LINEAR CONTROL SYSTEMS
|
|
- Marsha Bryant
- 5 years ago
- Views:
Transcription
1 LINEAR CONTROL SYSTEMS Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad
2 Root Locu Criteria Topic to be covered include: v v v v Root locu criterion. u u u Root loci (RL). Complement root loci (CRL). Complete root loci. Effect of adding pole and zero on root locu. Effect of moving pole and zero. Root contour.
3 Root locu مکان ریشه ها Root locu, how the poition of root of the following equation for different value of مکان ریشه ها موقعیت ریشه های معادله زیر را بر حسب نشان می دهد. f( ) مقادیر مختلف Root loci (RL) Complement root loci (CRL) Complete root loci R R R 3
4 Root locu مکان ریشه ها Why root of +f()= i important for u?
5 The Root Locu procedure f( ) نحوه رسم مکان ریشه ها Which point lie on the root loci? چه نقاطی بر روی مکان ریشه قرار دارند Condition of magnitude f ( ) Condition of angle R f ( ) R شرط اندازه شرط زاویه f ( ) or f ( ) R f ( ) or f ( ) R 5
6 The Root Locu procedure f( ) نحوه رسم مکان ریشه ها Rule : Specify the equation exactly in the following form. f( ) قانون اول: سیستم را دقیقا بصورت زیر بیان کنید. How many branche in root loci? چند شاخه در مکان ریشه ها Rule : Specify the pole and zero of f(). The root loci lie on the pole of f() for = and lie on the zero of f() for =± قانون : قطب و صفرهای f() را مشخص کنید. مکان ریشه در = روی قطبهای f() و در ±= روی صفرهای f() قرار دارد. Rule 3: Define the real axi ection for poitive and negative value of. :3 6 قانون محور حقیقی را برای مقادیر مثبت و منفی مشخص کنید
7 The Root Locu procedure f( ) نحوه رسم مکان ریشه ها Rule 4: Find the aymptote and centered of aymptote for poitive and negative value of. قانون 4: مجانبها و محل تالقی مجانبها را برای مقادیر مثبت و منفی تعیین کنید. number of aymptote np n z Rule 5: Find the brea point. f ( ) (m ) n n n m p m,,,... قانون 5: نقطه شکست را بیابید. brea point Rule 6: Find the cro of root locu with imaginary axi by Routh Hurwitz criteria. قانون 6: نقطه تالقی با محور موهومی را توسط روش روت هرویتز تعیین کنید. p n z z m,,,... Aymptotecenter n p p i i i n p n z n z 7 z i
8 The Root Locu procedure f( ) نحوه رسم مکان ریشه ها f( ) قانون : سیستم را دقیقا بصورت مقابل بیان کنید. قانون : قطب و صفرهای f() را مشخص کنید. مکان ریشه در = روی قطبهای f() و در ±= روی صفرهای f() قرار دارد. قانون 3: محور حقیقی را برای مقادیر مثبت و منفی مشخص کنید number of f ( ) :4 8 قانون و محل مجانبها تالقی مجانبها را برای مقادیر مثبت و منفی تعیین کنید. aymptote np n z (m ) n n brea point n m p p n z z m,,,... m,,,... Aymptotecenter n p p i i i n p n z n z :5 z i قانون قانون نقطه شکست را بیابید. 6: نقطه تالقی با محور موهومی را توسط روش روت هرویتز تعیین کنید.
9 Example : Draw the complete root loci of the following ytem. مثال : مکان کامل ریشه ها را در سیستم زیر بیابید. ( ) - 9
10 Example : Draw the complete root loci of the following ytem. مکان کامل ریشه ها را در سیستم زیر بیابید. ( 5)( ) 7.7 j مثال : j
11 Example : Draw the complete root loci of the following ytem. ( 5)( )
12 ( 5)( ) rlocu(,[ 5 5 ]); hold on; rlocu(-,[ 5 5 ]) Root Root Locu Locu 4 4 Root Root Locu Locu Imaginary Axi Imaginary Axi - - Imaginary Axi Imaginary Axi Real Real Axi Axi Real Real Axi Axi
13 Example 3: Draw the complete root loci of following ytem. مثال 3: مکان کامل ریشه ها را در سیستم زیر بیابید. ( )( 3) ( ) Rule : Specify the equation exactly in the tandard form. قانون اول: سیستم را دقیقا بصورت زیر استاندارد کنید. ( 3) ( ) ( )( 3) ( 9) 3
14 Example 3: ( 3) ( 9) Rule : Specify the pole and zero of f(). The root loci lie on the pole of f() for = and lie on the zero of f() for =± : قطب و صفرهای f() را مشخص کنید. مکان ریشه در = و در ±= روی صفرهای f() قرار دارد. قانون f() روی قطبهای 5 3 4
15 Example 3: ( 3) ( 9) Rule 3: Define the real axi ection for poitive and negative value of. قانون 3: محور حقیقی را برای مقادیر مثبت و منفی مشخص کنید 5 3 5
16 Example 3: ( 3) ( 9) Rule 4: Find the aymptote and centered of aymptote. Aymptotecenter n p p z ( 3) i i i i n p n n z z 3.5 قانون 4: و محل مجانبها تالقی مجانبها. (m ) 3, n p nz m, n p nz 5 3 6
17 Example 3: ( 3) ( 9) Rule 5: Find the brea point. (3 f ( ) 9)( 3) ( ( 3) ( 3 3 قانون 5: نقطه شکست را بیابید. 9) ( 3) 9)
18 ( 3) ( 9) 6: نقطه تالقی با محور موهومی Rule 6: Find the cro of root locu with imaginary axi 3 (9 ) 3? قانون 5 3 We need another rule. 8 به قانون دیگری نیاز داریم.
