Top
Back: control_lib
Forward: controlDim
FastBack:
FastForward:
Up: control_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.11.2.1 control

Procedure from library control.lib (see control_lib).

Usage:
control(R); R a module (R is the matrix of the system of equations to be investigated)

Return:
list

Purpose:
compute the list of all the properties concerning controllability of the system (behavior), represented by the matrix R

Note:
the properties and corresponding data like controllability, flatness, dimension of the system, degree of controllability, kernel and image representations, genericity of parameters, obstructions to controllability, annihilator of torsion submodule and left inverse are investigated

Example:
 
LIB "control.lib";
// a WindTunnel example
ring A = (0,a, omega, zeta, k),(D1, delta),dp;
module R;
R = [D1+a, -k*a*delta, 0, 0],
[0, D1, -1, 0],
[0, omega^2, D1+2*zeta*omega, -omega^2];
R=transpose(R);
view(R);
==> D1+(a),(-a*k)*delta,0                ,0         ,
==> 0     ,D1          ,-1               ,0         ,
==> 0     ,(omega^2)   ,D1+(2*omega*zeta),(-omega^2)
view(control(R));
==> number of first nonzero Ext:
==> 
==> 2
==> 
==> controllable, not reflexive, image representation:
==> 
==> (a*omega^2*k)*delta                                               ,
==> (omega^2)*D1+(a*omega^2)                                          ,
==> (omega^2)*D1^2+(a*omega^2)*D1                                     ,
==> D1^3+(a+2*omega*zeta)*D1^2+(2*a*omega*zeta+omega^2)*D1+(a*omega^2)
==> 
==> dimension of the system:
==> 
==> 2
==> 
==> Parameter constellations which might lead to a non-controllable system:
==> 
==> a,k,omega
==> 
==> 


Top Back: control_lib Forward: controlDim FastBack: FastForward: Up: control_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.3.2, 2023, generated by texi2html.