Discretized bounded sliding mode control for simulation of differential-algebraic systems

Sliding mode control has recently proved to be a highly effective method for state space modeling of differential-algebraic equation systems (DAEs). Sliding control realizations have great potential for simulation since they allow more computationally efficient robust modeling approximations to be constructed for DAE systems. However, efficient discretization of such methods poses a significant problem due to the well known chattering phenomena that often occurs due to limited computational bandwidth. While some errors are inevitable due to limited bandwidth, the chattering phenomenon can be reduced by minimizing the frequency at which the system crosses the sliding surface. In this work, we find relations between controller parameters, error bounds, and the crossing frequency. They are then used to synthesize efficient discretized sliding mode realizations that optimize crossing frequency and the associated controller sampling period. Together, these results form an efficient discretized bounded sliding mode control approach for simulation of differential-algebraic systems.