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Re: sys variables for control theory


From: Doug Stewart
Subject: Re: sys variables for control theory
Date: Thu, 06 Nov 2003 11:56:41 -0500
User-agent: Mozilla/5.0 (Windows; U; Windows NT 5.0; en-US; rv:1.2.1) Gecko/20021130






Andy Adler wrote:
On Wed, 5 Nov 2003, Doug Stewart wrote:


These thoughts are for those that use octive for control theory and design.
I was trying to model a PID controller and use it in a closed loop
negative feed back loop. The PID numerator is a quadratic equation and
the denominator is first order. Thus the numerator is of higher order
than the denominator. Octave's tf2sys.m does not like this but Matlab's
tf.m thinks it is OK. I understand that you can't do a step or bode etc.


Is this allowed? If so, I'll need to appologize to my students.
I've been teaching that a control system with more poles than zeros
(ie numerator of higher order than denominator) is inherently unstable.

Are there control gurus out there that can clarify?

No you don't have to apologize to your students!! :-) that I am talking about is part of a complete system. Some times you cam start with an unstable plant and add a controller to stabilize it. In my example the plant is too slow so we add a "Fast" controller to speed up the system.
The generalize equations for the PID controller are

PID= Kp +Ki/s +sKd which gives

   Kd S^2  + Kp S  +Ki
------------------------
          S

All I want to do is form up each part of the overall system as a sys variable and then join them all together using sysmult and feedback.
This can be done in Matlab, but not Octave.



Thanks

Andy





A S Hodel wrote:
> The reason behind octave's restriction is to ensure the ability to
> convert between
> rational polynomial representations (tf, zp) and state-space
> representations.  That is,
> a PID in the form described is not physically realizable, that is, the
> transfer function
> is not proper.   A hardware (or software)
> implementation requires an extra pole with very fast settling time
> (relative to open loop
> poles and closed loop design poles).
>

With all due respect to A S Hodel, I will just note that my students build and test this PID opamp circuit every year and then they model it in "C" and so it is realizable. Also you can buy them off the shelf for industry.

Now for the real question.
This conversion between tf zp ss representations is where the work will be needed.

Would it be OK if we checked for proper form at the start of the conversion and reported an error at this point?

OR

Should we allow improper form for zp ss and tf and only do the checking when we try and get a time space result ie. "step impulse bode? rlocus?".


Doug Stewart



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