Dear Jose, Thank you very much! Now it is working perfectly. Best,Mariusz
Wysłano z telefonu Samsung -------- Oryginalna wiadomość --------Od: Jose Luis Marín <[email protected]> Data: 20.05.2018 23:01 (GMT+01:00) Do: MATPOWER discussion forum <[email protected]> Temat: Re: CPF with Modal Analysis Hi Mariusz, I think the problem is that you have to provide a *solved* target case, because the Jacobian should be evaluated *at the solution*. Even for the base case, it wouldn't hurt to run a powerflow, since you can't always trust that the input file is a solved case. -- Jose L. Marin Grupo AIA 2018-05-20 11:58 GMT+02:00 Mariusz Drabecki <[email protected]>: Dear All, I am working on Modal Analysis. I would like to show to my students, that in the bifurcation point at least one of the reduced Jacobian eigenvalues is zero. This is why I calculate these values once for the base case and then for the nose point ( lambda max calculated by the CPF). Unfortunately there is no change in the results. Could anyone help? The results of the eigenvalues are as follows (for case14) Eigb= [65,420739,953321,993918,911816,449211,34212,706585,568867,66373] And exactly the same ones in the nose points. I would greatly appreciate any help from you as I got terribly stuck. Best,Mariusz Drabecki Here is my code: define_constantsmpc=loadcase(case14);inc=2.5; %% CPF optionsmpopt = mpoption('out.all', 0, 'verbose', 2);mpopt = mpoption(mpopt, 'cpf.stop_at', 'NOSE', 'cpf.step', 0.1);mpopt = mpoption(mpopt, 'cpf.plot.level', 2); %% Base case (base solution operating points)%CPFmpcb=mpc;mpct = mpcb; % set up target case withmpct.gen(:, [PG QG]) = mpcb.gen(:, [PG QG]) * inc; % increased generationmpct.bus(:, [PD QD]) = mpcb.bus(:, [PD QD]) * inc; % and increased loadcpf1 = runcpf(mpcb, mpct, mpopt);lambda_max=cpf1.cpf.max_lam; %Modal Analysis for Base Case[jb11,jb12,jb21,jb22,jacb,~,~,~] = makeJac(mpcb);jb11=full(jb11);jb12=full(jb12);jb21=full(jb21);jb22=full(jb22); Hb=jb11;Mb=jb12;Nb=jb21;Kb=jb22; % The reduced Jacobian for the base case (Q-V sensitivities)jacb_red=Kb-Nb*inv(Hb)*Mb; % The eigenvalues of the reduced Jacobian (Q-V sensitivities)[leftb eigb rightb]=(eig(jacb_red)); %% Target case (nose point)mpct.gen(:, [PG QG]) = mpct.gen(:, [PG QG]) * lambda_max; % increased generationmpct.bus(:, [PD QD]) = mpct.bus(:, [PD QD])* lambda_max; % and increased load % The Jacobian for the target case[jt11,jt12,jt21,jt22,jact,~,~,~] = makeJac(mpct); jt11=full(jb11);jt12=full(jb12);jt21=full(jb21);jt22=full(jb22);njact=size(jact,1); Ht=jt11;Mt=jt12;Nt=jt21;Kt=jt22; % The reduced Jacobian for the target casejact_red=Kt-Nt*inv(Ht)*Mt; % Eigenvalue decomposition of the reduced Jacobian for the target case[leftt eigt rightt]=(eig(jact_red)); ----_com.samsung.android.email_243159952681830 Content-Type: text/html; charset="utf-8" Content-Transfer-Encoding: base64 <html><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"></head><body><div>Dear Jose,</div><div><br></div><div>Thank you very much! Now it is working perfectly. </div><div><br></div><div>Best,</div><div>Mariusz</div><div><br></div><div><br></div><div><br></div><div id="composer_signature"><div style="font-size:85%;color:#575757" dir="auto">Wysłano z telefonu Samsung</div></div><div><br></div><div style="font-size:100%;color:#000000"><!-- originalMessage --><div>-------- Oryginalna wiadomość --------</div><div>Od: Jose Luis Marín <[email protected]> </div><div>Data: 20.05.2018 23:01 (GMT+01:00) </div><div>Do: MATPOWER discussion forum <[email protected]> </div><div>Temat: Re: CPF with Modal Analysis </div><div><br></div></div><div dir="ltr">Hi <span lang="EN-US">Mariusz</span>,<br><div><div class="gmail_extra"><br></div><div class="gmail_extra">I think the problem is that you have to provide a *solved* target case, because the Jacobian should be evaluated *at the solution*.<br></div><div class="gmail_extra"><br></div><div class="gmail_extra">Even for the base case, it wouldn't hurt to run a powerflow, since you can't always trust that the input file is a solved case.<br></div><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><span><div><div dir="ltr"><div>-- <br></div>Jose L. Marin<br>Grupo AIA<br><br><br></div></div></span></div></div></div></div></div> <br><div class="gmail_quote">2018-05-20 11:58 GMT+02:00 Mariusz Drabecki <span dir="ltr"><<a href="mailto:[email protected]"; target="_blank">[email protected]</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div link="#0563C1" vlink="#954F72" lang="PL"><div class="m_-7027355414623167184WordSection1"><p class="MsoNormal">Dear All,<u></u><u></u></p><p class="MsoNormal"><u></u> <u></u></p><p class="MsoNormal"><span lang="EN-US">I am working on Modal Analysis. I would like to show to my students, that in the bifurcation point at least one of the reduced Jacobian eigenvalues is zero. This is why I calculate these values once for the base case and then for the nose point ( lambda max calculated by the CPF). <u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">Unfortunately there is no change in the results. Could anyone help?<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">The results of the eigenvalues are as follows (for case14)<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">Eigb= <u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">[<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">65,4207<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">39,9533<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">21,9939<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">18,9118<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">16,4492<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">11,3421<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">2,70658<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">5,56886<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">7,66373<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">]<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">And <b>exactly the same ones</b> in the nose points.<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">I would greatly appreciate any help from you as I got terribly stuck.