PSN-L Email List Message
Subject: Re: Other thoughts on an inverted pendulum
From: "George Harris" gjharris@.............
Date: Mon, 27 Jan 2003 22:59:06 -0800
Some comments on inverted pendulums based on experiments some years ago.
1. I believe that the inverted pendulum becomes unstable for anything =
but very=20
small displacements. It is very difficut to get long periods. It is =
important to
limit the maximum displacement so that the spring (or springs) do not =
take s
permanent set. =20
2. The most usefull configuration found was a mass supported on two flat =
springs.
The base support and the mass were the same width and flat springs =
clamped
to both sides. Adjusting the unsupported spring length provides the =
major=20
adjustment of period, and adding weight is the final adjustment.
3. I had planned to make the structure into a feedback unit. The two =
springs
can be used to provide the conductors to a flat coil on the top of the =
mass.
Two flat magnets on the top can them be used for both feedback and =
damping.
4. It is my belief that a feed back unit can be used in the slightly =
unstable mode. =20
It depends on having the amplifier response designed for good stability.
George Harris
----- Original Message -----=20
From: ChrisAtUpw@..........
To: psn-l@.................
Cc: Ed Ianni ; johnjan@...........
Sent: Sunday, January 26, 2003 10:06 PM
Subject: Re: Other thoughts on an inverted pendulum
At 07:40 AM 1/26/2003, you wrote:=20
John, some other thoughts......I am attaching a drawing......I hope =
you receive it. I will describe it to you anyway.......=20
I am thinking of possibly extending the brass rod down into the =
spring while it still protrudes from the top. I would also attach a very =
small level at the bottom of the brass rod to insure leveling and =
possibly increase damping. Instead of placing four wooden dowels (as =
shown in the drawing) around the spring to possibly prevent the =
magnet/weight from getting to the point where it falls/hangs over the =
spring I would replace them with a transparent (to view the level) =
glass/plastic circular column that reached the elevation of the magnet. =
Please remember one thing....I don't know what I'm talking about.....Ed.
In a message dated 26/01/03, johnjan@........ writes:=20
Hi Ed,=20
The way to think about the inverted pendulum is that we are =
balancing two forces.=20
Gravity wants to tip the pendulum over, and the greater the angle =
the greater this=20
force is. The spring at the base wants to keep the pendulum =
upright, and the=20
greater the angle the greater the force of the spring is in this =
direction.=20
If I have the math correct, then the problem I had with instability =
may have=20
been due to my setup. My inverted pendulum was made from mounting a =
thin metal rod vertically and putting a mass at the top. The entire =
rod bent.=20
When I tried to achieve a long period, the rod would bend to one =
side and=20
stay there!=20
The CSM student design has a solid rod with a spring at the base.=20
http://jjlahr.com/science/psn/epics/reports/sens/index.html=20
I think for that design.....=20
Damping is another thing that will need to be worked out......=20
My suggestion would be to first work on getting as long a period as =
possible and then work on the damping.=20
Cheers,=20
John=20
Hi John, Ed,=20
I have some serious reservations about the above design. =
Firstly, with a brass rod and a magnet weight supported by a coil =
spring, there is nothing to prevent the spring / rod system 'twanging' =
or oscillating, laterally or vertically. There is no damping at all for =
such motion. As a general rule in seismometer construction, if parasitic =
oscillations can occur and are not damped, they will give problems.=20
Secondly, since an equal voltage will be induced in the single =
coil for equal motion in any lateral direction, the output signal for a =
quake will be 'frequency doubled'. The output sensitivity will also be =
very low, since although the field through the coil is high, the total =
field over the coil is almost constant for small motions. I suspect that =
the largest signal would be due to vertical motions of the well sprung =
magnet!=20
This can be corrected if you use four small coils in place of =
the single one, with the same vertical axis, but connected in opposing =
pairs. The motion will be resolved into two signals. An increase in the =
flux through one coil of a pair will be added to a decrease in flux =
through the other coil. Since the coil centres are now offset to maybe =
about half the maximum field, the change in flux with any lateral =
movement will be high. Vertical motion will give opposing voltages in a =
coil pair which ~cancel out.=20
I would suggest that you try using a light ~1/8" Al rod =
(knitting needle?) with the magnet bob on one end and a single spring =
wire glued / swaged into an axial hole bored in the other end. If you =
have a two bar clamp on the baseplate, you can vary the length of spring =
wire used. This should be fairly rigid for vertical movements. The rod =
can be threaded through a disk of 1/4" Al plate with a 1/4" hole in the =
centre, to provide damping. This seems to give adequate damping with =
>1/8" separation. You centre the rod in the hole and move the plate =
vertically closer to the magnet to increase the damping. This hole would =
also control the maximum allowed lateral movement.=20
The overall stability could be finely adjusted by mounting a =
second axial magnet above the bob magnet and positioning it vertically. =
This could either increase or decrease the centralising force, depending =
on whether the two magnets attract or repel. You will need to adjust the =
final damping after setting the period.=20
However, I would expect the period to be limited by variations =
in the spring constant and the magnetic fields with temperature. If you =
used a stiffer spring and repelling fields, you might be able to =
partially compensate the decrease in stiffness of the spring with the =
decrease in the magnetic fields. Precision levelling / balancing the =
device will be critical. You won't need a spirit level - the rod will do =
that for you. HAVE FUN!=20
Regards,=20
Chris Chapman=20
Some comments on inverted =
pendulums based on=20
experiments some years ago.
