ROOT LOCUS NOTES STEP BY STEP PROBLEM

ROOT LOCUS NOTES STEP BY STEP PROBLEM - Angles of departure...

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Unformatted text preview: Angles of departure and arrival Looking at the open loop poles and zeros below, the root locus starts at the poles and ends at zeros but at what angles? j Taking a point ( ) close to a complex pole. Assuming this point lies on the root locus, the angles to this point must be (2 k +1)180 o . Us- ing the angles from the other poles and zeros to ( ) pole will give us angle close to (2 k + 1)180 o , the difference being the angle of de- parture. 1- 1 + 2 + 3- 4- 5 + 6 = (2 k + 1)180 o 1 = 2 + 3- 4- 5 + 6- (2 k + 1)180 o j 6 5 4 3 2 1 This is also the case with a point close to a complex zero for angles of arrival. 2 3 5 6 4 j 2 1- 1 + 2 + 3- 4- 5 + 6 = (2 k + 1)180 o 2 = 1- 3 + 4 + 5- 6 + (2 k + 1)180 o Example: Given a unity feedback system that has a forward transfer function G ( s ) = K ( s + 2) s 2- 4 s + 13 a)Sketch the root locus 3 b)Find the imaginary axis crossing;...
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ROOT LOCUS NOTES STEP BY STEP PROBLEM - Angles of departure...

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