1. TRNG I HC BCH KHOA H NI KHOA IN B MN IU KHIN T NG CC BI TH NGHIM MN HC L THUYT IU KHIN T NG PHN TUYN TNH KHI IN EE3381 ( 3 bi) KHI IN EE3382 ( 4 bi) C IN T ( 4 bi) KHI IN T( 3 bi) H NI 8/2008 12. CC BI TH NGHIM MN HC L THUYT IU KHIN T NG PHN 1. H THNG IU KHIN T NG TUYN TNH BI TH NGHIM 1 CC C TNH CA H THNG IU KHIN T NG I. MC CH Matlab l mt trong nhng phn mm thng dng nht dng phn tch , thit k v m phng cc h thng iu khin t ng. Trong bi th nghim ny sinh vin s dng cc lnh ca Matlab phn tch h thng nh xt tnh n nh ca h thng, c tnh qu , sai lch tnh.. II. CHUN B thc hin cc yu cu trong bi th nghim, sinh vin cn phi chun b k trc cc lnh ca Matlab. Khi khi ng chng trnh Matlab 6.5 ca s COMMAND MATLAB xut hin vi du nhc lnh">>". thc hin cc lnh sinh vin s g lnh t bn phm theo sau du nhc ny. phn tch c tnh ca h thng, sinh vin cn phi hiu k v cc lnh sau: num b0 s m + b1s m 1 + .... + bm 1s + bm W (s) = = den a0 s n + a1s n 1 + .... + an 1s + an Cho hm truyn t c dng: Khi ng MATLAB v ca s COMMAND MATLAB ta thy hin ra du nhc >> ta s nh cc cu lnh sau: >>num=[b0 b1 bm-1 bm]; % nh ngha t s nu h s no khng c % gn bng 0 >>den=[a0 a1 an-1 an]; % nh ngha mu s nu h s no khng c % gn bng 0 >>w=tf(num,den) % nh ngha hm truyn t w >>step(w) % V hm qu h(t) >>impulse(w) % V hm qu xung k(t) >>nyquist(w) % V c tnh tn bin pha ca h thng >>bode(w) % V c tnh logarit >>[A,B,C,D]=tf2ss(w) % Chuyn t hm truyn t sang khng gian %trng thi >>step(A,B,C,D) % V ng qu t cc ma trn trng thi >>impulse(A,B,C,D) % V ng qu xung t cc ma trn trng thi >> rlocus(w) : v QNS h thng hi tip m n v c hm truyn vng h w >>rlocfind(w): Tm im Kgh >> hold on : gi hnh v hin ti trong ca s Figure. Lnh ny hu ch khi ta cn v nhiu biu trong cng mt ca s Figure. Sau khi v xong biu th nht, ta g lnh hold on gi li hnh v sau v tip cc biu khc. Cc biu lc sau s v ln biu th nht trong cng mt ca s Figure ny. Nu khng mun gi hnh na, ta g lnh hold off. >>grid on : k li trn ca s Figure. Nu khng mun k li , ta g lnh grid off. >> subplot(m,n,p) : chia Figure thnh (mxn) ca s con v thao tc trn ca s con th p. 23. V d : Chia Figure thnh 2 ca s con, sau v Y ln ca s th 1 va Z ln ca s th 2 >> subplot(2,1,1), subplot(Y); % ve Y len cua so thu 1 >> subplot(2,1,2), subplot(Z); % ve Z len cua so thu 2 >> ltiview({'step','impluse','bode','nyquist'},w) v tt c cc ng c tnh ln mt th Ch : sinh vin nn tham kho phn Help ca Matlab nm r chc nng v c php ca mt bng cch g vo dng lnh : help III. TH NGHIM III.1. Kho st cc c tnh ca cc khu ng hc c bn a.Khu tch phn Hm truyn ca khu tch phn K W ( s) = s Kho st cc c tnh trong min thi gian v cc c tnh trong mi tn s trong 2 trng hp K=5, K=20; V d vi K=5 chng trnh c vit nh sau: >>num=[5]; >>den=[1 0]; >>w=tf(num,den) % nh ngha hm truyn t w >>step(w) % V hm qu h(t) >>impulse(w) % V hm trng lng w(t) >>nyquist(w) % V c tnh tn bin pha ca h thng >>bode(w) % V c tnh tn loga b. Khu vi phn thc t Ks W (s) = Ts + 1 Vi cc tham s K=20;T=0.1 Nhim v: - Vit chng trnh - Kho st cc c tnh trong min thi gian h(t),w(t) v cc c tnh trong min tn s nyquist v bode c. Khu qun tnh bc nht Hm truyn K W (s) = Ts + 1 Cho cc tham s K=20; T=50 v K=20; T=100 Nhim v: - Vit chng trnh - Kho st cc c tnh trong min thi gian h(t),w(t) v cc c tnh trong min tn s nyquist v bode - Xc nh cc tham s K v T trn th 34. d.Khu bc hai K W (s) = T s + 2dTs + 1 2 2 Cho cc tham s K=20, T=10,d=0,0.25,0.5,0.75,1. Nhim v: - Vit chng trnh - Kho st cc c tnh trong min thi gian h(t),w(t) v cc c tnh trong min tn s nyquist v bode - Nhn xt nh hng ca suy gim d n c tnh qu ca khu bc hai. III.2. Tm hm truyn tng ng ca h thng Mc ch: Gip sinh vin lm quen vi cc lnh c bn kt ni cc h thng Th nghim: Bng cch s dng cc lnh c bn conv, tf, series,parallel,feedback, tm biu thc hm truyn tng ng G(s) ca h thng sau: X G1 G2 Y G3 H1 s +1 s 1 1 Trong : G1 = ; G2 = ; G3 = ; H 1 = ( s + 3)( s + 5) s + 2s + 8 2 s s+2 Hng dn: Bc u tin nhp hm truyn cho cc khi G1, G2, ... dng lnh tf. Sau tu theo cu trc mc ni tip, song song hay phn hi m ta g lnh series ( hoc du *) , parallel ( hay du +), feedback tng ng thc hin vic kt ni cc khi vi nhau. Trong bo co trnh by r trnh t thc hin cc lnh ny. V d: >> G1=tf([1 1],conv([1 3],[1 5])) % Nhp hm truyn G1 >> G3=tf(1 ,[1 0]) % Nhp hm truyn G3 >>G13=G1+G3 % Tnh hm truyn tng ng ca G1, G3 % hoc G13=parallel(G1,G3) >>G21=feedback(G2,H1) % Tnh hm truyn tng ng ca G2, H1 Tip tc tnh tng t cho cc khi cn li Nhim v: - Vit chng trnh xc nh hm truyn t ca h thng - Kho st cc c tnh trong min thi gian h(t),w(t) ca h thng kn v cc c tnh trong min tn s nyquist v bode ca h thng h 45. III.3. Kho st cc c tnh ca h thng Cho h thng kn c cu trc nh hnh v: X(s) K 1 Y(s) s+2 (0.5s +1)(s +1) 1 0.005s +1 Cho K= 8; K=17.564411; K=20 - Nhim v: - Vit chng trnh xc nh hm truyn t ca h thng khi thay i K trong ba trng hp cho - Kho st cc c tnh trong min thi gian h(t),w(t) ca h thng kn v cc c tnh trong min tn s nyquist v bode ca h thng h IV. YU CU VIT BO CO Cu 1. - Vit chng trnh MATLAB cho tng khu ng hc c bn - V cc ng c tnh trong min thi gian v trong min tn s ca tng khu Cu 2. - Vit chng trnh tnh hm truyn ca h thng v in ra hm truyn ca h thng - Kho st cc ng c tnh trong min thi gian v tn s ca h thng Cu 3. Vit chng trnh xc nh hm truyn t ca h thng khi thay i K trong ba trng hp cho Kho st cc c tnh trong min thi gian h(t),w(t) ca h thng kn v cc c tnh trong min tn s nyquist v bode ca h thng h - Nhn xt g v cc c tnh trong min thi gian v trong min tn s khi K thay i 56. BI TH NGHIM 2 NG DNG MATLAB KHO ST TNH N NH V CHT LNG CA H THNG II.1. Xc nh Kgh Co h thng c s nh hnh v X K1 Y K (T 1s + 1)(T 2s + 1) K2 T3 s + 1 Cc thng s c o trong bng Nhm K K1 K2 T1 T2 T3 1 25 8 1 0,1 0,4 2 25 7 2 0,2 0,8 3 25 9 0.5 0,4 0,05 