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kpure
continuous SISO system limit feedback gain
Syntax
K=kpure(sys [,tol]) [K,R]=kpure(sys [,tol])
Arguments
- sys
A SISO linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.
- 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')
![](/docs/6.0.1/en_US/kpure_1.png)
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')
![](/docs/6.0.1/en_US/kpure_2.png)
History
Version | Description |
6.0 | Handling zpk representation |
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