By Hans Berger
For the instance of the particular SIMATIC S7 programmable controller, the reader is given an outline of the functioning and layout of a contemporary automation method, an perception into the configuring and parameterization of with STEP 7, and the answer of regulate issues of various PLC programming languages
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Additional resources for Automating with SIMATIC: integrated automation with SIMATIC S7-300/400: controllers, software, programming, data communication, operator control and process monitoring
It was obtained employing Bellman's dynamic programming technique . Rumyantsev [1970J, [1971b] extended this theorem to the problem of optimal stabilization with respect to part of the variables. ) to denote the dot product of the corresponding vector functions. 12. 2), the inequalities b(llwll), Ilwll = (xi + ... + x~/h, m ~ k ~ n a(IIyll) ~ VO(t,x) ~ and a vector function u = UO(t,x) E U such that (1) W(t,x) == -w(t,x,UO(t,x)) ~ -c(llwll); O()] oV o (oVO _ . 5. THE PROBLEM OF STABILITY OF LINEAR SYSTEMS 41 (3) B[VO, t, x, u] 2": 0 for any u E U; and (4) for any u* (t, x) E U that ensures asymptotic y-stability of the unperturbed motion x = 0 the following equality is true: lim VO(t,x*[t]) = 0, t -+ 00.
Zubov's method of constructing auxiliary systems . 1) which then can be used as a basis for constructing a certain auxiliary system of differential equations. Then the Lyapunov function for the auxiliary system, having been constructed, solves the PSt-problem for the original system. 3. The method of constructing different-type limiting systems and limiting V-functions. Of course, this method is not really a method of constructing V-functions, though the possibilities for finding "appropriate" V-function are extended within its scope.
The intensive development of this method resulted in a rather general principle of comparison with the Lyapunov vector function (Lakshmikantham et al. ) being worked out. This principle has been successfully used in both theoretical and applied research on the dynamics of nonlinear systems, especially high-dimensional complex systems. Matrosov [1965J applied the MLVF to the PSt-problem. The same problem was considered by Peiffer , Peiffer and Rouche ' Shoichi et al. [1982J, and Vorotnikov [1991aJ.
Automating with SIMATIC: integrated automation with SIMATIC S7-300/400: controllers, software, programming, data communication, operator control and process monitoring by Hans Berger