LINEAR CONTROL SYSTEMS. Ali Karimpour Associate Professor Ferdowsi University of Mashhad
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1 LINEA CONTOL SYSTEMS Ali aimpou Aoia Pofo Fdowi Univiy of Mahhad
2 Tim domain analyi of onol ym Topi o b ovd inlud: Tim domain analyi. v v v v T ignal. Sady a o and o offiin Eo i Inoduing om pfoman iia ISE, ITSE, IAE and ITAE. D. Ali aimpou Fb
3 چىذ سیگىال تست Som ignal Sp inpu يريدی پل u Vloiy inpu يريدی شیة u Alaion inpu يريدی شتاب u D. Ali aimpou Fb
4 Eo in onol ym خطا در سیستم ای کىترل inpu Eo ignal oupu = E=C Loop anf funion... m j... d d سیستم و ع صفر j= yp zo ym سیستم و ع یک j= yp on ym j= yp wo ym.. سیستم و ع دي.. dn T 4 D. Ali aimpou Fb d
5 D. Ali aimpou Fb 5 لرتىک یا متسیس رد اطخ Eo in onol ym T E E T E If h ym i abl: vy impoan T E
6 D. Ali aimpou Fb 6 لپ یديري ی ارت لرتىک یا متسیس رد اطخ Eo in onol ym fo p inpu E E T T E p E p Poiion onan T
7 D. Ali aimpou Fb 7 ةیش یديري ی ارت لرتىک یا متسیس رد اطخ Eo in onol ym fo vloiy inpu v E v Vloiy onan E E T T T E
8 D. Ali aimpou Fb 8 کیل تاراپ یديري ی ارت لرتىک یا متسیس رد اطخ Eo in onol ym fo paaboli inpu a E a Alaion onan E E T T T E
9 Eo in onol ym خطا در سیستم ای کىترل... m Td j d d... dn poiion vloiy alaion Typ p v a 9 D. Ali aimpou Fb
10 Exampl : Find h diffn o in following ym. مثال : خطا ای مختلف را ترای سیستم زیر تؼییه کىیذ. 9 9 T 9 Sym i abl o w oninu Eo fo uni p inpu v o a 9.9. p 9. T Eo fo uni vloiy and uni paaboli inpu o T D. Ali aimpou Fb
11 Ampliud Exampl : Sp pon مثال : پاسخ پل 9 Sp pon T p9,[ ] hold on;p, Tim D. Ali aimpou Fb
12 Ampliud Exampl : Vloiy pon مثال : پاسخ شیة یا سرػت 9.5 vloiy pon T 9.5 p9,[ ].5 hold on;p,[ ] Tim D. Ali aimpou Fb
13 Exampl : Find h diffn o in following ym مثال : خطا ای مختلف را ترای سیستم زیر تؼییه کىیذ p a Eo fo p inpu Eo fo vloiy inpu v. Eo fo paaboli inpu T Sym i abl o w oninu o T o o T. T D. Ali aimpou Fb
14 Ampliud Exampl : Sp pon مثال : پاسخ پل.4. Sp pon T.8.6 p,[ ] hold on;p, Tim 4 D. Ali aimpou Fb
15 Ampliud Exampl : Vloiy pon مثال : پاسخ شیة یا سرػت.5 vloiy pon T.5 p,[ ] hold on;p,[ ] Tim 5 D. Ali aimpou Fb
16 Exampl : Th lod loop anf funion of a ym i givn. Dmin a uh ha h ym o o p inpu i zo. a T 6 مثال : ترای سیستم حلق تست داد شذ a را چىان تىظیم کىیذ ک خطای سیستم ت يريدی پل صفر گردد Fi of all h h abiliy: 49 6 Claly i i abl T T a a 6 D. Ali aimpou Fb
17 Exampl 4: Th lod loop anf funion of a ym i givn. Dmin a and b uh ha h ym o o vloiy inpu i zo. a b T 6 Fi of all h h abiliy: مثال 4: ترای سیستم حلق تست داد شذ a ي b را چىان تىظیم کىیذ ک خطای سیستم ت يريدی سرػت صفر گردد I i abl by xampl a b T 6 6 a b a 6 6 b 7 D. Ali aimpou Fb
