that uses a library of candidate functions, composed of state and input variables, to determine the fewest number of terms required to represent the set of nonlinear differential equations which govern dynamic system behavior. Using the three control inputs -- aileron, elevator, and rudder -- the S-211 model is aggressively excited as to sufficiently express its nonlinearities, and the resulting time histories of each state are recorded. This data is used with the SINDYc algorithm to reconstruct the nonlinear dynamic equations. Several iterations are performed with variations in the type of state noise and filtering, the method of numerical differentiation, and constraints imposed upon the library of candidate functions. In most cases, SINDYc is able to determine the terms present in the nonlinear dynamic equations with reasonable accuracy. Finally, the identified systems are excited using simple control inputs, and their dynamic response is compared to that of the true system.
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Thesis (M.S.)-- Wichita State University, College of Engineering, Dept. of Aerospace Engineering