{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw6 - EML 4312 Fall 2009 State Space Homework 1 Consider...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
EML 4312 Fall 2009 State Space Homework 1. Consider the following block diagram K G p + Input Output Block diagram. where G p = s 2 + 3 s 3 + s 2 + 5 s + 1 . Express the transfer function in terms of a state space realization. CHECK your Answer using methods from class. Sol: Using the Reachable cannonical form gives A = 0 1 0 0 0 1 1 5 1 B = 0 0 1 C = £ 3 0 1 ¤ check H = £ 3 0 1 ¤ s 1 0 0 s 1 1 5 s + 1 1 0 0 1 = s 2 + 3 s 3 + s 2 + 5 s + 1 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2. Are the following state space systems controllable, observable, or both? a) A = 1 1 0 1 ¸ B = 1 0 ¸ C = £ 0 1 ¤ Sol: C ( A, B ) = £ B AB ¤ = 1 1 0 0 ¸ det 1 1 0 0 ¸ = 0 Not controllable O ( C, A ) = £ C CA ¤ = 0 1 0 1 ¸ det 0 1 0 1 ¸ = 0 Not Observable b) A = a 0 0 b ¸ B = 0 1 ¸ C = £ 0 1 ¤ C ( A, B ) = £ B AB ¤ = 0 0 1 b ¸ det 0 0 1 b ¸ = 0 Not controllable. O ( C, A ) = £ C CA ¤ = 0 1 0 b ¸ det 0 1 0 b ¸ = 0 Not Observable. c) A = a 1 0 b ¸ B = 0 1 ¸ C = £ 1 1 ¤ C ( A, B ) = £ B AB ¤ = 0 1 1 b ¸ det 0 1 1 b ¸ = 1 2
Background image of page 2
Controllable.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}