Page 96 - Neural Network Modeling and Identification of Dynamical Systems

84 2. DYNAMIC NEURAL NETWORKS: STRUCTURES AND TRAINING METHODS

FIGURE 2.34 Test excitations as functions of time used in studying the dynamics of controlled systems. (A) A random
signal. (B) A polyharmonic signal. Here, ϕ act is the command signal for the elevator actuator (full-movable horizontal tail) of
the aircraft from the example (2.123)on page 78.From[109], used with permission from Moscow Aviation Institute.

POLYHARMONIC EXCITATION SIGNALS FOR In the case where dynamical system param-
THE IDENTIFICATION OF SYSTEMS eter estimation is performed in real time, it is
To solve problems of identification of dy- desirable that the stimulating effects on the dy-
namic systems, including aircraft, frequency namical system are small. If this condition is
methods are successfully applied. The available met, then the response of the dynamical system
results show [104–107] that for a given frequency (in particular, aircraft) to the effect of the excit-
range, it is possible to effectively estimate the ing inputs will be comparable in intensity with
parameters of dynamical system models in real the reaction, for example, to atmospheric tur-
time. bulence. Then the test excitatory effects will be
The determination of the composition of the hardly distinguishable from the natural distur-
experiments for modeling the dynamical system bances and will not cause unnecessary worries
in the frequency domain is an important part of to the crew of the aircraft.
the identification problem solving process. The Modern aircraft, as one of the most impor-
experiments should be carried out with the aid tant types of simulated dynamical system, have
of excitation signals applied to the input of the a significant number of controls (rudders, etc.).
dynamical system covering a certain predeter- When obtaining the data required for frequency
mined frequency range. analysis and dynamical system identification, it