Search   Memberlist   Usergroups
 Page 1 of 1 [1 Post]
Author Message
Cheng Cosine
science forum Guru Wannabe

Joined: 26 May 2005
Posts: 168

Posted: Sun Apr 16, 2006 4:21 am    Post subject: ? thermal feedback

In Luenberger's Intro to dynamics sys, there is an example describing how

a simple feedback system works. For a system governed by

dx/dt = u(t),

suppose u(t) is designed so that u(t) = a*( x0-x(t) ), then

the system becomes

dx/dt = a*( x0-x(t) ), which will approach to x0 as time approaches
infinite.

This somehow mimics a thermal feedback regulator at home. But in real work,

temperature decays after a constant heating, so a more realistic system eqn
should be

dx/dt = -k*x+u(t), k>0 and u(t) = function of x(t) to send feedback to
original system.

A simplest one is just: dx/dt = -k*x+b*( x0-x(t) )-k*x0 so that we have

dx/dt = ( b-k )*( x0-x(t) ) and then system approaches to x0 as time
approaches to inifnite.

But how does one have a feedback u(t) that moves the system to x0 in

of at inifite time?

Furthermore, how about a cheap thermal regulator works like this: heat
up for a fixed time

period (tH) and then wait for a fixed time (tC). The amount of heat is

the deviation of x(t) to desired level x0, say, u(t) = b*( x0-x(t) ). Will
this appraoches to

desired x0 finally? How to estimate the time required for x(t) to reach x0
in, say, 99%?

Thanks,
by Cheng Cosine
Apr/16/2k6 NC

 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 Page 1 of 1 [1 Post]
 The time now is Mon Dec 17, 2018 6:44 pm | All times are GMT
 Jump to: Select a forum-------------------Forum index|___Science and Technology    |___Math    |   |___Research    |   |___num-analysis    |   |___Symbolic    |   |___Combinatorics    |   |___Probability    |   |   |___Prediction    |   |       |   |___Undergraduate    |   |___Recreational    |       |___Physics    |   |___Research    |   |___New Theories    |   |___Acoustics    |   |___Electromagnetics    |   |___Strings    |   |___Particle    |   |___Fusion    |   |___Relativity    |       |___Chem    |   |___Analytical    |   |___Electrochem    |   |   |___Battery    |   |       |   |___Coatings    |       |___Engineering        |___Control        |___Mechanics        |___Chemical

 Topic Author Forum Replies Last Post Similar Topics thermal wear Mark-T Chem 7 Fri Jul 14, 2006 9:39 pm Factoring idea, feedback needed jstevh@msn.com num-analysis 1 Sun Jul 02, 2006 7:30 pm Looking for feedback for a True/False question from a pra... Snis Pilbor Math 3 Sat Jun 17, 2006 12:08 am OMEGA of the thermal field, T=2.7 K is 2/3 NILS BÖRJESSON Math 0 Mon Jun 12, 2006 6:39 pm Need feedback on a basic integration concept lingyai Undergraduate 4 Wed May 24, 2006 8:37 am