Variable structure controllers design for discrete-time model-following systems

This paper proposes a design technique for the variable structure control (VSC) to stabilize the discrete-time model-following systems. That is, for a giving model with ideal response characteristics, a VSC is designed so that the error between the plant's state and the model's state is forced to exhibit like a sliding mode behavior, then the output of the plant faithfully follows that of the model. This VSC includes two portions, one is the “sliding control” which depends on the determination of the matrix G for the sliding surface such that the sliding mode is stable; the other is the reaching control which is designed to force the error state approching the sliding surface. It is also shown that in this controlled system the sliding surface is extended to a sliding region which is determined by a diagonalizing transformation matrix. Furthermore, the designed reaching control gain is a simple vector with the same elements. This may make the practical controller be easily implemented.