In the last class we have discussed Routh Hurwitz stability criteria with the help of solved examples. In this class we are going to discuss advantages and disadvantages of Routh Hurwitz stability criteria. So first we will discuss the advantages of Routh Hurwitz stability criteria.
First one is with the help of Routh Hurwitz criteria the stability of system can be judged without solving the characteristic equation. That means we don't need to calculate. the roots of the characteristic equation for finding the stability of any system in the Routh-Hervitz stability criteria.
Second one is in this method no evaluation of determinant as in Hervitz criteria. We have already studied this Hervitz criteria. In Hervitz criteria we used to calculate the sub determinants then according to the value of sub determinant we used to judge the stability of the system. So here In this Routh stability criteria we don't need to calculate the determinants which saves the calculation time. Third one is this method gives the number of roots with positive real part to find the unstable system.
Fourth one is this method can determine critical value of gain hence frequency of sustained oscillations can be determined. So using this Routh-Hurwitz stability criteria marginal stability of the system can be judged. Fifth one, this method helps in finding range of values of K for system stability.
Sixth one is, this method helps in finding the intersection points of the root locus with imaginary axis. Now, we are going to discuss the disadvantages of Routh-Hurwitz stability criteria. First disadvantage is, this method is only valid for algebraic characteristic equation.
That is, That means the characteristic equation should be algebraic in nature. Then only this method is applicable. Second one is if the coefficients of characteristic equation is complex or contains power of e.
This method cannot be applied. Third, this method only gives information about the number of poles lying in the right half of the S plane. But this method does not give any information.
values of roots or values of poles of the system. Next disadvantage is this method cannot distinguish between complex and real roots. Sixth one is it does not provide information about exact location of poles because they don't give the values of poles therefore we cannot find the exact location of poles with this method. Seventh one it does not suggest methods of stabilizing the unstable system so And eighth is this method is applicable only to the linear control systems. So these are the advantages and disadvantages of Routh-Hervitz criteria.
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