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A#20_Solutions

# A#20_Solutions - Assignment#20 w Solutions p.1 ECSE-2410...

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Unformatted text preview: Assignment #20 w Solutions p.1 ECSE-2410 Signals & Systems ~ Fall 2006 Tue 11/21/06 1(20). This problem illustrates a practical scheme for ﬁnding transfer functions, if we know something about the order of the system. This meter is basicaily a DC motor! A spring~restrained meter of inertia, J, is suspended on frictionless bearings. The meter movement has resistance, R, and negligible inductance. The permanent magnet ﬁeld may be regarded as radial in direction where it is cut by the windings of the movement. Test data are given below. pointer deﬂection 9 eter movement spring \J\ N S R input (a) If the movement is dispiaced mechanically with the input terminals open and then released, the pointer (output) Wiil oscillate with a frequency of 5 rad/sec. (b) A sinusoidal voltage of 0.1 volt amplitude and 5 rad/sec. frequency is applied to the input terminals, the pointer produces a steadlywstate oscillation of 0.2 rad. amplitude. (c) When 02 volt do is applied to the input terminals, the steady~state deﬂection of the pointer is 0.4 rad. Find the transfer function of the meter. Assignment #20 - Solutions p.2 ECSE-2410 Signais & Systems ¢ Fall 2006 Tue 1E/21/06 1(20). Continued (3») NM Wm M 1,;wa m “i’ée-Pvméalzﬂ; ¢ 719 ,E; A WHS} mm w“ W” E ,_, a £5. 3 \$2»;- B§+ZS 3%» (gm Fwd- (a?) 9+9 = m ﬁkW’i “7% W \g—v MS: a? {HS} Sm {3% +Z_QS}} ﬁgﬁﬁyﬁéﬁe 2 {9'1 {”5}! m2. M" ‘3 W \t “Ii “£ij 2 v:- [32531: L 092+ QQQ’i‘ZS 38 (5?) gm W; M?m+ v-UH 01W1+9£%M%}W\Mvﬁtﬁ’cﬁalﬁmi m ﬁlli- ‘3 \$51. {WEE}! \$2 \Hﬁoﬁl; is: §=SGJ :23 W" Tia Mm ﬁzinsmt Assignment #28 — Solutions p.3 ELISE-2410 Signals & Systems , Fali 2006 Tue 11/21/06 2(40). Text 11.57. This probiem deals with PID controllers that are used in the “RPI Segway”. m; -—-— " «ml HaiS} \ME] 615"“) (Q) LEA- “1"":‘5'9W‘? HMS-3% K (frowzjbw WV”) 39”.. K:+:§+Q.M15 get-U12 L0 3 Y 6". GEL-1%“?O ‘1}.KH'}=££‘H rm saw-7170 51W”W)- -—-—- 2 Mi 2—,. Ls; ,_ 4%.. .,__,_ 11L... 37\$) HHOLLMW 1+ :3 S+¢4+K°<~ s+°<O+I<J dam! L00? [33(23 Suva-40449} “713%“? 30’"! { m dead/31W Mum: m ' a ,_ ms) Ems—+4} 3:35,}: in) ... W 2.1-. {+- How {U M“ 91:"; 3+qUL-H) :4 Nﬁﬁgﬂ-IWELS’w-l 55\$... ksEﬁ): Lam: LO I gave swam g+¢<U§ (Jig-Lei) M II «ea ...... we) «=7 535?“? (Si-04 __ = W @S_%:;NW 34.0566?!) “HQ/(fir!) \K‘H 14b Assignment #28 —— Solutions p.4 BCSE-2410 Signals & Systems - Fan 2006 Tue 11/21/06 2(40). Texi 11.57. continueé. “£9” “if; +53 2: KMCS-i- 5%) m 1+ wH?) @0qu "IE: vied: 31343,; W 330““? \$1 F01 94\$ij 5‘ dCHK) amid—ea 3k; 7””: ¢KI<2? 0 91\$ t 1.: M £15): 319 l+~§-:'(Kl+ék§~ _52+ Sacémﬁd+¢<¥L Assignment #20 —— Solutions p.5 ECSE-2410 Signals & Systems - Fall 2006 Tue 11/21/06 2(40). Text 11.57. continued. Assignment #20 m Solutions 13.6 ECSE-2410 Signals & Systems — Fali 2006 Tue 11/21/06 2(40). Text 11.57. Continued, (C) cani- K54- ( K two a km W W @290me w 4oQ43-9WJ«-ma (142.“a ”£1214 grace. k 70 95145-400 Assignment #20 —— Solutions 13.7 ECSE~24IO Signals & Systems - Fall 2006 Tue 11/21/06 3(40). Text £1.54. This problem uses feedback (actually positive feedback) to realize an oscillator. (a) If) ”#31532 Heelézs) (—1) % E45331 gigs}; % 2 1+6gwom§w01 /. 314 wages-meg \E-M) AA 1 W m g _ ‘ W ‘m" '3‘ 4““ f3“ Assignment #20 w Solutions [3.8 BOSE-2410 Signals & Systems - Fall 2066 Tue 11/2lf06 3(40). Text1154. Continued. (6‘) twil- l”; “:30 (5) LOOP \$‘ﬂ 2/ wagerfad-Ea cam-14w A. 2.. “2* AZzW _ ,, (Ema: XXX-aﬁﬁ‘) ﬁﬂﬁogﬁazg £3) + @z J(g1+«as)1ﬂﬁr*ﬁ \W \$1“? “2.2,”? 1&3 {ii} {scam Lu— aAJw-v-xsfé‘lfawi \$21ij = 3 ngwl «£3 {5%) ﬂilxizvijh‘g3 Ta FYE‘ALLLQ, SEN MW @on 3W ism—'1 A Emmy) ;.-. -- ﬁbJCzamage-zca mﬂxm} Assignment #20 — Solutions p.9 ECSE-2410 Signals & Systems - 133112006 Tue 11/21/06 3(40). Text11.54. Continued. (C) Cm“?- {Eiﬂ L13? I{(§@)nxzijw)m £4.33... Kata +Xzfjw3+§§gwj gag b {maS “A“: wL+WL we 0 m; 2‘01“ inc, ...
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A#20_Solutions - Assignment#20 w Solutions p.1 ECSE-2410...

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