modeling8

# modeling8 - Modeling QUESTION 8 x t x Linearize the...

This preview shows pages 1–2. Sign up to view the full content.

Modeling Q UESTION 8 Linearize the differential equation ( 29 ( 29 ( 29 ( 29 3 2 x t x t x t x t e - + + = . The two states are ( 29 ( 29 1 x t x t = (1) ( 29 ( 29 2 x t x t = (2) The two first order nonlinear differential equations are ( 29 ( 29 ( 29 1 1 2 f t x t x t = = (3) ( 29 ( 29 ( 29 ( 29 ( 29 1 2 2 2 1 3 2 x t f t x t x t x t e - = = - - + (4) At equilibrium, the derivatives are equal to zero and equation (3) becomes 2 2 0 0 x x = = (5) At equilibrium equation (4) becomes 1 1 2 1 1 0 4 2 2 0 x x x x e x e - - = - - + - = (6) Using graphical techniques or the bisection method to solve equation (6), 1 0.3517 x = . The first incremental state and its first derivative with respect to time are ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 ˆ ˆ x t x t x x t x t = - = (7) The second incremental state and its first derivative with respect to time are ( 29 ( 29 ( 29 ( 29

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.

### Page1 / 2

modeling8 - Modeling QUESTION 8 x t x Linearize the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online