MODELLING & CONTROL: EVANS' RULES FOR ROOT LOCUS

Subscribe to the Channel:    / scuolatech  
VIDEO:    • MODELLING AND CONTROL OF CHEMICAL PRO...  
Info: [email protected]

Step 1. Locate the poles and zeros of the loop gain GH(s). First, compute the zeros of the loop gain (the roots of N(s)) and place an 'o' at their location in the complex plane. Next, compute the poles of the loop gain (the roots of D(s)) and place an 'x' at their location in the complex plane.

Step 2. Determine what, if any, portion of the real axis is part of the root locus. The angle condition requires that the real axis portion of the root locus lies to the left of an odd number of poles and zeros. Equivalently, since complex poles and zeros must occur in conjugate pairs, the real axis portion of the root locus lies to the left of an odd number of real poles and zeros.

Step 3. Determine the asymptotes of the root locus. Given that there are m zeros and n ≥ m poles, m of the closed-loop poles will approach the loop gain zeros as K → ∞ and the remaining n − m will converge to asymptotes which extend radially to infinity from some starting point on the real axis.

Step 4. Find the breakaway and breakin points. Recall that these points correspond to values of the gain K for which the closed-loop system has multiple closed-loop poles at a particular point.

Step 5. Determine the angles of departure from the loop gain poles and the angles of arrival at the loop gain zeros. Recall that as K → 0, the root locus approaches the poles of the loop gain and as K → ∞, m branches of the root locus approach the zeros of the loop gain.

For more information about this topic please contact Prof. Michele Miccio at [email protected]