Scilab Website | Contribute with GitLab | Mailing list archives | ATOMS toolboxes
Scilab Online Help
5.5.1 - English

Change language to:
Français - 日本語 - Português - Русский

Please note that the recommended version of Scilab is 2024.0.0. This page might be outdated.
See the recommended documentation of this function

Scilab Help >> CACSD (Computer Aided Control Systems Design) > ui_observer

ui_observer

unknown input observer

Calling Sequence

[UIobs,J,N]=ui_observer(Sys,reject,C1,D1)
[UIobs,J,N]=ui_observer(Sys,reject,C1,D1,flag,alfa,beta)

Arguments

Sys

syslin list containing the matrices (A,B,C2,D2).

reject

integer vector, indices of inputs of Sys which are unknown.

C1

real matrix

D1

real matrix. C1 and D1 have the same number of rows.

flag

string 'ge' or 'st' (default) or 'pp'.

alfa

real or complex vector (loc. of closed loop poles)

beta

real or complex vector (loc. of closed loop poles)

Description

Unknown input observer.

Sys: (w,u) --> y is a (A,B,C2,D2) syslin linear system with two inputs w and u, w being the unknown input. The matrices B and D2 of Sys are (implicitly) partitioned as: B=[B1,B2] and D2=[D21,D22] with B1=B(:,reject) and D21=D2(:,reject) where reject = indices of unknown inputs. The matrices C1 and D1 define z = C1 x + D1 (w,u), the to-be-estimated output.

The matrix D1 is (implicitly) partitioned as D1=[D11,D12] with D11=D(:,reject)

The data (Sys, reject,C1, D1) define a 2-input 2-output system:

xdot =  A x + B1  w + B2  u
   z = C1 x + D11 w + D12 u
   y = C2 x + D21 w + D22 u

An observer (u,y) --> zhat is looked for the output z.

flag='ge' no stability constraints flag='st' stable observer (default) flag='pp' observer with pole placement alfa,beta = desired location of closed loop poles (default -1, -2) J=y-output to x-state injection. N=y-output to z-estimated output injection.

UIobs = linear system (u,y) --> zhat such that: The transfer function: (w,u) --> z equals the composed transfer function: [0,I; UIobs Sys] (w,u) -----> (u,y) -----> zhat i.e. transfer function of system {A,B,C1,D1} equals transfer function UIobs*[0,I; Sys]

Stability (resp. pole placement) requires detectability (resp. observability) of (A,C2).

Examples

A=diag([3,-3,7,4,-4,8]);
B=[eye(3,3);zeros(3,3)];
C=[0,0,1,2,3,4;0,0,0,0,0,1];
D=[1,2,3;0,0,0];
rand('seed',0);w=ss2ss(syslin('c',A,B,C,D),rand(6,6));
[A,B,C,D]=abcd(w);
B=[B,matrix(1:18,6,3)];D=[D,matrix(-(1:6),2,3)];
reject=1:3;
Sys=syslin('c',A,B,C,D);
N1=[-2,-3];C1=-N1*C;D1=-N1*D;
nw=length(reject);nu=size(Sys('B'),2)-nw;
ny=size(Sys('C'),1);nz=size(C1,1);
[UIobs,J,N]=ui_observer(Sys,reject,C1,D1);

W=[zeros(nu,nw),eye(nu,nu);Sys];UIobsW=UIobs*W;   
//(w,u) --> z=UIobs*[0,I;Sys](w,u)
clean(ss2tf(UIobsW));
wu_to_z=syslin('c',A,B,C1,D1);clean(ss2tf(wu_to_z));
clean(ss2tf(wu_to_z)-ss2tf(UIobsW),1.d-7)
/////2nd example//////
nx=2;ny=3;nwu=2;Sys=ssrand(ny,nwu,nx);
C1=rand(1,nx);D1=[0,1];
UIobs=ui_observer(Sys,1,C1,D1);

See Also

  • cainv — Dual of abinv
  • ddp — disturbance decoupling
  • abinv — AB invariant subspace
Report an issue
<< trzeros CACSD (Computer Aided Control Systems Design) unobs >>

Copyright (c) 2022-2023 (Dassault Systèmes)
Copyright (c) 2017-2022 (ESI Group)
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 13:46:49 CEST 2014