This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EEL4657  Dr. Haniph Latchman Chapter 4: Example Problems 1. The transfer function for a system with unity negative feedback is given by: G ( s ) = 1 ( s + 1)( s + 3) a) Find the closedloop transfer function T ( s ) = Y ( s ) R ( s ) . b) Find the time response y ( t ) for a step input of r ( t ) = A. c) Use the final value theorem to find the steadystate value of y(t). d) Find the steadystate error. Solution a) We can use the formula for the closedloop transfer function given in sec tion 4.4.1 in the book. T ( s ) = G ( s ) 1 + G ( s ) = 1 ( s +1)( s +3) 1 + 1 ( s +1)( s +3) = 1 ( s + 1)( s + 3) + 1 = 1 s 2 + 4 s + 3 + 1 = 1 s 2 + 4 s + 4 T ( s ) = 1 ( s + 2) 2 1 b) The output Y ( s ) is given by Y ( s ) = R ( s ) T ( s ) and we use the fact that the Laplace transform of the step input r ( t ) = A is R ( s ) = A s . Y ( s ) = R ( s ) T ( s ) = A · 1 s · 1 ( s + 2) 2 Y ( s ) = A 1 s ( s + 2) 2 Use partial fractions method to transform Y ( s ), we can remove the term A for now, realizing that it is a constant and we can include it later in the final...
View
Full
Document
This note was uploaded on 01/11/2012 for the course EEL 4657l taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff

Click to edit the document details