Variable classification permutations

The classification of unmeasured variables and measurements is accomplished by permuting rows and columns of the occurrence matrix corresponding to the Jacobian matrix of the model equations. 

Remark 2. The permutation matrix IIU, obtained as a by-product of the Q-R factorization procedure of A2, enables an easy classification of the unmeasured process variables, as is indicated by Eq. (4.15). The variables in subset un ru correspond to the minimum number and the location of measurements needed for the system to satisfy the estimability condition, that is, that all unmeasured variables be determinable. 

Although not common, it is also possible to vary the air humidity. These operating process variables can be programmed in a fixed or variable frequency mode with fixed or variable amplitude. Since a very large number of combinations and permutations are available for optimization purposes, one often must rely on a liable mathematical model to affix the optimal conditions. A generalized classification scheme of the diverse types of intermittency is presented in Table 22.1. This classification is based mainly on the process parameters and the cycle frequency (i.e., cycle time). Other classification schemes are possible as well especially when different modes of heat input are employed in simultaneous or sequential fashion. 

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