Download PDF by Andreas Kugi: Non-linear control based on physical models: Electrical,

By Andreas Kugi

This booklet combines genuine difficulties of useful curiosity with an program of profound thought. The mathematical version is derived step-by-step at the foundation of actual rules, and the physics in the back of the keep an eye on difficulties serves as a foundation for the controller layout. The booklet demonstrates how the physics in the back of the mathematical versions may also help to effectively follow a definite regulate technique. The booklet goals to teach the sensible relevance of the provided tools, equipment that are frequently criticised as in basic terms of theoretical curiosity, via an exam in their business purposes. all through, the publication provides the original mathematical formula of the various disciplines concerned, specifically electric, hydraulic and mechanical engineering. but it additionally issues out the typical mathematical constitution of the several actual versions. This makes it attainable to move trustworthy regulate suggestions among the disciplines.

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Finally, for a laboratory model of a special dc-to-dc convcrtcr, namely the Cuk-convcrter, we will also show how the presented theory can contribute to the design of a non-linear H2-controller with and without integral term. 1 Basic Circuit Relations Throughout this section, we consider electric circuits that are interconnections of lumped dynamic (inductors, capacitors) and static (resistors, voltage and current sources) circuit elements. The topological relationship can best be exhibited by means of a digraph G -- (N, B), where N specifies the set of nodes with cardinality n and B denotes the set of branches with cardinality b.

The second case covers the situation where (-~-~) oy G~ (x) is generically zero with Ge (x) e = G~ (x) u + Gd (x) d. In the single-input singleoutput case G~ (x) can be expressed in the form Gu (x) = Ju (x) (~~o5 / with Ju (x) = _ j T (x). 73) can be written as ~--/x = ( J (x) + J~ (x) u - S (x)) \-~-x ] + Gd (x) d . 76) The physical interpretation of this case is that the control input u only influences the internal energy flow and thus does not change the total amount of energy stored in the system.

E. 46) takes the form - 5-; _p2+ \OzJ 5, provided thas the inequality condition is satisfied. e. 2. 5. As was already mentioned at the bcginning of this chapter, the non-linear H~-approach presented here is just what we need in the subsequent chapters for the controller design. , [84]. 4 Passivity-based Control (PBC) In recent years, passivity-based control has been, and is still, a field of extensive research and it goes without saying that we can only present a small part of the whole theory.

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