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Unformatted text preview: ME375 Handouts 1 School of Mechanical Engineering Purdue University ME375 Root Locus  1 A feedback control system is proposed. The corresponding block A feedback control system is proposed. The corresponding block diagram is: diagram is: Sketch the root locus of the closed Sketch the root locus of the closedloop poles as the controller gain loop poles as the controller gain K varies from varies from 0 to 0 to ∞ . Find closed Find closedloop characteristic equation: loop characteristic equation: Example 3 Example 3 Y ( s ) U ( s ) Plant G p ( s ) Controller R ( s ) 1 ( 2) s s + + − K s ( ) + 4 School of Mechanical Engineering Purdue University ME375 Root Locus  2 Example 3 Example 3 Step 1: Step 1: Formulate the (closed Formulate the (closedloop) characteristic equation into the standard form for loop) characteristic equation into the standard form for sketching root locus: sketching root locus: Step 2: Step 2: Find the open Find the openloop zeros, z loop zeros, z i , and the open , and the openloop poles, p loop poles, p i : ME375 Handouts 2 School of Mechanical Engineering Purdue University ME375 Root Locus  3 Example 3 Example 3 Step 3: Step 3: Determine locations of repeated roots, if any. Determine locations of repeated roots, if any. School of Mechanical Engineering Purdue University ME375 Root Locus  4 Example 3 Example 3 Step 4: Step 4: Determine the imaginary axis crossings, if any. Determine the imaginary axis crossings, if any. ME375 Handouts 3 School of Mechanical Engineering Purdue University ME375 Root Locus  5 Example 3 Example 3 Step 5: Step 5: Use the information from Steps 1 Use the information from Steps 14 to sketch the root locus. 4 to sketch the root locus....
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 Spring '10
 Meckle
 Mechanical Engineering Purdue, Engineering Purdue University, School of Mechanical Engineering Purdue University

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