1. I believe that the inverted pendulum =
becomes=20
unstable for anything but very
small displacements. It is very =
difficut to=20
get long periods. It is important to
limit the maximum displacement so that =
the spring=20
(or springs) do not take s
permanent set.
2. The most usefull configuration =
found was a=20
mass supported on two flat springs.
The base support and the mass were the =
same width=20
and flat springs clamped
to both sides. Adjusting the =
unsupported spring=20
length provides the major
adjustment of period, and adding weight =
is the=20
final adjustment.
3. I had planned to make the structure =
into a=20
feedback unit. The two springs
can be used to provide the conductors =
to a flat=20
coil on the top of the mass.
Two flat magnets on the top can them be =
used for=20
both feedback and damping.
4. It is my belief that a feed back =
unit can=20
be used in the slightly unstable =
mode. =20
It depends on having the amplifier =
response=20
designed for good stability.
George Harris
----- Original Message -----
Sent: Sunday, January 26, 2003 =
10:06=20
PM
Subject: Re: Other thoughts on =
an=20
inverted pendulum
At 07:40 AM =
1/26/2003,=20
you wrote:
John, some other thoughts......I am attaching a =
drawing......I=20
hope you receive it. I will describe it to you =
anyway.......
=
I am thinking of=20
possibly extending the brass rod down into the spring while it still =
protrudes from the top. I would also attach a very small level at =
the bottom=20
of the brass rod to insure leveling and possibly increase damping. =
Instead=20
of placing four wooden dowels (as shown in the drawing) around the =
spring to=20
possibly prevent the magnet/weight from getting to the point where =
it=20
falls/hangs over the spring I would replace them with a transparent =
(to view=20
the level) glass/plastic circular column that reached the elevation =
of the=20
magnet. Please remember one thing....I don't know what I'm talking=20
about.....Ed.
In a message =
dated 26/01/03,=20
johnjan@........ writes:
Hi Ed,
The way to think about the inverted =
pendulum is=20
that we are balancing two forces.
Gravity wants to tip the =
pendulum=20
over, and the greater the angle the greater this
force is. =
The=20
spring at the base wants to keep the pendulum upright, and the =
greater=20
the angle the greater the force of the spring is in this direction.=20
If I have the math correct, then the problem I had with =
instability=20
may have
been due to my setup. My inverted pendulum was =
made from=20
mounting a
thin metal rod vertically and putting a mass at the =
top.=20
The entire rod bent.
When I tried to achieve a long =
period, the=20
rod would bend to one side and
stay there!
The CSM =
student=20
design has a solid rod with a spring at the base.
http=
://jjlahr.com/science/psn/epics/reports/sens/index.html=20
I think for that design.....
Damping is another thing =
that will=20
need to be worked out......
My suggestion would be to first =
work on=20
getting as long a period as possible and then work on the damping.=20
Cheers,
John
Hi John, Ed,=20
I have some serious =
reservations=20
about the above design. Firstly, with a brass rod and a magnet weight=20
supported by a coil spring, there is nothing to prevent the spring / =
rod=20
system 'twanging' or oscillating, laterally or vertically. There is no =
damping=20
at all for such motion. As a general rule in seismometer construction, =
if=20
parasitic oscillations can occur and are not damped, they will give =
problems.=20
Secondly, since an equal =
voltage will=20
be induced in the single coil for equal motion in any lateral =
direction, the=20
output signal for a quake will be 'frequency doubled'. The output =
sensitivity=20
will also be very low, since although the field through =
the coil=20
is high, the total field over the coil is almost constant for small =
motions. I=20
suspect that the largest signal would be due to vertical =
motions=20
of the well sprung magnet! =
This can be=20
corrected if you use four small coils in place of the single one, with =
the=20
same vertical axis, but connected in opposing pairs. The motion will =
be=20
resolved into two signals. An increase in the flux through one coil of =
a pair=20
will be added to a decrease in flux through the other coil. Since the =
coil=20
centres are now offset to maybe about half the maximum field, the =
change in=20
flux with any lateral movement will be high. Vertical motion will give =
opposing voltages in a coil pair which ~cancel out.=20
I would suggest that you try =
using a=20
light ~1/8" Al rod (knitting needle?) with the magnet bob on one end =
and a=20
single spring wire glued / swaged into an axial hole bored in the =
other end.=20
If you have a two bar clamp on the baseplate, you can vary the length =
of=20
spring wire used. This should be fairly rigid for vertical movements. =
The rod=20
can be threaded through a disk of 1/4" Al plate with a 1/4" hole in =
the=20
centre, to provide damping. This seems to give adequate damping with =
>1/8"=20
separation. You centre the rod in the hole and move the plate =
vertically=20
closer to the magnet to increase the damping. This hole would also =
control the=20
maximum allowed lateral movement. =
The=20
overall stability could be finely adjusted by mounting a second axial =
magnet=20
above the bob magnet and positioning it vertically. This could either =
increase=20
or decrease the centralising force, depending on whether the two =
magnets=20
attract or repel. You will need to adjust the final damping =
after=20
setting the period. =
However, I=20
would expect the period to be limited by variations in the spring =
constant and=20
the magnetic fields with temperature. If you used a stiffer spring and =
repelling fields, you might be able to partially compensate the =
decrease in=20
stiffness of the spring with the decrease in the magnetic fields. =
Precision=20
levelling / balancing the device will be critical. You won't need a =
spirit=20
level - the rod will do that for you. HAVE FUN!=20
Regards,=20
Chris Chapman=20
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