28 - cont_decomp28 filled

28 - cont_decomp28 filled - ME 575 Handouts Controllable...

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ME 575 Handouts 1 ME575 Session 28: Controllable Decomposition School of Mechanical Engineering Purdue University Slide 1 Controllable Canonical Form Controllable Canonical Form Let Let’ s show that it must be controllable: C C 0 1 2 0 1 0 0 A 0 0 1 , B 0 1 ⎡ ⎤ ⎢ ⎥ = = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ a a a ME575 Session 28: Controllable Decomposition School of Mechanical Engineering Purdue University Slide 2 Controllable Canonical Form Controllable Canonical Form Thus, a controllable system can always be Thus, a controllable system can always be transformed into controllable canonical form: where where x T z C C x A x B u z A z B u = = + = + ± ± 1 1 C C A T A T , B T B = = n 1 C W [B A B A B] = " C n 1 C C C C C C W [B A B A B ] = "
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ME 575 Handouts 2 ME575 Session 28: Controllable Decomposition School of Mechanical Engineering Purdue University Slide 3 Controllable Canonical Form Controllable Canonical Form 1 2 n 1 2 1 T [B A B A B] 1 0 1 0 0 = " a a a ME575 Session 28: Controllable Decomposition School of Mechanical Engineering Purdue University Slide 4 Controllable Canonical Form Controllable Canonical Form In general, to transform to controllable canonical In general, to transform to controllable canonical form: where 1 2 3 n 1 2 3 4 C n 2 n 1 n 1 1 1 0 T W 1 0 0 1 0 0 0 1 0 0 0 0
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