dynamic mode for optimal control

On Fri, 07 Dec 2007 22:58:48 +0000, Everett X. Wang wrote:


If the robot is stable by itself, set all your gains to zero.

If you want more than just a stable robot you may need to use more
information than what you've shared with us.

I've got a pretty jaundiced view of "optimal control".  It works great,
as long as you jigger the process by putting a cost on the control
variables.  This is almost never done because the control variables are
expensive -- it's done to fake the algorithm into making a 'safer'
controller, and the margins are hard to figure out.

I suggest you try the high-control-variable-cost approach, but go back
and check your system for stability as you vary the parameters of of your
plant.  If you want to do this in a formal manner, study up on robust
control.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

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Thanks for your suggestions. Yes, I have picked a control cost and control
variable and obtained a two point boundary value problem, which is solved
by using relaxtion method. The process requires iteration. But it is not too
bad for a P3 machine. What is the high-control-variable-cost approach? I
have
not studied robust control. What is the main difference between optimal
control
and robust control? Can you tell me the pros and cons of the two methods?

Thanks a lot and have a nice weekend,

Everett
ps. You have given me quite a few suggestions already on the selection of
brushless
vs. step motor, optimal control etc before. Thanks a lot.

It is a matter of means that you use. The following refers to linear and
nonlinear systems:

1. The transfer function should be as accurate as possible.
2. Then you can find best feedforward use.
3. In addition disturbances should also be best compensated.

What I mean can be seen in an example with 2 disturbances:

Page 1: Definitions
Page 2: PID control
Page 3: PID and feedforward
Page 4: PID and feedforward and disturbance compensations

http://home.arcor.de/janch/janch/_control/20071208-controlcomparison/

The examples are based on a linear system. The linear ODEs can be replaced
by nonlinear ODEs if known. The process transfer function can be preferably
found via measurements.


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Jan C. Hoffmann  eMail aktuell: janch@nospam.arcornews.de
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