5. Conclusion

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**Residue 4**

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**Residue 1**

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**Residue 4**

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Figure 8. Fault affecting uy. - -, detection threshold; —, residues.

Figure 7. Fault affecting uz. - -, detection threshold; —, residues.

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**Residue 5**

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**Residue 2**

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**Residue 5**

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Time 0 5 10

**Residue 6**

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**Residue 3**

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**Residue 6**

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**Residue 3**

**Residue 2**

R3

R6

R3

R6





**Residue 1**

R2

R5


R2

R5




R1

R4


R1

R4




144 Lagrangian Mechanics

This work presents a fault detection and isolation approach applied to Lagrangian systems.

Every fault is detectable and isolable as it can be seen in Tables 1 and 2, this result is obtained thanks to the special design of the state feedback controller, by consequence the faults affecting the sensors are easily isolable, and the residues affected during a control input fault are those related to the measures affecting the states, for instance a fault affecting uy triggers the residues related to the y and y\_ measures; on the other hand, the faults affecting the control input ℓ trigger all the residues, this is because the direct relation between this control input and the φ measure, as could be seen in Eq. (13) besides the φ measure appears in the other states, as a result every residue is triggered; however, this signature is unique, by consequence this fault is considered detected and isolated.
