Adaptive Variable Structure System with the Sliding Surfaces Adjustment for the Control of Nonstationary Linear Object

The method of the synthesis of multi-channel adaptive variable structure system with the sliding mode for the centralized control of spatial motion of the nonstationary linear object is developed in this paper. The conditions of the existences of stable sliding mode with the presence of essential dynamic reciprocal effect between all control channels are obtained and strictly proved. The new law of the adaptive adjustment of the position of sliding hyper-surfaces in each control channel is proposed and mathematically substantiated. The application of these control laws allow to provide the high control quality and the maximally possible fast-action at any variations of the object parameters within the given ranges. The efficiency of synthesized control system is confirmed by numerical simulation results.