Modelling, State Observation and Diagnosis of Quantised by Jochen Schröder (auth.)

By Jochen Schröder (auth.)

The publication issues quantised platforms which emerge from continuous-variable platforms via quantising the values of all indications. it's proven how this results in an summary procedure description through a stochastic automaton. according to stochastic automata, new equipment for the answer to kingdom remark and fault diagnostic difficulties are derived. The tools are prolonged to networks of stochastic automata, permitting component-oriented modelling and, hence, to house complicated structures. the sensible applicability and usability of the process is proven at numerous examples.

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Partition of the relevant output space (left) and input space (right) of the two–tank system. Fig. 3. Quantisation of a numerical output signal of the two–tank system. for the moment assumed to be bounded. The selection of a numerical input u(k) by the injector is according to the equivalence relation [u(k)] = i ⇔ u(k) ∈ Qu (i) . 4) This means that the injector must incorporate some mechanism to choose a numerical input from the set Qu (i). Therefore, the injector is described such that it randomly selects one numerical input of the set Qu ([u]) corresponding to the given quantised input [u].

1 metre. 3 shows the effect of the quantiser on a numerical output signal of the tank system. On the left–hand side the sequences of numerical values for y1 (k) and y2 (k) are shown. The quantisation introduced by the partition is shown by the light grey boxes at each time step. The quantiser transforms the numerical sequence Y (0, 1, . . , 8) into the quantised sequence [Y (0, 1, . . , 8)] = (9, 8, 8, 8, 8, 3, 3, 3, 1). 3. Injector. The injector is the causal inverse of the quantiser. This means, given a quantised input [u(k)] ∈ Nu = {1, 2, .

8) into the quantised sequence [Y (0, 1, . . , 8)] = (9, 8, 8, 8, 8, 3, 3, 3, 1). 3. Injector. The injector is the causal inverse of the quantiser. This means, given a quantised input [u(k)] ∈ Nu = {1, 2, . . , M }, the injector must determine a numerical input u(k). 6 y1 Fig. 2. Partition of the relevant output space (left) and input space (right) of the two–tank system. Fig. 3. Quantisation of a numerical output signal of the two–tank system. for the moment assumed to be bounded. The selection of a numerical input u(k) by the injector is according to the equivalence relation [u(k)] = i ⇔ u(k) ∈ Qu (i) .

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