Biomedical Engineering Reference
In-Depth Information
of a controllable dynamical system. It relates the
input function
(distur-
bance)
v(t)
,the
state variables
(the coordinate
y
and the velocity
y
), and
the
control variable
(control force)
u
. For the general case, the control force
should be determined as a function of the state variables and time, that is,
u
y,t)
, to provide the desired behavior of the dynamical system.
As applied to shock isolators, it is reasonable to design the control so as
to minimize the load transmitted to the object for a constrained rattlespace
or to minimize the rattlespace for a constrained transmitted load. The con-
trol
u
=
u(y,
˙
y,t)
is referred to as a
feedback
(closed-loop)
control
,since
the
output
(measured) variables
y
and
=
u(y,
˙
y
are transmitted (fed back) to the
controller. The control depending only on time (
u
˙
u(t)
) is referred to
as an
open-loop control
. It is a feedback control that is commonly uti-
lized in real-world systems because open-loop control does not respond
to unpredictable perturbations of the state of the system due to random
uncontrolled excitations and, hence, cannot provide stability for the desired
motion. Open-loop control, however, plays a very important role in control
theory and practice. Open-loop control is easier to calculate using optimal
control methods and it plays a key role in the
limiting performance analysis
of a controlled system aimed at determining the absolute minimum of the
performance index
. This minimum characterizes the hypothetically perfect
system and can be used as a reference index to judge the quality of an
existing system or the prototype of a system to be designed. The motion of
a system governed by optimal open-loop control can be used as the refer-
ence motion to be tracked by feedback control. The previous section dealt
with open-loop controls of Eqs. (2.30), (2.53), and (2.68) that mitigate the
load transmitted to the object to be protected from the shock pulses of Eqs.
(2.27), (2.50), and (2.67).
Shock isolators that involve autonomous sources of energy, sensors,
microprocessors, and actuators are called
active isolators
. Isolators that
consist of only elastic and dissipative elements are referred to as
passive
isolators
. The forces produced by elastic and dissipative elements depend
only on the strain and strain rate of these elements. Therefore, the control
force of a passive isolator does not explicitly depend on time. Consequently,
an isolator driven by open-loop control is an active isolator.
Passive isolators are usually considered within the framework of
mechanical engineering rather than control engineering because they
consist of purely mechanical components such as springs, dashpots, levers,
or resilient paddings. Modern active isolators designed as electromechan-
ical (combining mechanical and electrical components) or mechatronic
(combining mechanical, electrical, and electronic components) systems are
activated to produce a desired control force in response to a shock
disturbance. The control force of a passive isolator is a function of the state
=
Search WWH ::
Custom Search