Figure 8: Control signal of the design that uses the GSHF
to locate the zero in z=-0.2 and this zero is cancelled by
the discrete controller.
5 CONCLUSION
In this paper, it has been noticed by means of an
application example that the variable GSHF can
improve the performance of the pole-placement
control scheme. The variable GSHF allowed us to
place the discretization zero of a second order
continuous plant in more beneficial location from the
viewpoint of the control strategy, improving in that
way the performance of the closed loop.
On the one hand, when the ZOH discretization zero
is sufficiently damped, it is possible to cancel it with
one of the controller poles and to locate the closed-
loop zero in the place where the reference model has
its zero. In such situations, the ZOH discretization
zero does not impose limitations to the attainable
performance and, therefore, the possibility of
relocating it that GSHF provides does not suppose
any advantage. On the other hand, when the ZOH
discretization zero is unstable or poorly damped,
which often happens when the sampling time used is
small enough (Aström et al., 1984), it is not advisable
to cancel it and, therefore, the performance that can
be attained by the classical design method is limited
given that the designer is forced to transmit such a
zero to the reference model in order to avoid
intersample ripple. This is the case studied in this
paper and it has been noticed that it is possible to
match the closed-loop discrete behaviour to the
reference model by the variable GSHF, without
generating intersample ripple.
From the carried out study it is concluded that the
GSHF ability to move the zeros can be used to
improve the transient response of a pole-placement
control. It has been also noticed that this
improvement is obtained at expense of the
amplification of the control signal during transient
state. It is important to point out that in this study it
has been used a variable GSHF with two subintervals
and it may be possible to reduce the control
amplitude by using more subintervals.
During the study, the possible deterioration of the
sensitivity functions, both discrete and hybrid ones,
have not been taken into account. That is one of the
possible drawbacks that the use of the GSHF can
generate (Freudenberg et al., 1997) and future
investigations on this device should integrate the
analysis of such functions.
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IMPROVEMENT ON THE POLE-PLACEMENT CONTROL SCHEME BY USING GENERALIZED SAMPLED-DATA
HOLD FUNCTIONS
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