4 25 5 4 0,8 0,6 5 25 6.5 5 0,5 0,2 _ Mc ch: Kho st c tnh ca h thng tuyn tnh c h s khuch i K thay i, tm gi tr gii hn Kgh ca K h thng n nh. Nhim v: - Xc nh Kgh ca h thng theo iu kin n nh ( Yu cu sinh vin phi tnh trc khi ln th nghim) Cch 1: Cng thc tnh Kgh: 1 1 1 1 K gh = (T1 + T2 + T3 )( + + ) 1 K1K 2 T1 T2 T3 Cch 2: V QNS ca h thng. Da vo QNS, tm Kgh ca h thng, ch r gi tr ny trn QNS. Lu QNS ny thnh file *.bmp vit bo co. - Hm truyn t ca h thng h: K1K 2 Wh (s) = K (T1s + 1)(T2s + 1)(T3s + 1) - Chng trnh >>K1=25;K2=8;T1=1;T2=0.1;T3=0.4 - Vit chng trnh MATLAB cho h thng >>w=tf(K1, [T1 1])*tf(1, [T2 1])*tf(K2, [T3 1]); >>rlocus(w) >>rlocfind(w) >>[K,p]=rlocfind(w) - Kho st c tnh trong min thi gian ca h kn trong 3 trng hp H thng n nh KKgh H thng bin gii n nh K=Kgh - Kho st c tnh trong min tn s cho h thng h trong 3 trng hp sau: K=Kgh ;KKgh 67. Nhn xt v tr ca im (-1,j0) so vi ng c tnh tn s trong cc trng hp trn II.2. Hiu chnh b PID Cho h thng c s nh sau: X Y WPID(s) W DT(s) + Hm truyn ca b PID: 1 Td s WPID ( s ) = K PID (1 + + ) Ti s Td s + 1 Trong : KPID l h s khuych i ca b iu khin Ti l hng s thi gian tch phn Td l hng s thi gian vi phn l h s t l ca khu vi phn ( thng nh hn 1) + Hm truyn ca i tng K DT WDT (s) = (T1s + 1)(T2 s + 1) Cc thng s ban u ca b iu khin PID v i tng iu khin c cho trong bng sau: Nhm KPID Ti Td KDT T1 T2 1. 50 2 0.5 0.05 5 1 0.2 2. 1 50 5 0.05 4 200 40 3. 1 50 2 0.05 20 100 50 4. 70 150 2 0.05 5 10 2 5. 10 100 2 0.05 5 80 40 Nhim v: a. Vit chng trnh Matlab cho h thng b. V qu trnh qu vi cc thng s ban u, tnh qu iu chnh, thi gian qu , sai lch tnh c. Thay i cc tham s KPID,Ti,Td ca b iu khin PID nng cao cht lng ca h thng IV. YU CU VIT BO CO - Vit chng trnh MATLAB cho h thng - V cc ng c tnh trong min thi gian ca h kn v cc ng c tnh trong min tn s ca h thng - Nhn xt v qu trnh qu thu c qua thc nghim 78. BI TH NGHIM 3 NG DNG SIMULINK TNG HP H THNG IU KHINT NG I. MC CH : SIMULINK l mt cng c rt mnh ca Matlab xy dng cc m hnh mt cch trc quan v d hiu. m t hay xy dng h thng ta ch cn lin kt cc khi c sn trong th vin ca SIMULINK li vi nhau. Sau , tin hnh m phng h thng xem xt nh hng ca b iu khin n p ng qu ca h thng v nh gi cht lng h thng. II. CHUN B : thc hin cc yu cu trong bi th nghim ny, sinh vin cn phi chun b k v hiu r cc khi c bn cn thit trong th vin ca SIMULINK. Sau khi khi ng Matlab 6.5, ta g lnh simulink hoc nhn vo nt simulink trn thanh cng c th ca s SIMULINK hin ra: 2 th vin chnh p dng trong bi th nghim ny Cc th vin con trong II.1. Cc khi c s dng trong bi th nghim: a. Cc khi ngun tn hiu vo (source): Khi Step ( th vin Simulink \ Sources) c chc nng xut ra tn hiu hm bc thang. Double click vo khi ny ci t cc thng s: Step time : khong thi gian u ra chuyn sang mc Final value k t lc bt u m phng. Ci t gi tr ny bng 0. Initial value : Gi tr ban u. Ci t bng 0. Final