Modern Control System EKT 308 Aspects of State Equation & Root Locus Method

Transfer Function from State Equation

Transfer Function from State Equation (contd…)

Answer:

Concept of Root Locus Characteristic equation (above fig), Fig 1

Concept of Root Locus (contd…) The root locus is the path of the roots of the characteristic equation traced out in the s-plane as the system parameter varies from zero to infinity. Root Locus Procedure Step 1:

Root Locus Procedure (contd…) Locate poles and zeros in the s-plane (‘x’ for poles, ‘o’ for zeros Let us vary K from 0 to infinity. When K = 0, So, when K=0, values of s coincide with poles of P(s). Note:

The locus of the roots of the characteristic equation 1+KP(s)=0 begins at the poles of P(s) and ends at the zeros of P(s) as K increases from 0 to infinity. If n > M, (n-M) branches of root locus approach the (n-M) zeros at infinity. Step 2: Locate the segments of the real axis that are root loci. The root locus on the real axis lies in a segment of the real axis to the left of an odd number of poles and zeros.

Example fo step 1 an 2.