Canonical formulation and general principles of variable structure controllers

This chapter has essentially two goals: first it introduces a new variable structure controller using a canonical system representation, orthogonal sliding hyperplanes, and a straightforward synthesis and analysis procedure. The second goal is more didactically oriented. Some basic facts of VSC will become evident from the special formulation. In first section it has been shown that the canonical formulation and the rank conditions are equivalent. In second section the new controller is presented which consists of two distinct terms. The first is linear state feedback which produces a pole-zero cancellation leaving only integrators in the transfer matrix of the known part of the system. The second term, a relay type controller, forces the initially nonzero outputs to zero and stabilises the pole-zero cancellation in the presence of parameter disturbances. In third section some interesting remarks on the nature of sliding variable structure systems are listed. Fourth section shows that the presented regulator can be modified in a straightforward way in order to accomplish the requirements of model-following VSC . The numerical example demonstrates the synthesis and analysis procedure.