value : Gi tr lc sau. Ci t theo gi tr ta mun tc ng ti h thng. Nu l hm bc thang n v th gi tr ny bng 1. Sample time : thi gian ly mu. Ci t bng 0. Khi Signal Generator ( th vin Simulink \ Sources) l b pht tn hiu xut ra cc tn hiu hng sin, hng vung, hng rng ca v ngu nhin (ci t cc dng hng ny trong mc Wave form). b. Cc khi ti thit b kho st ng ra (sink): Khi Mux ( th vin Simulink \ Signals Routing) l b ghp knh nhiu ng vo 1 ng ra, t ng ra ny ta a vo Scope xem nhiu tn hiu trn cng mt ca s. Double click vo khi ny thay i s knh u vo (trong mc Number of inputs) 89. Khi Scope ( th vin Simulink \ Sinks) l ca s xem cc tn hiu theo thi gian, t l xch ca cc trc c iu chnh t ng quan st tn hiu mt cch y . Khi XY Graph dng xem tng quan 2 tn hiu trong h thng (quan st mt phng pha). c.Cc khi x l khi ng hc : Khi Sum ( th vin Simulink \ Math Operations) l b tng (cng hay tr) cc tn hiu, thng dng ly hiu s ca tn hiu t vi tn hiu phn hi. Double click thay i du ca b tng. Khi Gain ( th vin Simulink \ Math Operations) l b t l. Tn hiu sau khi qua khi ny s c nhn vi gi tr Gain. Double click thay i gi tr li Gain. Khi Transfer Fcn ( th vin Simulink \ Continuous) l hm truyn ca h tuyn tnh. Double click thay i bc v cc h s ca hm truyn. Ci t cc thng s: _ Numerator : cc h s ca a thc t s _ Denominator : cc h s ca a thc mu s Khi Relay ( th vin Simulink \ Discontinuities) l b iu khin rle 2 v tr c tr (cn gi l b iu khin ON-OFF). Cc thng s : _ Switch on point : nu tn hiu u vo ln hn gi tr ny th ng ra ca khi Relay ln mc on _ Switch off point : nu tn hiu u vo nh hn gi tr ny th ng ra ca khi Relay xung mc off _ Output when on : gi tr ca ng ra khi mc on _ Output when off : gi tr ca ng ra khi mc off Nu tn hiu u vo nm trong khong (Switch on point, Switch off point) th gi tr ng ra gi nguyn khng i. Khi PID controller ( th vin Simulink Extras \ Additional Linear) l b iu khin PID vi hm truyn ( ) KP : h s t l (proportional term) KI: h s tch phn (integral term) KD: h s vi phn (derivative term) Khi Saturation ( th vin Simulink \ Discontinuities) l mt khu bo ha. Cc thng s ci t: _ Upper limit : gii hn trn. Nu gi tr u vo ln hn Upper limit th ng ra lun bng gi tr Upper limit _ Lower limit : gii hn di. Nu gi tr u vo nh hn Lower limit th ng ra lun bng gi tr Lower limit Khu bo ho dng th hin gii hn bin ca cc tn hiu trong thc t nh : p ra cc i ca b iu khin t vo i tng, p ngun II.2. Cc bc tin hnh xy dng mt ng dng mi trong SIMULINK: 910. _ Sau khi khi ng Matlab, g lnh simulink hoc nhn vo nt simulink trn thanh cng c th ca s SIMULINK hin ra (nh hnh v Trang 1) _ Trong ca s SIMULINK, vo menu File / New m ca s cho mt ng dng mi. Kch chut vo cc th vin gii thiu mc II.1 chn khi cn tm. Kch chut tri vo khi ny, sau ko v th vo ca s ng dng va mi to ra. Double click vo khi ny ci t v thay i cc thng s. _ C th nhn s lng cc khi bng cch dng chc nng Copy