MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems--Fall 2003 PROBLEM SET 10 Issued: November 25. 2003 Due: December 5. 2003 REMINDER: Computer Lab 3 is also due on December 5 Reading Assignments Lectures #21-22 PS#10: Chapters 10 11(through Subsection 11. 3.4)of O& Lectures #23-24 PS#11: Chapters 10 11(through Subsection 11.3.4)of O&w Exercise for home study (not to be turned in, although we will provide solutions): El)O&W 11.32(a)through(d) Problems to be turned in Problem 1 Consider the following feedback configuration G(s Sketch the root loci for K>0 and K <0 for each of the following (a)G(s)= )c(s)=(-5(8+8 +1 (c)G(s) For this part, clearly indicate the point at which the closed-loop system has a double-poley(t) MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems—Fall 2003 Problem Set 10 Issued: November 25, 2003 Due: December 5, 2003 REMINDER: Computer Lab 3 is also due on December 5. Reading Assignments: Lectures #21-22 & PS#10: Chapters 10 & 11 (through Subsection 11.3.4) of O&W Lectures #23-24 & PS#11: Chapters 10 & 11 (through Subsection 11.3.4) of O&W Exercise for home study (not to be turned in, although we will provide solutions): (E1) O&W 11.32 (a) through (d) Problems to be turned in: Problem 1 Consider the following feedback configuration. x(t) − + e(t) K G(s) Sketch the root loci for K > 0 and K < 0 for each of the following: 1 (a) G(s) = . s + 1 1 (b) G(s) = (s − 5)(s + 3) s + 1 (c) G(s) = 2 . For this part, clearly indicate the point at which the closed-loop system s has a double-pole. 1