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Designing Robust Controllers by the Mini-Max Search Method
The problem of regulators (controllers) design is
extremely relevant in connection with the penetration into all
technological areas of the methods of precise control of objects
with feedback. Such devices are being more and more used,
which increases the variety of controlled objects. This list
includes all new objects of robotics and technological setups,
which have much more complex mathematical models. One of
the most urgent problems in this area is control of nonstationary
objects. Parameters of mathematical model of these
objects are given with some uncertainty, but not in fixed
values, i.e. by only intervals of their possible changes. If the
intervals are too wide, adaptive systems have to be designed,
but if they are not too wide, then one can try to find a universal
regulator setting that will be sufficiently effective for all ratios
of the model parameters within the acceptable intervals of
their changes. The paper proposes a new method of the
numerical optimization of regulator for finding such a setting
for the worst object model that is for the worst combination of
all variable parameters. Finding the worst model is also
carried out by a numerical optimization method, in which a
combination of model parameters is found where the best
regulator gives the worst result. The problem is proposed to
solve in several optimization cycles with alternation of
objective functions. The technique has been well illustrated by
a numerical example.
In book
