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gosbank2

This function compute the gains for an bank of observers using a proportiona-integral observer with unknown inputs. [1]

Calling Sequence

[N,G,L,Ti,H2,Phi]=GOSbank2(E,A,B,C,R,alpha,flag)

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])

flag:

flag='s' for sensor faults and 'a' for actuator faults. By default is programed for sensor faults

N, G, L, Ti, H2, 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 an bank of observers based in the following proportional observer 


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

Followign the methodology presented in [1]  
Example for fault detection in actuators (AFD)

u inputs (in)         outputs
__________ 
-------| Process  |-------------
------ |__________|------------

__________
in2-------| obsv1    |-------------
in2------|__________|-------------
inm------

__________
in1-------| Observer2|-------------
in3-------|__________|-------------
inm--------     
__________
in1    ----| Observer3|-------------
in2 -------|__________|-------------
in(m-1)----

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
alpha=3;
sensors='a'
 [N,G,L,Ti,H2,Phi]=GOSbank2(E,A,B,C,R,alpha,sensors)
//subindex (j) incates for the 1,2,..j th observer

See also

Author

Bibliography

[1] Paul M. Frank, (1990). Fault Diagnosis in Dynamic Systems Using Analytical and Knowledge-based Redundancy A Survey and Some New Results. Automatica, Vol. 26, No. 3, pp. 459-474.

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