Critério de Routh Modificado

Prévia do material em texto

Problem 3.59PP
Modify the Routh criterion so that it applies to the case in which ali the poies are to be to the left 
of -a when a > 0. Apply the modified test to the polynomial 
S3 + (6 + K)s2 + ( 5 + 6K)s + 5K = 0.
finding those values of K for which all poles have a real part less than -1.
Step-by-step solution
step 1 of 1
Shift the root to origin and then Routh’s Criteria.
- s tep 1 o n
Shift the root to origin and then Routh’s Criteria. 
Replacing s by s-a.
For the given Equation
(s - lf +(64*;)(s-l)“ +(5+6k)(s-l)+3k=0
=>(s=-l+3s-3s’ )+(sH l-2s)(64k)+(5+6fc)(!-l)+5k=0
=> s’+ s ' (-343c«) +s (3-12-2k+5+€k) -l+€4k-5.61d-5k=0
s*+(lri-3)!^+s(4M )=0
s’ 1
s’ Icf3 0
s’ 4k-4
s" 0