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MathGroup Archive 2005

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Re: Modeling Saturation - Sensor or Acutuator

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62440] Re: Modeling Saturation - Sensor or Acutuator
  • From: John Doty <jpd at whispertel.LoseTheH.net>
  • Date: Thu, 24 Nov 2005 06:33:39 -0500 (EST)
  • References: <dluq25$nfu$1@smc.vnet.net> <dm1aa0$hqo$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Gmac wrote:

> I should add that I want to do this in the S-plane, not in the time
> domain.
> 
> I have a transfer function in the s-plane that maps the output of a PID
> controller to the angle of the output shaft of the motor, but how do I
> add in saturation of the amplifier (it can only supply limited
> voltage), the motor torque and motor speed? 

In general, you can't do this. This is not a software limitation: it is 
a fundamental limitation of the S-plane formalism. The S-plane formalism 
*postulates* linearity, but you're asking how to incorporate 
nonlinearity into it!

The usual way of doing this is to linearize the system around an 
equilibrium point and then analyze things like the stability of that 
equilibrium in the s-plane. But often that's only the beginning: if you 
need to understand system behavior sufficiently away from equilibrium 
that the linear postulate is no longer a decent approximation, you'll 
need to resort to other approaches such as time domain simulations or 
phase space analysis.

-jpd


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