# lect1 - Lecture 1 EE743 Lecture 1 EE743 Dynamic Systems...

This preview shows pages 1–10. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document

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.

Unformatted text preview: Lecture 1 - EE743 Lecture 1 - EE743 Dynamic Systems Professor: Ali Keyhani Professor: Ali Keyhani 2 Dynamic Systems ■ Consider a system that can be modeled by the following equivalent electric circuit Figure 1 3 Dynamic Systems ■ Using KVL, Loop 1 : dt di L Ri R R i v dt di L i R i i R v 1 1 2 1 1 1 1 1 1 2 1 ) ( ) 1 ( ) ( + + + =- + + + = 4 Dynamic Systems ■ Using KVL, Loop 2 : dt di L Ri R R i v dt di L i R i i R v 2 2 1 2 2 2 2 2 2 2 1 ) ( ) 2 ( ) ( + + + =- + + + = 5 Dynamic Systems ■ Solving Equation (1) for i 2 , ) 4 ( ) 3 ( 2 1 2 1 1 1 2 1 1 1 1 2-- +- =-- +- = dt i d R L dt di R R R dt di dt di R L i R R R R v i 6 Dynamic Systems ■ Substituting (3) in (4), we will obtain equation (5) ( 29 ( 29 2 2 1 1 2 2 1 2 1 2 1 2 1 1 1 2 2 1 ) 5 ( vR u R R R R RR c L R RL L R RL b L L a u ci dt di b dt di a = + + = + + + = =- = + + 7 Dynamic Systems ■ For the dynamic system described by equation (5), we have two energy storing elements: L 1 and L 2 . Therefore, the system is represented by a second order differential equation. ■ Let , then eq.(5) can be written as, dt d p = ) 6 ( 2- = + + c bp ap 8 Dynamic Systems ■ Equation 6 represents the characteristic equation of the system described by Figure 1. ■ The roots of eq.(6) are called eigenvalues eigenvalues of the system, and are determined by, β α ±- =- ±- = 2 1 2 2 1 , 2 4 , p p a ac b b p p 9 Dynamic Systems ■ The value of β strongly depends of the kind of elements of the system. The following combination of storage elements give an idea of the numerical value of β : – For R-L-L R-L-L systems β is real – For R-C-C R-C-C systems β is real – For R-L-C R-L-C systems : ●...
View Full Document

{[ snackBarMessage ]}

### Page1 / 28

lect1 - Lecture 1 EE743 Lecture 1 EE743 Dynamic Systems...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online