By Stephen L. Campbell, Ramine Nikoukhah
Many industries, similar to transportation and production, use regulate platforms to insure that parameters resembling temperature or altitude behave in a fascinating far more than time. for instance, pilots want insurance that the airplane they're flying will continue a specific heading. a vital part of regulate structures is a mechanism for failure detection to insure security and reliability.
This e-book deals another failure detection procedure that addresses of the basic difficulties within the secure and effective operation of recent regulate platforms: failure detection--deciding whilst a failure has occurred--and version identification--deciding which sort of failure has happened. a lot of the paintings in either different types has been according to statistical tools and below the idea given process used to be monitored passively.
Campbell and Nikoukhah's booklet proposes an "active" multimodel method. It demands using an auxiliary sign that may have an effect on the output in order that it may be used to simply verify if there was a failure and what kind of failure it really is. This auxiliary sign needs to be stored small, and sometimes short in period, so as to not intrude with process functionality and to make sure well timed detection of the failure. The process is strong and makes use of instruments from powerful keep an eye on concept. not like a few ways, it truly is appropriate to advanced platforms. The authors current the idea in a rigorous and intuitive demeanour and supply useful algorithms for implementation of the procedures.
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Thus we have that k (|νi |2 − |zi |2 ) < 0, ∀ k ∈ [0, N − 1]. 22) we get the uncertainty on the initial state νk , and zk satisfies (x0 − x ¯0 ) T P0−1 (x0 k −x ¯0 ) + (|νi |2 − |zi |2 ) < d, ∀ k ∈ [0, N − 1]. 23) can also be used to model (with some conservatism) systems where both additive noise and model uncertainties 40 CHAPTER 2 are present. 24c) (x0 − x ¯0 )T P0−1 (x0 − x ¯0 ) + N −1 |wi |2 < d. 25c) k with ν1k = ∆k zk , wk = ν2k . 26) But then we have |ν1k | ≤ |zk |. 23). 23). 22). 19d). 22).
4, for the above example, corresponds to an uncertainty on the slope of the line relating y to u. 2 where the uncertainty is not in the slope but in the origin. In many cases, neither of these two models is satisfactory. What is needed is an uncertainty model that can capture both of the above uncertainties. 34) to be |ν|2 − |z|2 < d for some positive d. 36). This model captures many natural system uncertainties. 4 The realizable set {u, y}. 54) with ν1 ν2 T ν1 ν2 < 1. 2. The realizable set is defined by y 2 − 2uy < 1.
35a). 24), we introduce some conservatism. Indeed, the set of system trajectories allowed under the latter model can be a lot larger than that of the former. 22). This will always be there since some additional ∆(t) are now permitted. For example, if σ ¯ (∆(t)) < 1 for a while, then σ ¯ (∆(t)) > 1 is possible later. We give a specific illustration in the next example. 23). For example, if (x(0) − x0 )T P0−1 (x(0) − x0 ) = c < d, then we allow ∆ for which s (|ν|2 − |z|2 ) dt < d − c, ∀ s ∈ [0, T ].