This function compute the gains for an bank of observers using a proportiona-integral observer with unknown inputs. [1]
[N,G,L,Ti,H2,Phi]=GOSbank2(E,A,B,C,R,alpha,flag)
Continuos matrices of descriptor system. E singular
For the stabilize the observer in a stable LMI region (see [1])
flag='s' for sensor faults and 'a' for actuator faults. By default is programed for sensor faults
Gains matrices of the observer
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)----
[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.