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D.10.2.2 controlDim
Procedure from library control.lib (see control_lib).
- Usage:
- controlDim(R); R a module (R is the matrix of the system of equations to be investigated)
- Return:
- list
- Purpose:
- computes list of all the properties concerning controllability of the system (behavior), represented by the matrix R
- Note:
- this procedure is analogous to 'control' but uses dimension calculations.This approach works for full row rank matrices only.
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(controlDim(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
==>
==>
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