EE313_system_zero_input_response

EE313_system_zero_input_response - System State and...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: System State and Differential Equations: Finding Zero Input Response EE 313 Linear Systems and Signals Fall 2008 Some Parts Adapted by Courtesy of Prof. Brian Evan s Prof. Adnan Kavak Dept. of Electrical and Computer Engineering The University of Texas at Austin 3 - 2 f y a y a y a y = + + + 1 2 y x y x y x = = = 3 2 1 ( 29 ( 29 ( 29 f x a x a x a x y x x y x x y +--- = = = 3 2 2 1 1 3 3 2 2 1 System State Example: Reformulate N th-order differential equation into N simultaneous first-order differential equations Define three state variables After substituting the state variables, we obtain a state-space description as Lathi, 2 nd ed, Section 1.10 3 - 3 f x x x a a a x x x + --- = 1 1 1 3 2 1 2 1 3 2 1 f b x A x + = System State By putting the state variables in vector x , If A is not a function of time, then solution is exp( M ) for matrix M yields a matrix dt t f e e t t t + = ) ( ) ( ) ( b x x A A 3 - 4 System State General form of state-space description State-space descriptions can Describe time-varying and nonlinear systems Be simulated by computer (e.g. Spice for circuit simulation) Knowledge of state variables allows one to determine every possible output of the system State-space descriptions covered in controls courses, e.g. EE 362K Intro. to Automatic Control f b x A x + = 3 - 5 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t f b t f dt d b t f dt d b t f dt d b t y a t y dt d a t y dt d a t y dt d N N M M M N M M M N N N N N N N + + + + = + + + +--- +----- 1 1 1 1 1 1 1 1 k k k dt d D dt d D dt d D = = = 2 2 2 ( 29 ( 29 ( 29 ( 29 t f b...
View Full Document

This note was uploaded on 02/10/2009 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas at Austin.

Page1 / 19

EE313_system_zero_input_response - System State and...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online