Self tuning control (STC) is a control technique to adjust the parameter of the on-line controller which adapts itself when plant parameter changes. There are minimum-variance control (MVC), generalized minimum-variance control (GMVC), generalized predicted control (GPC), and so on as a effective way of design STC. The structure of MVC and GMVC is especially easy and manageable.
It is necessary to use MVC that plant is minimum phase system and stable in the discrete time-domain. But, generally actual controlled system is continuous time. Then, when digitizing is given, it sometimes becomes non-minimum phase system. And if we set up sampling time very small, MVC controller has unstable poles.
In this paper, we propose that how to design MVC for plant which is stable and minimum phase system in continuous time domain by introducing a delta-operator and weight adjustment of the cost function. Then, we study about stability.