I am reading a book on nonlinear control and disturbance rejection, and in many examples, they distinguish between the "plant model" \$G_p(s)\$ and the "nominal plant model" \$G_p(s)\$. They also add that the discrepancy between these two models adds uncertainty that is lumped with disturbance. They specifically called this "unmodeled dynamics", or "modeling errors".
Nominal model was defined as the system's dynamics in the absence of modeling errors. On another hand, it was described as "the ideal model".
In another example, they provided expressions for \$G_p(s)\$ and \$G_n(s)\$.
I am very confused:
- Is the nominal model the desired model? (i.e. do we want to reach it?)
- Is the nominal model an imprecise idealization of the plant to simplify the mathematics?
- Do we know both \$G_p(s)\$ and \$G_n(s)\$? In the book both were provided. If we know both, then what is the point of idealization and/or modeling errors?
- How does it work in practice? Do implementations by researchers and engineers target \$G_p(s)\$ or \$G_n(s)\$?
I am really curious about both the theoretical and implementation side. Any insight is immensely appreciated.