In this paper, the problem of model reference adaptive control for unit memory discrete repetitive processes is analyzed and solved by employing a lifting technique that allow us to view the discrete repetitive processes as a first-order multivariable plant. An adaptive controller gain adjustment algorithm in iteration domain is given that ensures the monotonic convergence of the tracking error between the process and the desired reference model outputs under persistent excitation conditions.

Abstract

The substances of interest to the reservoir engineer are oil, gas and water. Normally we would expect these materials to be fluid; i.e., either liquid or vapor. In some instances, though, the oil can be quite viscous or even solid. While we would usually think that the water should be liquid, the interstitial water is solid in some locations. This can occur in permafrost regions.

Hydrocarbons may be gaseous, liquid, or solid at normal temperature and pressure, depending on the number and arrangement of the carbon atoms in the molecules. Those compounds with up to four carbon atoms are gaseous; those with twenty or more are solids; and those in between are liquid. Liquid mixtures, such as crude oils, may contain either gaseous or solid compounds or both in solution. For instance, some oils are liquids at the wellhead, but are solid upon cooling due to crystallization of the solid compounds