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# HWCE_7 - Assignment for HW/CE#7 Revised answer to Problem#2...

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Assignment for HW/CE#7 Revised answer to Problem #2, 4/29/10 No turn-in required. Some recommended problems for final exam preparation not covered in earlier quizzes: (Note: The final will be comprehensive!) 1. Consider the following nonlinear system: ) 2 ( ) 2 ( 2 2 1 1 2 1 2 1 + + - = u x x u x x x dt d a) Find the two equilibrium points for this system if: ) ( 16 ) ( ) ( ) ( 32 ) ( ) ( 2 2 o 2 2 1 1 o 1 1 t u t u u t u t u t u u t u + = + = + = + = Answer: + - - + = 2 4 Or 2 4 20 10 x x b) For each of the equilibrium points write a set of linear equations governing small displacements of the state variables from that equilibrium point assuming we have small displacements of the inputs from u 1o and u 2o . Answer: 1 0 0 1 8 4 0 16 Or 1 0 0 1 8 4 0 16 2 1 2 1 2 1 2 1 2 1 2 1 + - + + = + - - =

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HWCE_7 - Assignment for HW/CE#7 Revised answer to Problem#2...

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