v Paste. Kch chut tri ni cc ng vo / ra ca cc khi hnh thnh s h thng. _ C th di mt hoc nhiu khi t v tr ny n v tr khc bng cch nhp chut chn cc khi v ko n v tr mi. Dng phm Delete xa cc phn khng cn thit hay b sai khi chn. _ C th vit ch thch trong ca s ng dng bng cch double click vo mt v tr trng v g cu ch thch vo. Vo menu Format / Font thay i kiu ch. _ Nh vy, m hnh h thng xy dng xong. By gi tin hnh m phng h thng bng cch vo menu Simulation / Simulation Parameters ci t cc thng s m phng. Ca s Simulation Parameters hin ra nh sau: _ Start time : thi im bt u m phng. Mc nh chn bng 0. _ Stop time : thi im kt thc m phng. Gi tr ny chn theo c tnh ca h thng. Nu h thng c thi hng ln th gi tr Stop time cng phi ln quan st ht thi gian qu ca h thng. _ Cc thng s cn li chn mc nh nh hnh k bn. _ Chy m phng bng cch vo menu Simulation / Start. Khi thi gian m phng bng gi tr Stop time th qu trnh m phng dng li. Trong qu trnh m phng, nu ta mun dng na chng th vo menu Simulation / Stop. III. TH NGHIM: III.1. Kho st m hnh h thng iu khin nhit : _ Mc ch: c trng ca l nhit l khu qun tnh nhit. T khi bt u cung cp nng lng u vo cho l nhit, nhit ca l bt u tng ln t t. nhit l t ti gi tr nhit cn nung th thng phi mt mt khong thi gian kh di. y chnh l c tnh qun tnh ca l nhit. Khi tuyn tnh ho m hnh l nhit, ta xem hm truyn ca l nhit nh l mt khu qun tnh bc 2 hoc nh l mt khu qun tnh bc nht ni tip vi khu tr. Trong phn ny, sinh vin s kho st khu qun tnh bc 2 cho trc. Dng phng php Ziegler-Nichols nhn dng h thng sau xy dng li hm truyn. So snh gi tr cc thng s trong hm truyn va tm c vi khu qun tnh bc 2 cho trc ny _ Th nghim: Dng SIMULINK xy dng m hnh h thng l nhit vng h nh sau: Step : l tn hiu hm bc thang th hin phn trm cng sut cung cp cho l nhit.Gi tr ca hm nc t 01 tng ng cng sut cung cp 0%100% Transfer Fcn Transfer Fcn1 : m hnh l nhit tuyn tnh ha. 1011. Nhm K T1 T2 1 100 20 100 2 200 30 300 3 150 40 200 4 300 20 150 5 200 50 200 a. Chnh gi tr ca hm step bng 1 cng sut cung cp cho l l 100% (Step time =0, Initial time = 0, Final time = 1). Chnh thi gian m phng Stop time = 600s. M phng v v qu trnh qu ca h thng trn. b. Trn hnh v cu trn,hy x?p x? v? khu qun tnh b?c nh?t c tr? b?ng cch v tip tuyn ti im un tnh thng s L v T theo nh hnh v?. Ch r cc gi tr ny trn hnh v. So snh gi tr L, T va tm c vi gi tr ca m hnh l nhit tuyn tnh ha. _ Hng dn: Sau khi chy xong m phng, xem qu trnh qu ca tn hiu ta double click vo khi Scope. Ca s Scope hin ra nh sau: V ca s Scope ch c th xem p ng hoc in trc tip ra my in nhng khng lu hnh v thnh file *.bmp c nn ta phi chuyn Scope ny sang ca s Figure lu. Thc hin iu ny bng cch nhp chut vo Parameters. Ca s Parameters hin ra, nhp chut vo trang Data history v tin hnh ci t cc thng s nh hnh bn di: Tin hnh chy m phng li tn hiu lu vo bin ScopeData. Ch nu sau khi khai bo m khng tin hnh chy m phng li th tn