30 - ackermann30 filled

30 - ackermann30 filled - ME 575 Handouts Alternative...

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ME 575 Handouts 1 ME575 Session 30: Ackermann’s Formula School of Mechanical Engineering Purdue University Slide 1 Alternative Computation of Gains Alternative Computation of Gains For We want We want xA x B u = + ± uK x = − CL x( AB K ) x A = ± ²³´³µ CL 12 n s A (s s )(s s ) (s s ) −= " I ME575 Session 30: Ackermann’s Formula School of Mechanical Engineering Purdue University Slide 2 Ackermann Ackermann ’s Formula s Formula n1 1 K[ 0 01 ] [ BAB ]( A ) = "" φ
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ME 575 Handouts 2 ME575 Session 30: Ackermann’s Formula School of Mechanical Engineering Purdue University Slide 3 Ackermann Ackermann ’s Formula s Formula Proof: Uses Uses Cayley Cayley -Hamilton Theorem Hamilton Theorem , which , which states that a matrix satisfies its own states that a matrix satisfies its own characteristic equation, i.e., characteristic equation, i.e., Restrict attention to n = 3 case: Restrict attention to n = 3 case: CL ( s )0 ( A)0 = ⇒= φ 32 CL CL CL CL 210 (A ) A A A 0 =+ α + α+ α = I ME575 Session 30: Ackermann’s Formula
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This note was uploaded on 12/09/2011 for the course ME 575 taught by Professor Meckl during the Fall '10 term at Purdue.

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30 - ackermann30 filled - ME 575 Handouts Alternative...

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