The acceleration is indispensable as a state-variable for
precise analysis of the dynamic response of a drive system. This is because it
represents the direct, undelayed response of a mass being moved in reaction to
all the forces acting on it. If one assumes that in the typical drive control
loop there is usually a position sensor implemented to detect the actual value,
then it would – theoretically – be possible to calculate the acceleration by
double-differentiation of the position signal. In practice, the signal derived
in this way would be useless, since each differentiation exaggerates any errors
present, and so a double differentiation would inevitably produce a very noisy
signal. The situation is even more critical for highly dynamic systems. In this
case, even a directly produced velocity signal, such as the output signal from a
tachogenerator, is not suitable for the generation of a good acceleration signal
– even the short sampling time that is required by the control system for a
single differentiation will lead to sizeable quantization errors – quite apart
from the amplification of any errors. In other words, for the analysis of highly
dynamic systems, the acceleration must be measured directly.
Classic acceleration sensors on the spring-mass principle have
inherent disadvantages. They measure the absolute acceleration not the relative
acceleration, which may be relevant. For example, consider a handling robot,
with the hand axis mounted on a rotary axis, and where it is necessary to sense
the dynamics of the hand movement relative to the higher-level rotary axis.
Furthermore, a spring-mass system is frequently sensitive to motion orthogonal
to the measurement axis, so that the required measurement may be falsified. This
effect can arise, for instance, on a machine-tool compound slide, where the top
slide is moving in the X direction, while the cross slide is simultaneously
moving in the Y direction. And where rotary movements are concerned, the
application of absolute acceleration sensors is extremely complicated. The
energy supply and signal transmission requires the use of slip-rings or
contactless forms of transmission, such as rotary transformers or telemetry
systems.
Considerable improvements in the analysis of drive systems can
be achieved by using relative acceleration sensors based on the Ferraris
principle, named after the Italian Galileo Ferraris. The principle is that
permanent magnets mounted in a fixed detector unit induce eddy currents in a
moving, conductive, but non-magnetic material. For measuring rotary acceleration
this material can be in the form of a disk, for linear acceleration it is formed
as a strip of metal (see picture on top). The eddy currents and the magnetic
fields that they generate are proportional to the radial velocity of the disk
(or the linear velocity of the strip). A change in the eddy current produces a
voltage in the coils mounted in the detector unit that is proportional to the
rate of change of the velocity, i.e. proportional to the acceleration. The
reverse application of this principle has, incidentally, been used for a very
long time in electricity consumption meters. The decisive factor is that the
differentiation is not based on a sample over a discrete time period, but is a
physical effect, so that the user sees a dynamic, low-noise acceleration
signal.
Ferraris sensors for increasing control-loop
performance
Whenever a drive has to be controlled, a signal for the actual
speed is required, which is fed back to the control system. This speed signal
should be highly precise and ideally without any delay. In most cases this
purpose is achieved by a linear or angular encoder (glass scale linear encoder,
resolver, optical incremental encoder), where differentiating the position
signal yields the desired speed signal. The drawback of this method is that by
differentiation noise and fluctuations are pronounced. The situation is even
more critical for highly dynamic systems, where even the short sampling time
that is required by the control system will lead to sizeable quantization errors
- quite apart from the amplification of any errors.
If one uses not only the position signal from the position
encoder in the control loop, but also the integrated signal from a Ferraris
sensor as the velocity signal (instead of deriving it from the position signal),
then the dynamics, disturbance resistance and smoothness of the drive will be
significantly improved. In this way, the Ferraris sensor becomes part of the
control loop, and the resulting quietness of the system also reduces the wear on
mechanical components, prevents the generation of unwanted noise, and reduces
the power loss in the motor. |