<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">Best,<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US">Mariusz Drabecki<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US">Here is my code:<u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">define_constants</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpc=loadcase(case14);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black">inc=2.5;</span><span style="font-size:12.0pt;font-family:"Courier New""><u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">%% CPF options</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpopt = mpoption(</span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'out.all'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, 0, </span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'verbose'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, 2);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpopt = mpoption(mpopt, </span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'cpf.stop_at'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, </span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'NOSE'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, </span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'cpf.step'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, 0.1);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpopt = mpoption(mpopt, </span><span style="font-size:10.0pt;font-family:"Courier New";color:#a020f0" lang="EN-US">'cpf.plot.level'</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">, 2);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal"><span lang="EN-US"> <u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">%% Base case (base solution operating points)</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">%CPF</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpcb=mpc;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpct = mpcb; </span><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% set up target case with</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpct.gen(:, [PG QG]) = mpcb.gen(:, [PG QG]) * inc; </span><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% increased generation</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpct.bus(:, [PD QD]) = mpcb.bus(:, [PD QD]) * inc; </span><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% and increased load</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">cpf1 = runcpf(mpcb, mpct, mpopt);<u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">lambda_max=cpf1.cpf.max_lam;<u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">%Modal Analysis for Base Case</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">[jb11,jb12,jb21,jb22,jacb,~,~,<wbr>~] = makeJac(mpcb);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jb11=full(jb11);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jb12=full(jb12);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jb21=full(jb21);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jb22=full(jb22);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">Hb=jb11;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">Mb=jb12;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">Nb=jb21;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">Kb=jb22;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% The reduced Jacobian for the base case (Q-V sensitivities)</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jacb_red=Kb-Nb*inv(Hb)*Mb;<u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% The eigenvalues of the reduced Jacobian (Q-V sensitivities)</span><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">[leftb eigb rightb]=(eig(jacb_red));</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">%% Target case (nose point)</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpct.gen(:, [PG QG]) = mpct.gen(:, [PG QG]) * lambda_max; </span><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% increased generation</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">mpct.bus(:, [PD QD]) = mpct.bus(:, [PD QD])* lambda_max; </span><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% and increased load</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% The Jacobian for the target case</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">[jt11,jt12,jt21,jt22,jact,~,~,<wbr>~] = makeJac(mpct);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jt11=full(jb11);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jt12=full(jb12);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jt21=full(jb21);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jt22=full(jb22);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">njact=size(jact,1);</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">Ht=jt11;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Mt=jt12;</span><span style="font-size:12.0pt;font-family:"Courier New""><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Nt=jt21;</span><span style="font-size:12.0pt;font-family:"Courier New""><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black">Kt=jt22;</span><span style="font-size:12.0pt;font-family:"Courier New""><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span style="font-size:12.0pt;font-family:"Courier New""><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% The reduced Jacobian for the target case</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">jact_red=Kt-Nt*inv(Ht)*Mt;</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:forestgreen" lang="EN-US">% Eigenvalue decomposition of the reduced Jacobian for the target case</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US">[leftt eigt rightt]=(eig(jact_red));</span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;font-family:"Courier New";color:black" lang="EN-US"> </span><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u><u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal" style="text-autospace:none"><span style="font-size:12.0pt;font-family:"Courier New"" lang="EN-US"><u></u> <u></u></span></p><p class="MsoNormal"><span lang="EN-US"><u></u> <u></u></span></p></div></div></blockquote></div><br></div></div></div> </body></html> --
