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


.. _evans: evans.html
.. _krac2: krac2.html