18 Exampl 5: Th lod loop anf funion of a ym i givn. Find h ym o o uni p. a T b 6 مثال 5: ترای سیستم حلق تست داد شذ خطای سیستم ت يريدی پل ياحذ را تیاتیذ Fi of all h h abiliy: I i unabl o h o i infiniy 8 D. Ali aimpou Fb
19 Exampl 6: Find h diffn o in following ym مثال 6: خطا ای مختلف را ترای سیستم زیر تؼییه کىیذ Eo fo p inpu p T Sym i abl o w oninu Eo fo vloiy and paaboli inpu v a 9 No ha h abov mhod don ay anyhing abou how h o go o infiniy ت ج کىیذ ک ایه ريش راجغ ت چگ وگی میل خطا ت تیى ایت صحثت ومی کىذ. Eo i an xplain h ma. D. Ali aimpou Fb
20 D. Ali aimpou Fb اطخ یرس Eo i d w W E : aound Expand...!!...! d w d w d w
21 D. Ali aimpou Fb اطخ یرس Eo i...! d w d w d w Now onid ady valu fo...!! C C C C...! d w d w d w C C C
22 ضرائة سری خطا Eo i offiin C C C C...!! C w d C w d C w d... Calulaion of offiin محاسث ضرائة W w d C W C dw d n... d W Cn... n d D. Ali aimpou Fb
23 Exampl 7: Dmin h o i offiin fo ym in xampl مثال 7 : ضرائة سری خطا را ترای سیستم مثال تیاتیذ E W C W dw d C C d W d... D. Ali aimpou Fb
24 D. Ali aimpou Fb 4 :8لاثم لاثم رد ةیش ي لپ یا یديري یارت ار اطخ یرس ذیتایت. Exampl 8: Dmin h o i fo p and vloiy inpu in xampl.,...,, C C C Sp: C C C C...!!..., amp:...!! C C C C...,,
25 Exampl 9: Compa h ul of xampl and 7 مثال 9 : وتایج مثال ای ي 7 را مقایس کىیذ Sp: Exampl Exampl 7 amp: Thy hav imila ul bu o i how how h o go o infiniy مشخص است ک وتایج یکسان است يلی سری خطا وح میل ت تیى ایت را ویس وشان می د ذ. 5 D. Ali aimpou Fb
26 Exampl : Dmin h o fo following inpu = مثال : خطا را ترای يريدی داد شذ تیاتیذ in Thi poblm an ju b olv wih o i! By xampl 8 w hav C, C, C,... in, o, in, o... C C C...in C... o!! 6 D. Ali aimpou Fb
27 Exampl : Dmin h o fo following inpu oninu خطا را ترای يريدی داد شذ تیاتیذادام مثال : in C C C...in C... o , C.98, C.94, C C in.98 8o....88in.959o.in 6. 7 D. Ali aimpou Fb
28 Exampl : Dmin h xa valu of o in xampl 8. 8 تیاتیذ. مثال : مقذار دقیق خطا را ترای مثال E in E 4 j 4 j 4 j 4 j j 4 j j j 4 j j.98 j j j.47 j j j.94in.96o.7in D. Ali aimpou Fb
29 Ampliud Exampl : Dmin h pon xampl 5. 5 تیاتیذ. مثال : پاسخ سیستم را ترای مثال in Lina Simulaion ul.8 [u,]=gnig'in',; T=f,[ ] T,u,; hold on; T=f, T,u,; Tim D. Ali aimpou Fb 9
30 Pfoman indi شاخص ای ػملکردی ISE IAE T d T d Ingal of h Squa of h Eo Ingal of h Abolu magniud of h Eo No ha h a poiiv valu and low valu i b ITSE ITAE T d T d Ingal of Tim muliplid by h Squad Eo Ingal of Tim muliplid by h Abolu Eo Thi pfoman i ud whn h iniial valu of o i no vy impoan D. Ali aimpou Fb
31 Exi Find h o of following ym o p inpu. x y [ Find h o of h following ym o p inpu. x u 4 ] x a M 5 5 b M M Find h o of h following ym o vloiy inpu. 5 a M b M 5 5 D. Ali aimpou Fb
32 Exioninu 4 pa xampl 7 fo paaboli inpu. 5 Find h o of following ym o p inpufinal 9. D. Ali aimpou Fb
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