Question

9. Consider the plant T(s)= A10and the given root locus plots. a. Which plot was generated for the plant with a proportional controller? (1) (2) (3) b. Which plot was generated for the plant with a pure integral controller? (1) (2) (3) c. Which plot was generated for the plant with a PI-controller? (1) (2) (3) d. What is the smallest time constant that closed-loop systems represented by plot (2) can have? s24+100 Which plot has the possibility of non-oscilating closed-loop systems? (1) (2) (3) f. Which plot shows closed-loop systems whoes damping ratio increases by increaing the K value? (1) (2) (3) e. (6 points) L 30- (1) A Bu ee (2) Bet Locu (3) 30 Ral As n

Answer 1

Angwer: Consider the plant is). I s'45+100 Answerca) correct answer is plot (2) Answer (b) connect angwer is plot (3). answer (c) correst answer is plot (1), answer (d) see plot is when the system .cses only proporal Controller hence for second order system. 5?+5+100 =0 compare with second order system s++ (2x Zeta xwx5) +w?=0 . we get W = 10 rad i ser samping ratio Creta : 1/2 XW))

Zeta xw = 1 and time constant. Is given by : T= (zetarw) :55. 2 seconde smatest time constant hence anstever is a seconds.