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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 ``` ``````// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab // Copyright (C) INRIA - Serge Steer // // This file must be used under the terms of the CeCILL. // This source file is licensed as described in the file COPYING, which // you should have received as part of this distribution. The terms // are also available at // http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt function [K,R]=kpure(sl,eps) //if sl is a transfert function N(S)/D(s) kpure looks for K producing //pure imaginary roots for // P(s)=D(s)+K*N(s) //There is a pair of pure imaginary poles if and only if // P(%i*q)=0 (1) // and // P(-%i*q)=0 (2) // because N and D are polynomials with real coefficients. //Author: Serge Steer, INRIA y=[];R=[]; msg=_("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n") if argn(2)==1 then eps=1e-6,end if size(eps,'*')==2 then eps=eps(2),end //compatibility select typeof(sl) case 'rational' then if size(sl.num,'*') <> 1 then error(msprintf(msg,"kpure",1)) end case 'state-space' then if size(sl.D,'*') <> 1 then error(msprintf(msg,"kpure",1)) end sl=ss2tf(sl) else error(msprintf(msg,"kpure",1)) end //(1) give K(s)=-D(s)/N(s) s=poly(0,varn(sl.den)) K=-sl.den/sl.num; // replace K by the previous value in (2) and find the roots s=roots(numer(horner(sl.den,-s)+K*horner(sl.num,-s)),'e'); //retain pure imaginary roots s=imag(s(abs(real(s))0).'*%i); //find the K(s) values K(s)=-D(s)/N(s) K=-real(freq(sl.den,sl.num,R)) endfunction ``````