When root locus intersects the imaginary axis then the system is?
The root locus diagram is plotted by using the open-loop poles but not the closed-loop poles. If the root loci intersect with the imaginary axis, it indicates that there are roots on the imaginary axis and hence the system is marginally stable.
What should be nature of root locus about the real axis?
The number of branches to the root locus is equal to the number of roots of the character- istic equation, usually n. Each branch starts at an open loop pole and ends at an open loop zero. Root loci are always symmetrical with respect to the real axis.
How many roots are on the JW axis?
There are no roots on the jw axis since there were no 0s in the the first column. The third system is the same as the second system except that the gain has been increased by a factor of 10.
How is the locus of an imaginary axis determined?
Locus crosses imaginary axis at 2 values of K. These values are normally determined by using Routh’s method. This program does it numerically, and so is only an estimate. Locus crosses where K = 0, 30.2, corresponding to crossing imaginary axis at s=0, ±2.45j, respectively.
Where do root locus branches lie on the real axis?
Branches of the root locus lie on the real axis to the left of an odd number of poles and zeros. Complex-conjugate pairs of poles and zeros are not counted, since they contribute no net angle to the real axis. Rule 4
How are the values of the locus determined?
Locus crosses imaginary axis at 2 values of K. These values are normally determined by using Routh’s method. This program does it numerically, and so is only an estimate. Locus crosses where K = 0, 30.2, corresponding to crossing imaginary axis at s=0, ±2.45j, respectively. These crossings are shown on plot.
How is the root locus of the characteristic equation symmetric?
Rule 1: Symmetry Since the characteristic equation has real coefficients, any zeros must occur in complex conjugate pairs (which are symmetric about the real axis). Since the root locus is just a diagram of the roots of the characteristic equation as K varies, it must also be symmetric about the real axis.