By Laurent Fribourg, Romain Soulat
This booklet offers correct-by-design keep watch over recommendations for switching platforms, utilizing diversified equipment of balance research. Switching structures are more and more utilized in the electronics and mechanical industries; in energy electronics and the car undefined, for instance. this is often as a result of their flexibility and straightforwardness in effectively controlling business mechanisms. by means of adopting applicable regulate principles, we will be able to steer a switching method to a zone based at a wanted equilibrium aspect, whereas averting “unsafe” areas of parameter saturation.
The authors clarify numerous correct-by-design tools for regulate synthesis, utilizing diversified equipment of balance and invariance research. additionally they supply a number of purposes of those tips on how to business examples of energy electronics.
1. regulate concept: uncomplicated Concepts.
2. Sampled Switched Systems.
3. defense Controllers.
4. balance Controllers.
5. software to Multilevel Converters.
6. different concerns: Reachability, Sensitivity, Robustness and Nonlinearity.
About the Authors
Laurent Fribourg is head of the LSV (Laboratoire Spécification et Vérification) and medical Coordinator of the Institut Farman, Institut Fédératif de Recherche CNRS, which brings jointly the services of 5 laboratories from ENS Cachan, in France, within the fields of modeling, simulation and validation of complicated structures. He has released over 70 articles in overseas journals and reviewed complaints of overseas meetings, within the area of the idea of formal equipment and their business applications.
Romain Soulat is within the 3rd 12 months of his doctorate on the LSV at ENS Cachan in France, below the supervision of Laurent Fribourg. he's engaged on the modeling and verification of hybrid platforms. specifically, his pursuits predicament robustness in scheduling difficulties – in particular as a part of a collaborative undertaking with EADS Astrium at the verification of an element within the launcher for the long run Ariane 6 rocket. He has released five articles in reviewed complaints of overseas conferences.
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Extra resources for Control of Switching Systems by Invariance Analysis: Applcation to Power Electronics
The parameter τ is called the sampling period. We call such switched systems sampled switched systems, and refer to them as S 2 -systems. For an S 2 -system of sampling period τ , the control synthesis problem then amounts to ﬁnding the value of the switching signal at times τ , 2τ , . . In addition, we make assumptions that are commonly met in practice in 14 Control of Switching Systems by Invariance Analysis embedded control applications of power electronics and the automotive industry. They are as follows: – (A1) We focus on afﬁne dynamics: the function fu (x) is of the form Au x + bu .
PIC 08, ABA 09]). The smallest box containing a zonotope Z =< c, G > is called the bounding box of Z, and denoted by (Z). We have: (Z) =< c, D >, where D is an n × n diagonal matrix whose (i, i)th element is equal to Σp=1 |Gi, |, for 1 ≤ i ≤ n. Given a zonotope Z =< c, G >, the transformation of Z via an afﬁne function x → Cx + d is a zonotope of the form < Cc + d, CG >. The successor set P ostu (Z) of Z via a mode u can thus be simply computed using zonotopes, using matrix multiplication whose complexity is (at most) cubic.
This corresponds to the speciﬁcation of a safety area S. The safety control problem is to ﬁnd a strategy for deciding which sequence of patterns to apply in order to keep the state within S. 2: it corresponds to the application of mode 2 on (0, τ ] and mode 1 on (τ, 4τ ]. The control can be state-independent, consisting of the repeated application of the same sequence of patterns (computed off-line), or state-dependent, with the application of a pattern depending on the current value of the electrical state.