Chapter 4 examples - EEL4657 - Dr. Haniph Latchman Chapter...

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: 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 closed-loop 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 steady-state value of y(t). d) Find the steady-state error. Solution a) We can use the formula for the closed-loop 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

Page1 / 8

Chapter 4 examples - EEL4657 - Dr. Haniph Latchman Chapter...

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