• University of Texas, Dallas

• MECH 4310

Name: Tyler Summers Exam 2 Instructions. This is an open book, open notes exam. Use of a calculator is allowed but not necessary. No computers or phones. Please show all work with clear and complete explanations, and clearly indicate your final answers. Good luck! (1) (25 points) Consider the feedback control system shown below. (a) 1 R(s) O K(s) Y(s) 8(8-1) (12 points) Sketch root locus plots that show how the locations of the closed-loop poles vary in terms of the control gain k for two different controller structures: (i) simple proportional controller with K(s) = k imag real n=2 m=0 =) n-m= 22 asymptotes $= = 90° 0+1 T 2 2 (ii) a PD controller with K(s) = k(s+1) imag n=2, m= | =) n-m = / I asymptote 4 = 180° - 1 MECH 4310: Systems and Control, Fall 2017 (b) Exam 2 (10 points) Based on your root locus plots, describe the closed-loop stability properties achievable by adjusting the gain k for each controller structure. Is it possible to stabilize? Does increasing or decreasing the the gain lead to stability/instability? For what range(s) of the gain k is the closed-loop system stable? propontional: both tranches alwags cn RHP closed-loop system unstable for ang gain K PD branches s