hiu s khng lu vo bin ScopeData mc d trn ca s Scope vn c hnh v. Sau , vo ca s Command Window nhp lnh sau: >> plot(ScopeData.time, ScopeData.signals.values) %ve dap ung >> grid on %ke luoi Lc ny ca s Figure hin ra vi hnh v ging nh hnh v ca s Scope. Vo menu Insert/ Line, Insert/ Text tin hnh k tip tuyn v ch thch cho hnh v. Kt qu cui cng nh hnh bn di : 1112. Vo menu [File]/[Export] lu thnh file *.bmp nh Bi th nghim 1. III.2. Kho st m hnh iu khin nhit dng phng php Ziegler-Nichols (iu khin PID): _ Mc ch: Kho st m hnh iu khin nhit dng b iu khin PID, cc thng s ca b PID c tnh theo phng php Ziegler-Nichols. T so snh cht lng ca h thng b iu khin PID . _ Th nghim: Xy dng m hnh h thng iu khin nhit PID nh sau: Trong d _ Tn hiu t u vo l hm bc thang u(t) = 100 ( tng trng nhit t 100 oC) _ B iu khin PID c cc thng s cn tnh ton. _ Transfer Fcn Transport Delay : m hnh l nhit tuyn tnh ha. a. Tnh gi tr cc thng s KP, KI, KD ca khu PID theo phng php Ziegler- Nichols t thng s L v T tm c phn III.1. b. Chy m phng v lu p ng ca cc tn hiu Scope vit bo co. C th chn li Stop time cho ph hp. Trong hnh v phi ch thch r tn cc tn hiu. c. Nhn xt v cht lng phng php iu khin PID _ Hng dn: Cch tnh cc thng s KP, KI, KD ca khu PID theo phng php Ziegler-Nichols nh sau: 1213. KI WPID (s) = K P + + K Ds s Vi 1.2T K KP = ; K I = P ; K D = 0.5K P L K.L 2L Trong L, T, K l cc gi tr tm c phn III.1.a. IV. YU CU VIT BO CO Bi 1. - Xy dng s h thng trn SIMULINK - Xp x i tng v khu qun tnh bc nht theo phng php th - So snh gia m hnh cho trc v m hnh nhn dng Bi 2. - Xy dng s h thng trn SIMULINK - Tnh cc thng s ca b iu khin theo ZieglerNichol v chnh nh cc thng s trn my tnh - V ng c tnh qu trnh qu - Nhn xt v qu trnh qu thu c qua thc nghim 1314. PHN 2. H THNG IU KHIN TRONG KHNG GIAN TRNG THI BI TH NGHIM 4 Cho i tng c hm truyn: 5 W(s) = (T1s + 1)(T2s + 1)(T3s + 1) Vi T1=STT ( STT l s th t theo danh sch lp); T2=100;T3=5 a. Xc nh phng trnh trng thi: . x = Ax+Bu y = Cx+Du A,B,C,D l cc ma trn ca phng trnh trng thi b. Kim tra tnh iu khin c v tnh quan st c ca i tng c. Kim tra tnh n nh ca i tng da trn h phng trnh trng thi d. Kho st cc c tnh trong min thi gian v trong min tn s ca i tng e. Xy dng s cu trc trn SIMULINK f. Thit k b iu khin phn hi trng thi sao cho h kn nhn cc im s=-1; s=-2; v s=-n ( vi n l s th t theo danh sch lp) lm cc im cc g. Kho st c tnh trong min thi gian ca h thng >>num=[K]; >>den=[a0 a1 a2 a3 ]; >>[A,B,C,D]=tf2ss(num,den) % nh ngha hm truyn t w >>co=ctrb(A,B) % Tnh ma trn iu khin c >>ob=obsv(A,C) % Tnh ma trn quan st c >>step(A,B,C,D) % V hm qu h(t) >>impulse(A,B,C,D) % V hm trng lng w(t) >>nyquist(A,B,C,D) % V c tnh tn bin pha ca h thng >>bode(A,B,C,D) % V c tnh tn loga >>K=acker(A,B,[s1 s2 s3]) % Tm ma trn phn hi trng thi theo ackerman IV. YU CU VIT BO CO - In ra cc ma trn A,B,C,D - Tnh ma trn iu khin c v hng ca n - Tnh ma trn quan st c v hng ca n - Vit phng trnh c tnh - V c tnh hm qu v hm trng lng ca i tng - V cc c tnh BTL v bin tn s pha ca i tng - Xy dng s h thng trn SIMULINK - Tnh ma trn iu khin phn hi trng thi - V c tnh hm qu v hm trng lng ca h kn - V cc c tnh BTL v bin tn s pha ca h h Bo co phi np sau 1 tun th nghim . Ai lm khng y hoc ly c tnh sai phi lm li .Khng np bi th nghim khng c d thi mn hc 14

