Re: evplace (eigenvalue placement)

Path	csiph.com!usenet.pasdenom.info!weretis.net!feeder4.news.weretis.net!ecngs!feeder2.ecngs.de!newsfeed.freenet.ag!news2.euro.net!postnews2.euro.net!news.wanadoo.nl!not-for-mail
From	mhx@iae.nl (Marcel Hendrix)
Subject	Re: evplace (eigenvalue placement)
Newsgroups	comp.lang.forth
Message-ID	<00641598978435@frunobulax.edu> (permalink)
Date	Tue, 5 Jun 2012 20:39:03 +0200
References	<a7c45f39-a778-4c4f-b653-326b1af1c3b2@w24g2000vby.googlegroups.com>
X-Newsreader	iForth 2.0 console (October 21, 2006)
Lines	37
Organization	Wanadoo
NNTP-Posting-Date	05 Jun 2012 18:38:56 GMT
NNTP-Posting-Host	s529d937f.adsl.wanadoo.nl
X-Trace	1338921536 dr5.euro.net 227 82.157.147.127:52412
X-Complaints-To	abuse@wanadoo.nl
Xref	csiph.com comp.lang.forth:12720

Show key headers only | View raw

Krishna Myneni <krishna.myneni@ccreweb.org> writes Re: evplace (eigenvalue placement)

> On Jun 4, 1:47 pm, m...@iae.nl (Marcel Hendrix) wrote:
[..]

> Is this the ev->coeffs word that caused you a problem? 

>                                                        Does the
> present code work for the general case?

In my application p(z) will always have real coefficients. This is 
equivalent to saying that the poles p1,..pn are either real or appear 
in complex conjugated pairs. Arbitrary isolated complex poles don't 
happen in electrical networks. I use this fact to make the type of 
p(z) DOUBLE instead of COMPLEX. However, with a slight change the 
code should work for complex coefficients, too (and be even simpler).

[..]
>> Having evplace, obsv, and ctrb means one doesn't need access to Matlab
>> for the design of simple digital controllers.

> Does it apply as well to continuous analog controllers, or does your
> implementation assume some sort of discretization?

I use this for digitally controlled power electronics circuitry. 
The code that I've shown only works when an analog circuits is 
sampled, i.e. dx/dt = A x + B u should be converted to x[k+1] = 
Phi x[k] + Gamma u[k]. This can be done by using the EXPM function 
(exponential matrix) and Van Loan's famous formula to prevent 
integrating the B u term. The pi are poles in the Z domain, and 
for a stable system they have the property that zabs(pi) <= 1. 
Maybe this can be used to further simplify the code.

An SMPS is inherently a discrete circuit. 

-marcel

Thread

evplace (eigenvalue placement) mhx@iae.nl (Marcel Hendrix) - 2012-06-04 20:47 +0200
  Re: evplace (eigenvalue placement) Krishna Myneni <krishna.myneni@ccreweb.org> - 2012-06-04 21:08 -0700
    Re: evplace (eigenvalue placement) mhx@iae.nl (Marcel Hendrix) - 2012-06-05 20:39 +0200
  Re: evplace (eigenvalue placement) Arnold Doray <invalid@invalid.com> - 2012-06-05 16:15 +0000

csiph-web