This problem actually consists of two parts: the first is to stabilize
the position of the spool mass, the second is to reduce the spool mass
position error to zero, with respect to the command input. Stability
here just means that the mass position holds a 'steady state' constant
value, and does not tend towards large erroneous magnitudes.
The basic circuit layout may in fact be accomplished with analog
components such as amplifier stages, or filters, consisting of
resistors and capacitors.
Fundamentally, you take the spool position sensor output voltage and
use it as one of two inputs to a summation amplifier. The other input
to the summing amp is the command, or desired input. The objective of
the summing amp is to generate an error signal, consisting of the
difference between the input magnitude and the output magnitude. This
error signal is what drives the servoactuator, which is probably a
hydraulic pump or valve. Note that when utilizing amplifiers, you must
account for inversions and proportionality factors, which are usually
readily apparent.
In order to effect a stable mass position, you will employ lead-lag filters.
These are merely R and C constructions, which affect the error signal
coming from the summing amp. I would suggest starting off with two
identical lead-lag filters, placed after the the summing amp, and
prior to the actuator input. If you still observe instability with two
lead-lag filters, then you will have to try a different number of
lead-lags units, until you see the desired result ... three might work
... four might work ... it is difficult to say without a more accurate
analysis.
The detailed construction of lead-lag filters is given in certain
textbooks on feedback control systems, but is not too complicated. The
placement or specification of the lead-lag filters is probably the
most critical factor as far as achieving a stable mass position. The
lead, or numerator component, should be as small as is practical, and
the lag component should be larger, that is, it should 'break' at a
higher frequency. Ideally, you will not require more than two lead-lag
units. However, this is merely a guess, and actually requires a more
detailed analysis.
Once you have achieved a noticeable improvement in the desired mass
position performance, you can focus on zeroing the mass position error
by adding a 'unity factor' integration amplifier, after the summing
amp. However, this addition to the circuit will probably bring about
the unstable condition, which can then be corrected by the use of one
additional lead-lag filter.
When you have achieved a stable, and 'zero error' mass position, you
may readjust the lead-lag filter components in a manner which brings
about the required settling time specifications. |
