RouthHurwitzAnalysis

RouthHurwitzAnalysis - ROUTH HURWITZ ANALYSIS The Routh...

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http://www.teicontrols.com/notes [email protected] page 1 of 5 ROUTH HURWITZ ANALYSIS The Routh Hurwitz analysis tells you how many roots are located in the a) left-hand plane, b) right-hand plane, and c) on the j ϖ -axis. The technique is illustrated here with an example. The Routh Hurwitz analysis involves creating an array of values. There are two special cases which may be involved, 1) a row of the array is all zeros (this happens in our example) and 2) a row begins with zero but is not all zeros (this does not occur in our example but is covered on the last page). THE PROBLEM Given the system equation 0 16 16 20 12 8 2 2 3 4 5 6 7 8 = + + + + + + s s s s s s s find the number of roots located in the left-hand plane, right-hand plane, and on the j ϖ -axis. FIND THE ZEROS Since the equation can be factored by s 2 , there are two zeros in the polynomial, i.e. two roots at the origin. ( 29 0 16 16 20 12 8 2 2 3 4 5 6 2 = + + + + + + s s s s s s s STARTING THE ROUTH HURWITZ ARRAY We can drop the s 2 factor and consider only the remaining equation 0 16 16 20 12 8 2 2 3 4 5 6 = + + + + + + s s s s s s The order of this polynomial is n =6, so we will be construction an array having n +1 or 7 rows.

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This note was uploaded on 04/03/2012 for the course EE 366 taught by Professor Pore during the Spring '08 term at University of Texas.

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RouthHurwitzAnalysis - ROUTH HURWITZ ANALYSIS The Routh...

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