These techniques can provide a starting point for building the nominal model
for the quantitative model-building in our framework.
The two previous subsections addressed scenarios where (1) the system is modeled explicitly at several operating conditions or (2) a nominal model of the system is available with an assumed level of frequency domain uncertainty.
In the case that explicit models for the system are not available at different operating conditions, a nominal model with frequency domain uncertainty may be assumed.
Given a nominal step response model, a robust model can be defined with respect to that nominal model by using the concept of uncertainties as follows.
n] and the uncertainty related to each of the nominal model parameters.
However, the key advantage of calculating analytically a bound on the variability based on a nominal model with uncertainty as per Equation (10) is that long dynamic simulations are avoided and this is essential in order to reduce the duration of the optimization.
This figure also shows that the maximal deviation with respect to the nominal model is expected to occur at steady state.
Then, the model uncertainty can be calculated and the variability in the output variables can be computed from the nominal models and the uncertainty around different operating conditions.
The theoretical motivations include the frozen point non-linearity measure, time variation of scheduling parameter and the selection of the best nominal model.
nl](NL, L*), is obtained, the corresponding linear model L* is called the best nominal model, which plays a crucial role in formulating the non-linearity measure, as seen in The Choice for the Nominal Model subsection.
To construct the uncertainty ball induced by the non-linearity, a nominal model is first chosen among the local models.
The v-gaps of the chosen nominal model and all other members in the set are computed (i.