Proposal of Incremental Sliding Mode Control

An incremental sliding mode controller for a class of second-order underactuated systems is proposed to achieve asymptotic stability and favorable performance. The second-order underactuated systems include two subsystems. Firstly, two state variables of a subsystem are chosen to construct the first-layer sliding surface. Secondly, the first-layer sliding surface and one of the left state variables are used to construct the second-layer sliding surface. The last sliding surface is constructed by the second-layer sliding surface and the left state variable. This proposed design method is applied to investigate the decoupled control of an inverted pendulum. The simulation results show the validity of incremental sliding mode control. At the same time, we analyze the way to construct the sliding surfaces and a rule of selecting parameters to construct the sliding surfaces