Lesson_28 - Lesson28 Challenge27...

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

View Full Document Right Arrow Icon
Lesson 28 Lesson 28 Challenge 27 Lesson 28  -  State variable models Challenge 28
Background image of page 1

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

View Full DocumentRight Arrow Icon
  Lesson 28 Challenge 27 134kHz  If H(s)=(s-a)/((s-a) 2 ϖ 0 2 ), what is the ODE? 
Background image of page 2
  Lesson 28 Challenge 27 From           (s 2  -2as +(a 2 + ϖ o 2 ))V 0 (s) = (s-a)V(s) it must follow that: d 2 v 0 (t)/dt 2  -2a dv 0 (t)/dt + (a 2 + ϖ o 2 )v 0 (t) = dv(t)/dt – av(t) Suppose, for illustrative purposes, a=0.02,  ϖ 0 =10, then   H(s) = (s-.01)/(s 2  – 0.02s + (.01 2  +10 2 = (s-.01)/(s 2  – 0.02s + (100.0001)) » [H,w] = freqs([1,-.01],[1, 0.02, 100.0001]); » plot(w,abs(H)) » plot(w,360*angle(H)/(2*pi))
Background image of page 3

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

View Full DocumentRight Arrow Icon
  Lesson 28 Challenge 27 90 ° -90 °
Background image of page 4
  Lesson 28 Lesson 28 Have previously introduced transfer functions. H(s) and H(z) What are their limitations? State variables are information variables.   They reside at locations where the  system stores or saves information. Analog locations? Discrete-time locations?
Background image of page 5

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

View Full DocumentRight Arrow Icon
  Lesson 28 Lesson 28 Core idea: The future states of a state-determined system can be computed if, all past state values are known, and the mathematical relationship (sometimes called the bonds on  interaction) between the state variables are known.  Current States Past States State Model System Inputs Future States Memory
Background image of page 6
  Lesson 28 Lesson 28 The general form of a single-input single-output continuous-time  n -state state  model ( n  information storage locations) is: ( 29 Equation Output t dv t c t y Equation tate S t v t dt t d T ) ( ) ( ; ) 0 ( ); ( ) ( ) ( 0 + = = + = x x x b Ax x x 0 A b x (t) c T d y(t) v(t) x(t) an  n -vector of state variables
Background image of page 7

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

View Full DocumentRight Arrow Icon
  Lesson 28 Lesson 28 Example:  RLC circuit The system states are the inductor current and capacitor voltage.   R L C v(t) i L v C ) ( ) ( 1 ) ( ) ( ) ( ) ( 0 t v dt t i C t v t v t Ri dt t di L C t L C L L = = + +
Background image of page 8
  Lesson 28 Lesson 28 Define x 1 (t)=i L (t) and x 2 (t)=v C (t).
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.

Page1 / 26

Lesson_28 - Lesson28 Challenge27...

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

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