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