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Special technological applications like the construction of a dental attachment require structural parts which have very small operall dimensions. Very often these parts are subjected to high loadings. The failure of a small spring was the starting point for an investigation with the aim to design a suitable new spring shape.
We consider universal adaptive stabilization and tracking controllers for classes of linear systems. Under the technical assumption of linear scaling invariance necessary and sufficient conditions for adaptive stabilization are derived. For scalar systems sufficient conditions for adaptive tracking of finite dimensional reference signals are explored.
We present the concept of a universal adaptive tracking controller for classes of linear systems. For the class of scalar minimum phase systems of relative degree one, adaptive tracking is shown for arbitrary finite dimensional reference signals. The controller requires no identificaiton of the system parameters. Robustness properties are explored.
Industrial mathematics has many faces; but its essential feature is the cooperation of partners - from industry and from universities - with quite different interest (business versus academic carreer), normally working on different time scales. They measure success in a different way (selling rate against citing index), they have different hierarchies of values and are very often distrusting each other. Industry doubts that mathematicians are willing and/or able to produce something real practical and useful (and the mathematicians should not be too much surprised about this attitude, they very often doubt themselves) - mathematicians are afraid to loose their competence (their ideal of scientific truth, to say it more idealistically), to sell their souls.