Predictive Control

4Quantitative Analysis of SISO Unconstrained Predictive Control Systems

In Chapter 3, some trend conclusions on the stability of the DMC controller and on closed‐loop robust stability affected by the DMC filter were given by transforming the DMC algorithm into the IMC structure and analyzing the corresponding characteristic polynomials. Here “trend” means that in the theorem conditions some design parameters are set as extreme values, such as M = 1, P → ∞, r → ∞, α sufficiently small, etc. (see Theorems 3.1 to 3.3 and 3.6, respectively), which is sometimes also called the “limiting case” or “marginal stability” in the literature and is caused by the lack of an explicit relationship between the design parameters and the characteristic polynomial.

Indeed, since the appearance of predictive control algorithms such as DMC and GPC, in order to get more guidance for applications, many efforts have been put into exploring the relationship between the design parameters and the control performance. Except for the trend conclusions mentioned above, more explicit and analytical relationships between design parameters and system performance were required. During the 1980s and a little later, some interesting quantitative results for analyzing GPC and DMC algorithms were achieved. Since these studies focused on quantitative analysis for existing predictive control algorithms, we call the theoretical study for this purpose quantitative analysis theory of predictive control.

In this chapter, ...