w=tf(20,[1 0])III.1.a.w=tf(20,[1 0])Transfer function:20--s>> ltiview({'step','impulse','bode','nyquist'},w)III.1.b.>> w=tf([20 0],[0.1 1])Transfer function:20 s---------0.1 s + 1>> ltiview({'step','impulse','bode','nyquist'},w)III.1.cTH1w=tf(20,[50 1])Transfer function:20--------50 s + 1>> ltiview({'step','impulse','bode','nyquist'},w)TH2w=tf(20,[100 1])Transfer function:20---------100 s + 1>> ltiview({'step','impulse','bode','nyquist'},w)III.2.>> G1=tf([1 1],conv([1 3],[1 5]))Transfer function:s + 1--------------s^2 + 8 s + 15>> G2=tf([1 0],[1 2 8])Transfer function:s-------------s^2 + 2 s + 8>> G3=tf(1,[1 0])Transfer function:1-s>> H1=tf(1,[1 2])Transfer function:1-----s + 2>> G13=G1+G3Transfer function:2 s^2 + 9 s + 15------------------s^3 + 8 s^2 + 15 s>> G21=feedback(G2,H1)Transfer function:s^2 + 2 s-----------------------s^3 + 4 s^2 + 13 s + 16>> G=G13*G21Transfer function:2 s^4 + 13 s^3 + 33 s^2 + 30 s-------------------------------------------------s^6 + 12 s^5 + 60 s^4 + 180 s^3 + 323 s^2 + 240 s>> Gk=feedback(G,1)Transfer function:2 s^4 + 13 s^3 + 33 s^2 + 30 s-------------------------------------------------s^6 + 12 s^5 + 62 s^4 + 193 s^3 + 356 s^2 + 270 s>> ltiview({'step','impulse'},Gk)>> Gh=G*1Transfer function:2 s^4 + 13 s^3 + 33 s^2 + 30 s-------------------------------------------------s^6 + 12 s^5 + 60 s^4 + 180 s^3 + 323 s^2 + 240 s>> ltiview({'bode','nyquist'},Gk)\III.3.a.>> G1=tf(8,[1 2])Transfer function:8-----s + 2>> G2=tf(1,conv([0.5 1],[1 1]))Transfer function:1-------------------0.5 s^2 + 1.5 s + 1>> H=tf(1,[0.005 1])Transfer function:1-----------0.005 s + 1>> G=feedback(G1*G2,H)Transfer function:0.04 s + 8------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 10>> Gk=feedback(G,1)Transfer function:0.04 s + 8------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.05 s + 18>> ltiview({'step','impulse'},Gk)>> Gh=G*1Transfer function:0.04 s + 8------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 10>> ltiview({'bode','nyquist'},Gh)III.3.b.