19 The Root Locu procedure f( ) نحوه رسم مکان ریشه ها Rule 7: Find the arrival angle and departure angle. Departure angle. قانون 7: زوایای ورود و خروج را تعیین کنید. Zero pole Arrival angle. Zero pole 9
20 Rule 7: Find the arrival angle and departure angle. قانون 7: زوایای ورود و خروج را تعیین کنید (8 (8 tan tan ) 5 )
21 Rule 7: Find the arrival angle and departure angle (8 (8 tan tan ) 5 قانون 7: زوایای ورود و خروج را تعیین کنید. )
22 هبساحم هشیر ناکم یور Calculation of on the Root Loci ) ( f ) ( f Condition of magnitude m i i n j j z C p n j j m i i p z C f ) ( Let
23 Summary Rule : Specify the equation exactly in the form. f( ) Rule : Specify the pole and zero of f(). The root loci lie on the pole of f() for = and lie on the zero of f() for =± Rule 3: Define the real axi ection for poitive and negative value of. Rule 4: Find the aymptote and centered of aymptote. Aymptotecenter Rule 5: Find the brea point. n p p i i i n p n z n z z i (m ) np nz m np nz Rule 6: Find the cro of root locu with imaginary axi by Routh Hurwitz criteria. Rule 7: Find the arrival angle and departure angle. 3
24 Root Locu Technique Topic to be covered include: v u u Root locu criterion. Root loci (RL). Complement root loci (CRL). v v v u Complete root loci. Effect of adding pole and zero on root locu. Effect of moving pole and zero. Root contour. 4
25 Adding pole and zero inide the loop اضافه کردن صفر و قطب داخل تابع انتقال حلقه r + e - G() c Adding pole to the loop r e - G() b c r Adding zero to the loop e - G() b c 5
26 Adding pole inide the loop اضافه کردن قطب داخل حلقه ( a) ( a)( b) -a b -b -a 6
27 Adding zero inide the loop اضافه کردن صفر داخل حلقه ( a) ( b) ( a) -a b -b -a 7
28 Root Locu Technique Topic to be covered include: v u u Root locu criterion. Root loci (RL). Complement root loci (CRL). v v v v u Complete root loci. Property and contruction of complete root loci. Effect of adding pole and zero on root locu. Effect of moving pole and zero. Root contour. 8
29 Effect of moving pole اثرات حرکت قطبها Conider following equation: ( b) ( a) ( b) ( a) Let b= but a=, 9, 8, 3, ( ) ( a) 9
30 Effect of moving pole. Let a= اثرات حرکت قطبها ( ) ( ) and aymptote Breapoint
31 Effect of moving pole Let a=9 اثرات حرکت قطبها ( ) ( 9) and aymptote Breapoint
32 اثرات حرکت قطبها Effect of moving pole Let a=8 ( ) ( 8) and aymptote Brea Point, i
33 Effect of moving pole. Let a=3 اثرات حرکت قطبها ( ) ( 3) and aymptote Brea point -3 -,.5. 87i 3 33
34 Effect of moving pole. اثرات حرکت قطبها Let a= and aymptote ( ) ( ) Brea point 3-34
35 Effect of moving pole. اثرات حرکت قطبها a= 3 9 a=
36 More tudy on root locu criterion Remar #: Let f() be bi-proper: f( ) Jump in root locu Example 5: Draw the complete root loci of following ytem
37 More tudy on root locu criterion Example 4: Draw the complete root loci of following ytem
38 More tudy on root locu criterion Example 5: Univerity entrance exam 388 Find root locu for < ( ( 5)( 6)( 3) 4) Root Locu 6 4 Imaginary Axi Real Axi 38
39 More tudy on root locu criterion Example 6: Univerity entrance exam 39 A unity poitive feedbac ytem ha a loop tranfer function a: ( 5)(.5) G( ) ( )( 5) Draw root locu for > Imaginary Axi Root Locu Real Axi 39
40 Root Locu Technique Univerity entrance exam 393 Example 7: Univerity entrance exam 393 Root locu of a unity negative feedbac ytem for > i hown. Suppoe undamped ocillation period i π 3, find the teady tate error to unit tep. ) 7/9 ) 7/64 3)64/9 4) 64/7 4
41 Root Locu Technique Topic to be covered include: v u u Root locu criterion. Root loci (RL). Complement root loci (CRL). v v v v u Complete root loci. Property and contruction of complete root loci. Effect of adding pole and zero on root locu. Effect of moving pole and zero. Root contour. 4
