kpure — continuous SISO system limit feedback gain
K=kpure(sys [,tol]) [K,R]=kpure(sys [,tol])
SISO linear system (syslin)
a positive scalar. tolerance used to determine if a
root is imaginary or not. The default value is
1e-6
Real vector, the vector of gains for which at least one closed loop pole is imaginary.
Complex vector, the imaginary closed loop poles
associated with the values of K.
K=kpure(sys) computes the gains K such that the system
sys feedback by K(i) (sys/.K(i)) has poles on imaginary axis.
num=real(poly([-1+%i, -1-%i, -1+8*%i -1-8*%i],'s')); den=real(poly([0.5 0.5 -6+7*%i -6-7*%i -3 -7 -11],'s')); h=num/den; [K,Y]=kpure(h) clf();evans(h) plot(real(Y),imag(Y),'+r') num=real(poly([-1+%i*1, -1-%i*1, 2+%i*8 2-%i*8 -2.5+%i*13 -2.5-%i*13],'s')); den=real(poly([1 1 3+%i*3 3-%i*3 -15+%i*7 -15-%i*7 -3 -7 -11],'s')); h=num/den; [K,Y]=kpure(h) clf();evans(h,100000) plot(real(Y),imag(Y),'+r')