Synthesis of robust control systems based on the unification of modelling and design

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The uncertainty included in the nominal model given to the design engineer crucially depends on the method of modelling and the data reliability. Therefore, to handle the uncertainty properly, it is necessary to take into account the process of modelling. In this sense, modelling and design are inseparably connected in the design of robust control systems. This is the principal viewpoint of this project.Our primary concern has been on the robust stabilization which is the most fundamental issue of robust control. We derived a necessary and sufficient condition for the existence of robust stabilizer based on classical Nevanlinna-Pick interpolation theory. In this project, this result for SISO systems has been extended to MIMO cases in the two directions. One is based on the harmonic function theory of contraction operators and the other is based on the "directional interpolation theory". In both approaches, a complete parametrization of all robust stabilizers is obtained. However, the problem of quantification of the model uncertainty in this parametrization remains to be solved.We also derived a method of designing robust deadbeat control both for SISO cases and MIMO cases. In this method, a robustness index is introduced that is closely related to the sensitivity of the closed-loop system. Under the constraint of deadbeat response, this robustness index is optimized. The resulting system exhibits superior performance with respect to parameter variation.Finally, we derive an effective method of generating signals for identification. Actually, this result establishes the effectiveness of minimum phase systems.Though the problem now seems to be much more difficult than we assumed at the start of this project and the results obtained are not much, it can be said that the basis for future developement is obtained.