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Re: [python-control-discuss] LQR problem
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From: Ryan K. <rk...@si...> - 2013-06-15 14:19:31
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Thanks. That makes sense. Basically, I fit a transfer function model to an infinite dimensional model and then found the CCF model from the transfer function coefficients. So, I just took whatever the TF --> CCF conversion gave me and ran with it. In the end, I need to get back to a compensator/transfer function form to re-integrate it with my infinite dimensional model. So, as long as the observer and controller use the same states, I don't really need the original ones. It is kind of ridiculous that I have been working in controls for over a decade and know so little about practical implementation of state-space control. My work has all been transfer function SISO stuff and infinite dimensional (transfer matrix method) modeling. I have done very little practical/experimental stuff involving state-space. So, thanks for the tips to get me going. -- Ryan Krauss, Ph.D. Associate Professor Mechanical Engineering Southern Illinois University Edwardsville On Sat, Jun 15, 2013 at 3:09 AM, Rene van Paassen <ren...@gm... > wrote: > > > On 15 June 2013 05:36, Ryan Krauss <rk...@si...> wrote: > >> That seems to work, but I am trying to wrap my head around the validity >> of it. It seems to rescale the matrices to improve numeric conditioning. >> If the relationship between the input and outputs is not affected, do I >> just replace my old state-space model with this? >> >> Yes, no problem. The only thing is that you no longer have your original > states; so if you needed those, make sure you send them out in in the C > matrix before conditioning. > > You had a controllable canonical form of your state-space system. From > somewhere near order 8 and up, this almost never works out right > numerically. > > It also depends on the (time) scaling of your state variables. If you have > a slow system, your 1st derivative is going to be a small number compared > to the output state, the 2nd is even smaller, and by the time you get to > the 5th or 6th derivative, it is going to be numerically insignificant. > Another trick that is sometimes handy is picking another time scale, hours, > minutes, whatever it takes to make 1st, 2nd etc derivatives comparable > numerically to the signal itself. > > >> -- >> Ryan Krauss, Ph.D. >> Associate Professor >> Mechanical Engineering >> Southern Illinois University Edwardsville >> >> >> On Fri, Jun 14, 2013 at 4:16 PM, Rene van Paassen < >> ren...@gm...> wrote: >> >>> How about balancing the matrix first? >>> >>> Today I made a little fix in tb01id, at https://github.com/repagh/Slycot >>> >>> I get no errors with the attached modification. Don't know if the result >>> is valid, though. >>> >>> >>> On 14 June 2013 19:59, Ryan Krauss <rk...@si...> wrote: >>> >>>> I assume this is most likely an ill conditioning problem on my part >>>> (though I don't know how to fix the model if that is the case, since it is >>>> fitting experimental data as well as an infinite dimensional model), but I >>>> am getting the following error from control.lqr: >>>> >>>> /Users/rkrauss/siue/Research/papers/SFLR_2010_paper/CND_ASME_Special_Issue_Version/python/SFLR_ROM_2013/LQG_learn/lqr_problem.py >>>> in <module>() >>>> 54 >>>> 55 #K = control.lqr(ol_sys, Q, 1.0) >>>> ---> 56 K, S, E = control.lqr(A, B, Q, 0.01) >>>> 57 >>>> 58 >>>> >>>> /usr/local/Cellar/python/2.7.3/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/control-0.6d-py2.7.egg/control/statefbk.pyc >>>> in lqr(*args, **keywords) >>>> 236 >>>> 237 # Call the SLICOT function >>>> --> 238 X,rcond,w,S,U,A_inv = sb02md(nstates, A_b, G, Q_b, 'C') >>>> 239 >>>> 240 # Now compute the return value >>>> >>>> /usr/local/lib/python2.7/site-packages/slycot/synthesis.pyc in >>>> sb02md(n, A, G, Q, dico, hinv, uplo, scal, sort, ldwork) >>>> 348 e = ValueError('the Hamiltonian or symplectic matrix H >>>> has less than n stable eigenvalues') >>>> 349 e.info = info >>>> --> 350 raise e >>>> 351 if info == 5: >>>> 352 e = ValueError('if the N-th order system of linear >>>> algebraic equations is singular to working precision') >>>> >>>> ValueError: the Hamiltonian or symplectic matrix H has less than n >>>> stable eigenvalues >>>> >>>> In [5]: run lqr_problem.py >>>> >>>> --------------------------------------------------------------------------- >>>> ValueError Traceback (most recent call >>>> last) >>>> /usr/local/lib/python2.7/site-packages/IPython/utils/py3compat.pyc in >>>> execfile(fname, *where) >>>> 176 else: >>>> 177 filename = fname >>>> --> 178 __builtin__.execfile(filename, *where) >>>> >>>> /Users/rkrauss/siue/Research/papers/SFLR_2010_paper/CND_ASME_Special_Issue_Version/python/SFLR_ROM_2013/LQG_learn/lqr_problem.py >>>> in <module>() >>>> 53 Q = dot(Ca.T,Ca) >>>> 54 >>>> ---> 55 K, S, E = control.lqr(A, B, Q, 1.0) >>>> 56 >>>> 57 >>>> >>>> /usr/local/Cellar/python/2.7.3/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/control-0.6d-py2.7.egg/control/statefbk.pyc >>>> in lqr(*args, **keywords) >>>> 236 >>>> 237 # Call the SLICOT function >>>> --> 238 X,rcond,w,S,U,A_inv = sb02md(nstates, A_b, G, Q_b, 'C') >>>> 239 >>>> 240 # Now compute the return value >>>> >>>> /usr/local/lib/python2.7/site-packages/slycot/synthesis.pyc in >>>> sb02md(n, A, G, Q, dico, hinv, uplo, scal, sort, ldwork) >>>> 348 e = ValueError('the Hamiltonian or symplectic matrix H >>>> has less than n stable eigenvalues') >>>> 349 e.info = info >>>> --> 350 raise e >>>> 351 if info == 5: >>>> 352 e = ValueError('if the N-th order system of linear >>>> algebraic equations is singular to working precision') >>>> >>>> ValueError: the Hamiltonian or symplectic matrix H has less than n >>>> stable eigenvalues >>>> >>>> -- >>>> Ryan Krauss, Ph.D. >>>> Associate Professor >>>> Mechanical Engineering >>>> Southern Illinois University Edwardsville >>>> >>>> >>>> ------------------------------------------------------------------------------ >>>> This SF.net email is sponsored by Windows: >>>> >>>> Build for Windows Store. >>>> >>>> http://p.sf.net/sfu/windows-dev2dev >>>> _______________________________________________ >>>> python-control-discuss mailing list >>>> pyt...@li... >>>> https://lists.sourceforge.net/lists/listinfo/python-control-discuss >>>> >>>> >>> >>> >>> -- >>> René van Paassen | ______o____/_| Ren...@gm... >>> <[___\_\_-----< t: +31 15 2628685 >>> | o' mobile: +31 6 39846891 >>> >>> >>> >>> ------------------------------------------------------------------------------ >>> This SF.net email is sponsored by Windows: >>> >>> Build for Windows Store. >>> >>> http://p.sf.net/sfu/windows-dev2dev >>> >>> _______________________________________________ >>> python-control-discuss mailing list >>> pyt...@li... >>> https://lists.sourceforge.net/lists/listinfo/python-control-discuss >>> >>> >> >> >> ------------------------------------------------------------------------------ >> This SF.net email is sponsored by Windows: >> >> Build for Windows Store. >> >> http://p.sf.net/sfu/windows-dev2dev >> _______________________________________________ >> python-control-discuss mailing list >> pyt...@li... >> https://lists.sourceforge.net/lists/listinfo/python-control-discuss >> >> > > > -- > René van Paassen | ______o____/_| Ren...@gm... > <[___\_\_-----< t: +31 15 2628685 > | o' mobile: +31 6 39846891 > > > > ------------------------------------------------------------------------------ > This SF.net email is sponsored by Windows: > > Build for Windows Store. > > http://p.sf.net/sfu/windows-dev2dev > > _______________________________________________ > python-control-discuss mailing list > pyt...@li... > https://lists.sourceforge.net/lists/listinfo/python-control-discuss > > |
