<< dcontr en_US gosbank2 >>

DeCaToKi >> en_US > gosbank

gosbank

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

Calling Sequence

[N,G1,L,H2,Bo1]=gosbank(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, G1, L, H2

Gains matrices of the observer

Bo1

Auxliar matrix for simulation. see "puiobsv"

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))  

xe = stimated states
y(t)=output
ye(t)=stimated output
de= stimated unknown input 
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='s'
[N,G1,L,H2,Bo1]=gosbank(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.

<< dcontr en_US gosbank2 >>