NONLINEAR CONTROLLER COMPARISON ON A BENCHMARK ...

a robust design strategy would, in practice, stabilize a physical plant that di ers
substantially from its mathematical model. Thus the crudeness of our model only
helps to demonstrate the robustness of the control laws that succeed in yielding
adequate performance on the actual hardware system. Another advantage of this
mechanical model is that it is identical, in form, to the system equations presented
in [2] as a nonlinear benchmark problem. Since the object of this research is to
compare nonlinear robust control strategies, this model is ideal in the sense that it
is already widely used as a standard mathematical system for testing and comparing
nonlinear control techniques. The mathematical model in (2.4) is slightly di erent
than the standard model of the NLBP in that our input is voltage, not torque. This
adds one extra term and a few constants in order to incorporate the voltage to torque
transfer function into the model. Many of the papers involving the NLBP express the
system equation in a non-dimensionalized form. Since some of the control strategies in
this comparison make use of these dimensionless equations, and because they simplify
the model by combining all of the physical parameters into a single value, we include
them here:
0 1
_z
B C
B C
BzC
B C
B _ C
@ A
=
Where _ represents d
z = y
= t
=
d q
M +m
I+mc
q
k
M +m
0
B
@
v(x) =u(x) m+M
k(I+mc2 )
mc = p
(I+mc2 )(m+M )
_z
;z+ _2 sin( ); 2 cos( )_z K2 m K2 g
Rmmc
1; 2 cos( ) 2
_
cos( )[z; 2 sin( )]+ K2 m K2 g
Rmmc
1; 2 cos( ) 2
1
C
A
+
0
B
@
0
KmKg
Rm
cos( )
1; 2 cos( ) 2
0
KmKg
Rm
1; 2 cos( ) 2
and the following transformations are used:
12
1
C v(x): (2.5)
C
A