lec7 - 1 AE 383 System Dynamics Lecture Notes 7 (July 8 th...

Info iconThis preview shows pages 1–3. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 AE 383 System Dynamics Lecture Notes 7 (July 8 th 2006) Frequency Response (Sinusoidal Response) of 1 st Order Systems If we make our system input sinusoidal with amplitude q A and frequency ω rad /s, the system equation becomes t Kq q dt dq A ω τ sin = + Remember that for frequency response we are interested only in the sinusoidal steady state, which is achieved after transients die out; that is we want the forced, not the natural, part of the response. We can use the method of undetermined coefficients to find the particular solution. Let q op = Asin ω t + Bcos ω t Then t Kq t B t A t B t A A ω ω ω ω ω ω ω τ sin cos sin ) sin cos ( = + +- A Kq A B = +- ω τ = + B A τ ω 1 1 2 2 2 2 +- = + = τ ω ωτ τ ω A A Kq B Kq A so t Kq t Kq q A A op ω τ ω ωτ ω τ ω cos 1 sin 1 2 2 2 2 +- + = This may be simplified by using the trigonometric identity ) tan sin( cos sin 1 2 2 A B B A B A- + + = + α α α Using this, we finally have [ ] ) ( tan sin 1 1 2 2 ωτ ω τ ω- + + =- t Kq q A op Now let’s use the sinusoidal transfer function to find the same result, and see that this method is more simple 1 ) ( ) ( + = s K s q s q i o τ substituting j ω for s 2 ) ( tan 1 1 ) ( 1 2 2 ωτ τ ω ωτ ω- ∠...
View Full Document

This note was uploaded on 10/24/2011 for the course AEE 463 taught by Professor Melin during the Spring '11 term at Middle East Technical University.

Page1 / 6

lec7 - 1 AE 383 System Dynamics Lecture Notes 7 (July 8 th...

This preview shows document pages 1 - 3. Sign up to view the full document.

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