Abstract
ABSTRACT For the synthesis of optimal systems with multi-valued non-linearities in the plant modified phase space techniques can be applied. In this paper the modifications are discussed in detail and a rule is given for determining the number of phase coordinates. It is shown that the appropriate final state manifold is a line which passes through the origin, for typical cases of plants with backlash or hysteresis. For a wido class of such systems, with relay control, it is proved that if a zero switch path between two states exists, it is the time optimal path between those states. Finally the time optimal controllers for two simple plants containing multi-valued non-linearities are found.
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