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Robust fault detection observer design under fault sensitivity constraints. (English) Zbl 1395.93216
Summary: In this paper, a reduced-order robust fault detection observer (FDO) for continuous linear time-invariant systems with unknown inputs is designed by combining the algebraic unknown input decoupling principle with linear matrix inequalities (LMIs)-based optimization of fault sensitivity constraints. Algebraic unknown input decoupling is incorporated into the design of fault detection observers, thereby leading to a reduced-order robust FDO that is decoupled from unknown inputs. The gain matrix of the reduced-order robust FDO is determined from the optimal solution that maximizes the LMIs, which are based on the \(H_-\) index performance and the additional pole placement in a specified LMI region. This ensures that the designed robust FDO provides the optimal fault sensitivity on the residual. The efficiency of the proposed approach is evaluated through simulation studies and compared with the pole placement design and the mixed \(H_-/H_\infty\) observer given in the work of J. L. Wang et al. [Automatica 43, No. 9, 1656–1665 (2007; Zbl 1128.93321)].

MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
93C05 Linear systems in control theory
93B55 Pole and zero placement problems
93B36 \(H^\infty\)-control
Software:
YALMIP
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References:
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