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332-4solutions

# 332-4solutions - ECE 332 Homework#4 1 For each of the...

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Unformatted text preview: ECE 332 Homework #4 1) For each of the following plants G (3), ﬁnd the closed—loop transfer function H (3) under unity feedback. Using Routh—Hurwitz methods, determine the number of RHP poles in H (3) If H (s) is BIBO stable, ﬁnd its type number q and the steady-state error es,q to an order q singularity function. 20 a) K's—ﬁr) 31:2 b) (3—1)§s+1) c) (8+1)('s§+1)' 2) For each G (s) in problem I), draw the Nyquist plot and determine the number of RHP poles in H (3). Compare your answers to problem 1). 3) For each G (3) in problem I), draw the Bode plots and determine the number of RHP poles in H (5) Compare your answers to problem 1). 4) Let 7 5 (9(8) # 10 (3+10) _ 8(8 +1)3(s + 50)5' In MATLAB, type “hw44” to display the Bode plots of G (3) as well as the frequency and step response of the closed—loop system under unity feedback. a) Print the graphs and ﬁnd all crossover frequencies cup and my. Verify that 17(3) is BIBO stable. b) Find the type number q and steady-state error essq corresponding to H (s) c) From the graphs, ﬁnd 923p, Kg, wb, our, MT, Tr, T1,, and Mp. d) Compare tag and Lab. 5) Design a type 1 second-order system H (s) to meet the speciﬁcations i) tag 2 10 rad/s ii) a, 2 60° In MATLAB, type “932' = g; mm = tan; hw45” to display the Bode plots for the corresponding (1(3). Verify that your design gives appropriate values of 5 and w“. 6) Using your values of 5 and can from problem 5), type “xi = é; um 2 run; 1111246” in MATLAB to display |S(jw)| , where S is the sensitivity function corresponding to H. What is the maximum value of lS(jw)| and at what frequency does the maximum occur? ELL: 3;; HWMWL 1i? 5 \ [M'f “\va ‘ 1% (a/ [443/ x ﬂm :I S\$+3W+35""‘/ m 2,4) Ff Gm; l+s£§¥ﬁ77 W §§;;;§;Eﬁmﬁ 52.\\A{’(A” “ML/e: 1 3 O 3 1’ o ‘9’ c: ZN Mb :‘Moykwy fig/L. / Z» 0/)“ K5”) /,M/e..j' . 5+; 3+; - m» m '”(137' SL+S%/ E1 5*” %“ 653% E'GGN; m (~57, 1 m/ ‘ m S’H’cww ‘ “I, ”(3’ '3' 1 =1 3 " """"" i + “w b 5 +5354- L V LL». fa ﬂﬁmfa «'arx m INWOJM / La} WWI?“ ”:9 , EIED wé/ w/Fm 1) SUV 0006) km” ﬂags ﬂlwvh “/, 9 [9"2/2 7/ 1) 621”?“ M //\uaJ/\uo/7 in lo.» awﬂ‘ 2.w yam Wm c). 43%: Q0; w. -2, (ﬁﬂ/(Sﬂ/ (Pl) 645 ‘7‘?) A)! "3"} Q32” A)“ L) P *5' m J w 0' r! 2 Aw IM¥ /70\ JJ 74 I” WA -/ m. 2» “=0 H M W M1 W,“ / I9\’ (I I My Pq/e 0! 2 ({4} degrees 100 —100 -200 —-~-f -soo -4oo _ 10 Plant Magnitude radians/seCond Plant Phase (,4 , radians/second 10 O ”r radians/second 1 10" seconds degrees -100 “"}‘f'1'r:::r -150 -200_ 10 1O 1O . Plant Magnitude 10‘" radians/second Plant Phase 101 radians/second 10 10 1O 1 Sensitivity O radians/second L mu ...
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