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 -----
From:=20 ChrisAtUpw@.......
To: psn-l@..............
Cc: Ed Ianni ; johnjan@........
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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