NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...
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Figure 2.4: Translational Oscillation Model for FBS<br />
electrical resistance, and I is the inertia of the proof mass. Letting x =(y _y _ ) T ,<br />
and using the voltage applied to the motor as the input to the system, the resulting<br />
state space equations are as follows:<br />
0 1 0<br />
_y<br />
B C B<br />
B C B<br />
ByC<br />
B<br />
B C<br />
B _C<br />
= B<br />
C B<br />
@ A @<br />
_y<br />
_2 Rm sin( )(m 2 c 3 +Imc)+mc cos( ) _ K 2 m K 2 g;ykRm(mc 2 +I)<br />
Rm[(I+mc 2 )(M +m);m 2 c 2 cos 2 ( )]<br />
_<br />
;m2c2Rm cos( )sin( ) _2 +yRmkmc cos( );y(m+M )Rmk<br />
Rm[(I+mc2 )(M +m);m2c2 cos2 ( )]<br />
0<br />
B<br />
+ B<br />
@<br />
1<br />
C<br />
A<br />
0<br />
;mcKmKg cos( )<br />
Rm[(I+mc2 )(M +m);m2c2 cos2 ( )]<br />
0<br />
KmKg(m+M )<br />
Rm[(I+mc 2 )(M +m);m 2 c 2 cos 2 ( )]<br />
1<br />
C u(x) (2.4)<br />
C<br />
A<br />
Again, this state-space model was derived using the EL equations. One mightwonder<br />
at the validity of the simplifying assumptions necessary to derive this model. For the<br />
purpose of this thesis, modeling inaccuracy is highly desirable { the control strategies<br />
studied in this paper are purportedly \robust" in some sense. One would hope that<br />
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