Process Control: Modeling, Design, and Simulation

14.3. Scaling Considerations

To properly use the SVD method presented in Section 14.4, it is necessary to scale the process transfer function matrix such that expected ranges of all scaled inputs and outputs are approximately the same.

An output scaling matrix can be found to assure that the scaled outputs cover the same range. Let (*) represent the scaled variables. A diagonal scaling matrix for the output variable is

Equation 14.4

Similarly, a diagonal scaling matrix for the input variable is

Equation 14.5

Since the input-output relationship ...