Luenberger Observers

I need to explain Luenberger observers, but I don't like the references I have on the subject. Do you have a favorite linear
feedback controls reference? A favorite MIMO state space reference? A favorite observer reference?
I am interested in applied resources rather than theoretically sound derivations.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
Daniel Helmick wrote:

I found the explanation in "Linear Systems" by Kailath to be sufficient, but I'm hardly a connoisseur -- I've probably only got two or three books that really go into the subject, and Kailath's the only one I've gone into in depth.
--

Tim Wescott
Wescott Design Services
  Click to see the full signature.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

A book will describe how the Luenberger observer is derived and provide an example. I haven't seen the 'why bother' explained. I haven't seen the benefits explained anywhere. You must implement the Luenberger observer to see the benefits.
What I have found is that an Luenberger observer is just a model of the actual system that uses the feed back to correct for errors in the model. This isn't too much different that what a steady state Kalman filter does. The difference is the steady state Kalman filter at least calculates gains that statisically reduce the errors to a minimum. An observer doesn't necessarily minimize the error between the actual and the estimated but it is very easy to implement.
I have found there are two benefits of using an observer. 1. the estimated position, velocity and acclerations will have much more resolution than that derived directly from the feedback device. This is very beneficial for controlling higher order systemds where there is a need for using the derivative gain or the second derivative gain. 2. The observer looks like an ideal system to the closed loop control. This may be necessary when the controller is only a PID and the PID must control a higher order system or non linear system.
Look at this ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t0p5%20PID%20ITAE%20obs%20Andrew.pdf http://groups.google.com/group/sci.engr.control/browse_frm/thread/4f20f1443e7edf2d/ea41f9f771662b72?lnk=gst&q=observer#ea41f9f771662b72 There were actually several threads about this doing system identification and what to do with the generated model. The system identification was not quite right. If the gains generated from the model were used directly on the system the results would be unusable. Adding an second order observer allowed the second order PID gains to control a 5 pole system. A Luenberger obserser is very easy to implement and the gains can be great.
Peter Nachtwey
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

3. An observer can estimate system outputs that are not directly measurable. 4. An observer filters the sensed signals.
back on topic:
You say "A book will describe..." The point of this thread is to find out what book you prefer. Please use a title, author or other identifying information when refering to 'a book'.
Tim, thanks for the recommendation on Thomas Kailath. I was able to get my hands on a copy for a few minutes last night. I think it is better than my current reference from John Bay. It also seemed to have more detail than Chi-Tsong Chen had on observers and MIMO systems.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload
wrote:

What about David Luenberger's original book?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

Polytechforum.com is a website by engineers for engineers. It is not affiliated with any of manufacturers or vendors discussed here. All logos and trade names are the property of their respective owners.