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4.3 APPLICATION OF ANN MODELS TO ADAPTIVE CONTROL PROBLEMS UNDER UNCERTAINTY CONDITIONS 161
on the system which deviates the trajectory of was obtained initially, without performing the
the real object from the reference trajectory. We adaptive adjustment, only due to the robustness
try to reduce this deviation embedding a com- properties (see Figs. A.79–A.81 for the MRAC
pensating loop (compensator) into the system. system and Figs. A.82–A.84 for the MPC sys-
As showninSection 4.3.2.3, the embedding of tem).
the compensating loop into the adaptive sys- In the conducted experiments, the results of
tem increases its robustness, without which the which are presented in Figs. A.79–A.84, the sys-
adaptation algorithm may not meet the adjust- tem operation time was divided, as in the previ-
ment of the control law in that time window ous case, into two segments of 20 sec each. The
within which the situation must not have time nature of the control action concerning the an-
to grow from an emergency to a catastrophe. gle of attack is the same as in the last case, i.e.,
In a number of cases, changes in the dynam- the first 20 sec command signal is a random se-
ics of the controlled object and/or the condi- quence of frequently changing values of the an-
tions of its operation are not significant. In these gle of attack. With such a signal, the disturbance
cases, its robustness will be sufficient for the nor- from the input signal does not have enough time
mal operation of the system, and it is possible to decay, as the next signal acts on the object.
not to use the adaptation mechanism. For this Such a complicated signal makes it possible to
reason, questions arise about the importance of estimate the cumulative effect of several distur-
the mechanism of adaptation. We need to know bances whose responses intersect in time, i.e.,
what this mechanism provides in comparison it allows us to test the control system in fairly
with the version of the system without adapta- harsh conditions. Unlike the previous case, the
tion, but with robustness improved by using a adjustment of the control law was not carried
compensating loop. out, that is, the adaptation mechanism was dis-
The experiments were carried out to assess abled.
the contribution of adaptability and robust- In the second time interval, the control system
ness to the behavior of the system. We deac- is tested using a more traditional input signal,
tivate the adaptation mechanisms in these ex- which makes it possible to evaluate the behav-
periments. As in the previous case (analysis ior of the system with isolated stepwise distur-
of the influence of uncertainties in the source bances.
data on the properties of the system being syn- The results demonstrate that the inaccuracy
thesized), the system was initially set up in- of the adjusting is not critical for the stability
correctly. In the previous series of experiments of the system, but causes significant deviations
described in Section 4.3.4.2, the control sys- from the reference trajectory. In a steady state,
tem was adapted to the changed conditions for these deviations can be reduced to zero using
the operation of the controlled object. For this an integral compensator, but in transient modes,
purpose, in the experiments whose results are this cannot be handled, and the only way to im-
showninFigs. A.61–A.69 (MRAC scheme) and prove accuracy is to activate adaptation mecha-
Figs. A.70–A.78 (MPC scheme), we set up for nisms to reduce the error below some prescribed
20 sec the disturbing reference signal required level.
to adjust the control law, and then the test step- As we can see from the results presented in
wise signal for estimating the tuning quality. In Figs. A.79–A.84, the lack of mechanisms of adap-
a series of experiments, the results of which are tation leads to a sharp deterioration in the qual-
presented below, the control system continued ity of control. Namely, the error of tracking the
to operate with this “incorrect” setting, which reference signal with respect to the angle of at-