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Unformatted text preview: ME 132 Solutions # 11 1 Output feedback stabilization (a) The transfer function can be found by the standard formula, C ( sI A ) 1 B + D , or by recognizing that the system is almost in controllable canonical form. H u y = 1 s 3 + 4 s 2 + 3 s 2 (b) Plugging in the control law into the statespace description of the plant gives x = ( A BCk ) x + Br The output equation is not changed. This leads to the statespace realization of the closed loop system: x 1 x 2 x 3 y = 1 1 2 + k 3 4 1 1 x 1 x 2 x 3 r (c) The closed loop characteristic polynomial is ( s ) = s 3 + 4 s 2 + 3 s 2 (2 + k ). From the Routh array, the conditions for stability are 4 > (2 + k ) > 12 > (2 + k ) It is possible to satisfy the three inequalities above when 14 < k < 2. 2 Polezero diagrams (a) CC. The polezero diagram shows that this is a firstorder system without any zeros.(a) CC....
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 Spring '08
 Tomizuka

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