ABSTRACT
As specified in section 2.1, systems controlled using sliding mode, i.e. with control switched on the switching surfaces, possess high speed and small sensitivity to changes of parameters and external disturbances. However, when the system is in multidimensional sliding mode there is not just one but many discontinuous controls, and a problem arises with the sequence of their switching components. The existence conditions of a sliding mode, as it is known, look like inequalities and ambiguously define an algorithm of multidimensional discontinuous control. There are various possibilities for control design, which provide existence of sliding mode. A variety of sliding mode controls lead to a mixture of switching sequences. Moreover, the switching frequency is achieved using modern power switches: insulated gate bipolar transistor (IGBT), metal oxide semiconductor field-effect transistor (MOSFET), Gate Turn-Off (GTO) thyristor etc. Even if their switching frequency can reach tens or even hundreds of kHz, it is nonetheless finite. Therefore, the resulting sliding movement is carried out in the vicinities δ of the crossing of sliding surfaces. Such sliding movement is named real sliding motion or real sliding mode.
