A new design for model reference robust control using state space techniques

Proposes a model reference control (MRC) structure which is different from existing MRC structures. This new approach is based on state space techniques, but is not simply an alternative form of the input-output transfer function approach. It has the advantage of being a unified structure that processes systems with either time-invariant (TIV) or time-varying (TV) parameters. For systems with TV parameters, it requires a lower number of assumptions compiled with the input-output operator approach. This result can be achieved due to a new concept called dynamic coordinate transformation. This dynamic coordinate transformation has the effect of transforming the plant into a “big” system which is composed of two subsystems One subsystem has the matching property which is not enjoyed by the original plant, while all the unmatched unmodeled dynamics, as well as TV parameters which we do not like in the original plant, are drawn into the other unmatched subsystem. The control objective for the original plant is transformed into the control of the matched subsystem while the unmatched subsystem remains uniformly bounded as long as all the unmodeled dynamics, TV parameters, plant input, and the plant output are bounded. For simplicity, the authors discuss only systems with TIV parameters. A robust control approach and the backstepping method are used to guarantee that the overall states are globally uniformly bounded (GUB) and that the output tracking error is globally uniformly ultimately bounded (GUUB)