By Stephen L. Campbell, Ramine Nikoukhah
Many industries, resembling transportation and production, use regulate platforms to insure that parameters resembling temperature or altitude behave in a fascinating excess of time. for instance, pilots desire coverage that the aircraft they're flying will continue a specific heading. an essential component of keep watch over structures is a mechanism for failure detection to insure protection and reliability.
This publication bargains an alternate failure detection technique that addresses of the basic difficulties within the secure and effective operation of contemporary keep an eye on platforms: failure detection--deciding while a failure has occurred--and version identification--deciding which type of failure has happened. a lot of the paintings in either different types has been in accordance with statistical equipment and below the belief given approach was once monitored passively.
Campbell and Nikoukhah's booklet proposes an "active" multimodel procedure. It demands using an auxiliary sign that would have an effect on the output in order that it may be used to simply confirm if there was a failure and what kind of failure it really is. This auxiliary sign has to be saved small, and infrequently short in period, so as to not intrude with approach functionality and to make sure well timed detection of the failure. The process is powerful and makes use of instruments from strong regulate concept. in contrast to a few methods, it truly is acceptable to complicated 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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Additional resources for Auxiliary signal design for failure detection
13) converges exponentially to P = P¯ , which is the unique positive deﬁnite solution of the algebraic Riccati equation 0 = (A − SR−1 C)P¯ + P¯ (A − SR−1 C)T − P¯ C T R−1 C P¯ +Q − SR−1 S T . 19a) µ = R−1/2 (y − C x ˆ). 15) as a suboptimal solution. This is often done when using the Kalman ﬁlter. The advantages are considerable in terms of on-line implementation complexity. In particular, there is no Riccati equation to solve on-line, and the ﬁlter is time invariant. The loss of optimality can be neglected if T is large compared to the transient response time of the system.
15) as a suboptimal solution. This is often done when using the Kalman ﬁlter. The advantages are considerable in terms of on-line implementation complexity. In particular, there is no Riccati equation to solve on-line, and the ﬁlter is time invariant. The loss of optimality can be neglected if T is large compared to the transient response time of the system. 3 Model Uncertainty In the static problem when model uncertainty was allowed, the problem became more complex in part because the unconstrained noise bounds were no longer positive semideﬁnite and one had to carefully consider how the noise bound interacted with the constraints.
46) becomes bigger as t increases. The limit as t goes to inﬁnity gives us a bound of d instead of 1. For the case d < 1, the Riccati equation diverges at t = d/(1 − d). We have seen in the above example that the choice of the pair (d, P0 ) is important in obtaining a good approximation when reformulating the uncertain system. 20a) is a linear time-varying system with bounded coefﬁcients over [0, T ], so its solution is always bounded. Thus it would be reasonable, in general, to choose the pair (d, P0 ), if possible, in such a way that the Riccati equation associated with the new formulation does not diverge, no matter what the output equation is.