\( \DeclareMathOperator{\abs}{abs} \newcommand{\ensuremath}[1]{\mbox{$#1$}} \)
State-space model, algebraic degeneration example
(%i6) |
e1
:
i1
+
i2
=
0
;
e2 : u1 − v1 = 0 ; e3 : u2 − v1 = 0 ; e4 : u2 = eg ; e5 : C· Du2 − i2 = 0 ; T :[ e1, e2, e3, e4, e5] ; |
special vectors
(%i8) |
Dx
:[
Du2]
;
y :[ i1, i2, u1, v1] ; |
state equations
(%i9) | se : eliminate( T, y) ; |
algebraic degeneration!
solve for the degenerate variable
(%i10) | se : linsolve( se, u2)[ 1] ; |
algebraic relation!
subsitute for the degenerated state variable derivative
(%i11) | de : Du2 = Deg ; |
(%i12) | Tmod : ev( T, de) ; |
there are no state equations; only output equations remain
u2 is now an output variable, let's change the output vector
(%i13) | ynew :[ i1, i2, u1, u2, v1] ; |
(%i14) | oe : linsolve( Tmod, ynew) ; |
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tableau model, equations