Continuous analysis of move suppressed and shifted DMC

"Shifted DMC" (shifted dynamic matrix control) has been empirically shown to have significant improved closed-loop control characteristics over "move-suppressed DMC" where, in the latter, diagonal terms of the dynamic matrix DMC prediction model are augmented to reduce numerical ill conditioning. An added benefit of shifted DMC was that the so-called "shifting parameter," replacing the move suppression parameter, was easily found from the open-loop response. Therefore a novel analytical method, based on a closed form, continuous approximation to closed-loop DMC control, is introduced here and used to quantify the previous empirical results. The dependence of slow and fast time scales of the closed-loop response on the parameters is examined for move-suppressed and shifted DMC methods. It is found that in move-suppressed DMC the slow control time scale is sharply dependent upon the sampling time and move-suppression parameter and that these difficulties are eliminated in shifted DMC.