>> G1=tf(20,[1 2])Transfer function:20-----s + 2>> G2=tf(1,conv([0.5 1],[1 1]))Transfer function:1-------------------0.5 s^2 + 1.5 s + 1>> H=tf(1,[0.005 1])Transfer function:1-----------0.005 s + 1>> G=feedback(G1*G2,H)Transfer function:0.1 s + 20------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 22>> Gk=feedback(G,1)Transfer function:0.1 s + 20------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.11 s + 42>> ltiview({'step','impulse'},Gk)>> Gh=G*1Transfer function:0.1 s + 20------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 22>> ltiview({'bode','nyquist'},Gh)III.3.c>> G1=tf(17.564411,[1 2])Transfer function:17.56-----s + 2>> G2=tf(1,conv([0.5 1],[1 1]))Transfer function:1-------------------0.5 s^2 + 1.5 s + 1>> H=tf(1,[0.005 1])Transfer function:1-----------0.005 s + 1>> G=feedback(G1*G2,H)Transfer function:0.08782 s + 17.56---------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 19.56>> Gk=feedback(G,1)Transfer function:0.08782 s + 17.56----------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.098 s + 37.13>> ltiview({'step','impulse'},Gk)>> Gh=G*1Transfer function:0.08782 s + 17.56---------------------------------------------------0.0025 s^4 + 0.5125 s^3 + 2.52 s^2 + 4.01 s + 19.56>> ltiview({'bode','nyquist'},Gh)III.4.>> num=[2]num = 2>> den=[0.04 0.54 1.5 3]den = 0.0400 0.5400 1.5000 3.0000>> [A,B,C,D]=tf2ss(num,den)A = -13.5000 -37.5000 -75.00001.0000 0 00 1.0000 0B = 100C = 0 0 50D = 0>> step(A,B,C,D)>> impulse(A,B,C,D)>> nyquist(A,B,C,D)>> bode(A,B,C,D)III.1.d>> w=tf(20,[100 0 1])Transfer function:20-----------100 s^2 + 1>> step(w)>> hold on>> w=tf(20,[100 5 1])Transfer function:20-----------------100 s^2 + 5 s + 1>> step(w)>> w=tf(20,[100 10 1])Transfer function:20------------------100 s^2 + 10 s + 1>> step(w)>> w=tf(20,[100 15 1])Transfer function:20------------------100 s^2 + 15 s + 1>> step(w)>> w=tf(20,[100 20 1])Transfer function:20------------------100 s^2 + 20 s + 1>> step(w)>> hold off>> w=tf(20,[100 0 1])Transfer function:20-----------100 s^2 + 1>> impulse(w)>> hold on>> w=tf(20,[100 5 1])Transfer function:20-----------------100 s^2 + 5 s + 1>> impulse(w)>> w=tf(20,[100 10 1])Transfer function:20------------------100 s^2 + 10 s + 1>> impulse(w)>> w=tf(20,[100 15 1])Transfer function:20------------------100 s^2 + 15 s + 1>> impulse(w)>> w=tf(20,[100 20 1])Transfer function:20------------------100 s^2 + 20 s + 1>> impulse(w)>> hold off>> w=tf(20,[100 0 1])Transfer function:20-----------100 s^2 + 1>> nyquist(w)>> hold on>> w=tf(20,[100 5 1])Transfer function:20-----------------100 s^2 + 5 s + 1>> nyquist(w)>> w=tf(20,[100 10 1])Transfer function:20------------------100 s^2 + 10 s + 1>> nyquist(w)>> w=tf(20,[100 15 1])Transfer function:20------------------100 s^2 + 15 s + 1>> nyquist(w)>> w=tf(20,[100 20 1])Transfer function:20------------------100 s^2 + 20 s + 1>> nyquist(w)>> hold off>> w=tf(20,[100 0 1])Transfer function:20-----------100 s^2 + 1>> bode(w)>> hold on>> w=tf(20,[100 5 1])Transfer function:20-----------------100 s^2 + 5 s + 1>> bode(w)>> w=tf(20,[100 10 1])Transfer function:20------------------100 s^2 + 10 s + 1>> bode(w)>> w=tf(20,[100 15 1])Transfer function:20