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Reviewer #1:
Contrary to this reviewers comment, the time saving was significant. In the first example, it was 24.76 seconds versus 92.39 seconds, and in the second example it was 110 seconds versus 406 seconds.
Weighting filter selection is briefly explained in Section 3.1. This is almost the standard procedure used in robust control design.
We agree that the algorithm consists of two steps which can be obtained by replacing the subscripts 1 by 2, and 2 by 1. However, we believe that the writing both steps and the related equations explicitly makes the algorithm easier to understand at the expense of slightly increased length.
Equation numbers are provided only for some of the important equations. The equation number at the bottom of page 12 is correct, the notation used there is standard in generalized plant/controller framework. The only difference is the controllers input y2. The Figure 2 is for the standard frequency domain approach. It is intended to illustrate the multiobjective control problem, not the substructural approach. The capital Y in that figure will be y2 or y1 depending on in which phase of the algorithm we are.
Regarding the lack of recent references, the substructural approach is not a new problem, however using robust control techniques against modeling errors introduced by approximating dynamic parts by static parts, is one of our main contributions. We havent seen any results in this direction, thats why we dont have any references with dates in 2000s. We can cite many new and old robust control related results, but this paper is not about how to solve a general robust control problem, rather it is about how to solve a relatively older problem by using the advantages of robust control approach. This is mainly the guaranteed stabilizing controller design when there are modeling errors. In our case, these modeling errors are introduced because of approximating dynamic parts by static parts.
Reviewer #2:
The multiobjective robust controller design will significantly improve the convergence of the algorithm. Since every stabilizing controller will have some robustness, multiobjective robust controller design can be replaced by any other controller design procedure. However, convergence will be less likely.
We do ignore the dynamics of the second part, and represent it by its DC value. We do not assume infinite gains, however what we assume corresponds to the Second subsystem has very fast dynamics, compared to the first subsystem. What is new in our approach is the use of robust control techniques taking into account the ignored dynamics.
We also do not claim convergence guarantee, however taking into account ignored dynamics and doing design against these is new in our approach. On top of this, forcing certain dynamics, which will be later ignored, to be fast, is also new in our approach and requires multiobjective robust controller design based on LMIs.
The algorithm may have some similarities with that of the QFT approach. This is also called two time scale system approach in different contexts. In short, we can say that, one of our main contributions is Significant improvement of convergence, and this is achieved by multiobjective robust control design methods.
As suggested by the reviewer, we have added a brief discussion in Section 3.2 related to these issues.
Reviewer #3:
We also agree that the algorithm presented here will be of great benefit to engineers working with flexible structures. However, we do not agree that its usefulness is limited, we simply dont have a convergence proof. We do take into account the ignored dynamics in static condensation, and force certain dynamics which will be later ignored to be fast. These will improve the convergence considerably, and we believe that this is one of our main contributions, and therefore usefulness of the presented algorithm is not limited in our opinion.
We have tested this algorithm on several other examples. It works quite well for flexible structures when decomposition is done in a proper way.
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