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puiobsv

This function compute the gains for a full order Proportiona-Integral observer with unknown inputs and useful for fault detection [1]

Calling Sequence

[N,G,L,Ti,H2,Phi]=piuiobsv(E,A,B,C,R,alpha)

Parameters

E, A, B, C, R:

Continuos matrices of descriptor system. E singular

alpha:

For the stabilize the observer in a stable LMI region (see [1])

N, G1 L, H2, Ti, Phi:

Gains matrices of the observer

Description

Given a Descriptor system in the form
dxEdt=A x(t) + B u(t) +R d (t)
y   =C x(t) + D u(t) 
This compute the observer gains for 

dz/dt= Nz(t) + Gu(t) + Ly(t)+Tide(t)
xe= z(t) + H2y(t)
dde/dt= Phi (y(t)-ye(t))  

xe = stimated states
y(t)=output
ye(t)=stimated output
de= stimated unknown input 
alpha put the observer in the stability LMI region

Examples

Descriptor System

E=[1 0 0 0; 0 1 0 0; 0 0 0 0; 0 0 0 0];
A=[-0.75 1 0 0; -1 -0.85 0 0; 0 -1 -0.75 0; 0 0 0 -1];
B=[1 10 ;1 0.5 ; 0 0  ;1 0 ];
// is very important select a correct matrix C
// that meets the observability condition
C=[1 0 1 0; 0 1 0 1; 1 0 0 0]; 

R=[-1 0 0 0]';

// Observer Gains

[N,G,L,Ti,H2,Phi]=piuiobsv(E,A,B,C,R,1);

See also

Author

Bibliography

[1] Hamdi, H., Rodrigues, M., Mechmeche, C., & Theilliol, D. (2011). Fault Detection and Isolation for Linear Parameter Varying Descriptor Systems via Proportional Integral Observer. International Journal of Adaptive Control and Signal Processing, 2-16. doi:10.1002/acs

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