Inverse models/modeling basic concepts

The basic concept of a model-based control (MBC) is illustrated in Figure 2.51 where the "controller," Q, is the inverse of a model of the process... 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

Due to the universality in all glasses, physical aging can be theoretically explained in a straightforward way based on the free-volume concept. As proposed by Struik, This is the basic and rather obvious idea that the transport mobility of particles in a closely packed system is primarily determined by the degree of packing of the system or by its inverse measure, viz. the free volume [2]. The idea could date back to 1943 when Alfrey et al. proposed that the isothermal aging below Tg can be attributed to the diffusion of free volume holes from the interior of polymers into the surface [34]. This free volume diffusion model (FVDM) was developed by Curro et al. [35] to quantitatively analyze the volume relaxation experiments of poly(vinyl acetate) [36, 37]. The motion of free volume holes can be described by a diffusion equation ... 

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