Geology Reference
In-Depth Information
The main disadvantage of the clipped opti-
mal strategy is that it tries to change the voltage
of the MR damper from zero to its maximum
value, which makes the control force suboptimal.
Moreover, sometimes this swift change in volt-
age and therefore sudden rise in external control
force increases the system responses, which may
lead to an inelastic response of the structure.
Therefore there is, indeed, a need for better con-
trol algorithms that can change the MR damper
voltage slowly and smoothly, such that all volt-
ages between maximum and zero voltage can be
covered based on the feedback from the structure.
In addition, the algorithm needs to consider the
dynamics between the applied voltage and the
commanded voltage (given by Equation (4)).
Intelligent control algorithms are used to solve
the first of the above-mentioned constraints but
the inclusion of supplied to commanded voltage
dynamics is not addressed.
the desired control force,
f
d
, which is determined
by a linear optimal controller,
K s
k
( )
, based on
the measured structural responses,
y
and the
measured damper force,
f
c
at the current time.
The damper force is then calculated by
y
f
−
1
f
=
L
−
K s L
( )
(14)
d
k
c
where
L
( )
is the Laplace transform operator.
The linear controller is usually obtained using H
2
or LQG strategies. The applied voltage,
v
a
, to the
MR damper can be commanded and not the
damper force; hence when the actual force being
generated by the MR damper,
f
c
, equals the desir-
able force,
f
d
, the voltage applied remains the
same. Again, when the magnitude of the force
f
c
is smaller than the magnitude of
f
d
and both
forces have the same sign, then the voltage applied
is set to its maximum level, to increase the
damper force. Otherwise, the voltage is set to
zero.
This algorithm for selecting the voltage signal
is described by
Dynamic Inversion Control
Dynamic inversion (DI) control methodology
is a member of feedback linearization control
techniques and is applied to different types of
aircraft applications (Reiner et al., 1995). In this
technique the existing deficient or undesirable
dynamics in the system are nullified and replaced
by designer specified desirable dynamics (Reiner
et al., 1995; Ali and Padhi, 2009). This tuning of
system dynamics is accomplished by a careful
algebraic selection of a feedback function. It is for
this reason that the DI methodology is also called
the feedback linearization technique. Details of
feedback linearization and DI can be found in
Marquez (2003).
Like all other model based systems, a funda-
mental assumption in this approach is that the plant
dynamics are perfectly modeled, and therefore can
be cancelled exactly by the feedback functions.
Here also we assume that no uncertainty is involved
in the plant dynamics and parameters. Here, DI is
used as a two-stage controller formulation. The
v
=
v H f
(
−
f
)
f
(15)
a
max
d
c
c
where
v
max
is the voltage level associated with
the saturation of the magnetic field in the MR
damper, and
H
( )
is the Heaviside step function
operator.
The performance of the clipped optimal control
algorithm has been evaluated through numerical
simulations (Dyke et al., 1996) and demonstrated
for multiple MR dampers in Jansen and Dyke
(2000). Jansen and Dyke (2000) also presented a
comparison with other algorithms. In all cases the
clipped optimal controller is found to satisfactorily
reduce the structural responses and outperform
passive control strategies.
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