kpure

continuous SISO system limit feedback gain

Calling Sequence

K=kpure(sys [,tol])
[K,R]=kpure(sys [,tol])

Arguments

:sys SISO linear system (syslin) : :tol a positive scalar. tolerance used to determine if a root is

imaginary or not. The default value is 1e-6

: :K Real vector, the vector of gains for which at least one closed

loop pole is imaginary.

: :R Complex vector, the imaginary closed loop poles associated with

the values of K.

:

Description

K=kpure(sys) computes the gains K such that the system sys feedback by K(i) ( sys/.K(i)) has poles on imaginary axis.

Examples

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')

See Also

• evans Evans root locus
• krac2 continuous SISO system limit feedback gain