Download Electrical principles - second edition (1958) by H Cotton PDF

By H Cotton

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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.

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