42 Root contour (Multiple parameter variation ( ) کانتور ریشه ها ( تغییرات چند پارامتر Remember root loci f( ) Suppoe: Q( ) P ( ) P ( ) and are parameter Step : Put one variable equal to zero. Let u = Q ) P( ) ( Step : Retore the value of Q( ) P ( ) P ( ) P ) ( f ( ) Q( ) f( ) P ( ) Q ( ) P ( ) ( f ( ) f4 ( )
43 Example 8: Draw the root contour for following ytem. 3 Step : Let = then Aymptote are: ( ) 3, 3 مثال 8: کانتور ریشه ها را برای سیستم زیر بیابید. 3 = ( ) 3 Angle of departure i: = - = θ.5 ( ) / 3 6 = 43
44 Example 8: Draw the root contour for following ytem. 3 Step : Retore the value of مثال 8: کانتور ریشه ها را برای سیستم زیر بیابید. 3 Let: = = Let: = Let: = = - = = 44
45 Exercie 7- A unity feedbac ( negative ign ) control ytem ha an open loop tranfer function Setch the complete root loci, and find the correponding when the root loci croe jω axi. 7- The tranfer function of a ingle-loop control ytem are given a: G ( ). H( ) G( ) (.)(.5) ( )( 3) Contruct the root loci of the Zero of +G()H()= for - <T d < 7-3 The open loop tranfer function of a unity-feedbac (negative ign) ytem i: K G p ( ) ( 5) Contruct the complete root loci of the characteritic equation for Let n=, n= and n=3. n T d 45
46 Exercie 7-4 The open loop tranfer function of a unity-feedbac (negative ign) ytem i: K( )( 3) G( ) ( ) a) Contruct the root loci for - <K<, with α=5. b) Contruct the root loci for - < α <, with K = The open loop tranfer function of a unity-feedbac (negative ign) ytem i: 5 p G( ) ( )( p) Contruct the root loci for <p< 7-6 Conider following ytem Contruct the root loci for < < 3 46
47 Exercie 7-7 Contruct the root loci of the cloed loop pole of the following ytem for <a< (Midterm pring 8). R() C() a 7-8 Conider following ytem 3 For =, = and = contruct the root loci for < <. 47
48 Exercie 7-9 Find the root-locu graph for the following ytem. Anwer : 7- The open loop tranfer function of a unity-feedbac (negative ign) ytem i: G( ) ( p) Contruct the root loci for <p< (Final 39) 48
49 Supplementary Exercie 7- The open loop tranfer function of a unity-feedbac (negative ign) ytem i: G( ) K (. e )( ) Contruct the complete root loci of the characteritic equation. 7-The open loop tranfer function of a unity-feedbac (negative ign) ytem with PD controller i: G( ) ( K p K d ) Setch the root loci for different value of K p and K d. (Let Kp=,,5,.) 49
50 Supplementary Exercie Univerity entrance exam The open loop tranfer function of a unity-feedbac (negative ign) ytem i: ( )( 5) G( ) ( )( ) Setch the veru real part of root. (Univerity entrance exam 393) Anwer: Remar: Note that for any we have two root. 5
51 Supplementary Exercie Univerity entrance exam (Univerity entrance exam 393) 5
Lecture 7 CONTROL ENGINEERING. Ali Karimpour Associate Professor Ferdowsi University of Mashhad
CONTROL ENGINEERING Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Dr. Ali Karimpour Sep 5 Root Locu Criteria Topic to be covered include: Root locu criterion. Root loci (RL). Complement root
More informationAli Karimpour Associate Professor Ferdowsi University of Mashhad
LINEAR CONTROL SYSTEMS Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Root Locu Technique Topic to be covered include: Property and contruction of complete root loci. (Cont.) Effect of adding
More informationAli Karimpour Associate Professor Ferdowsi University of Mashhad
LINEAR CONTROL SYSTEMS Ali Karimour Aociate Profeor Ferdowi Univerity of Mahhad Root Locu Technique Toic to be covered include: Root locu criterion. Root loci (RL). Comlement root loci (CRL). Comlete root
More informationAli Karimpour Associate Professor Ferdowsi University of Mashhad
AUTOMATIC CONTROL SYSTEMS Ali Karimour Aociate Profeor Ferdowi Univerity of Mahhad Root Locu Technique Toic to be covered include: Root locu criterion. Root loci (RL). Comlement root loci (CRL). Comlete
More informationLINEAR CONTROL SYSTEMS Ali Karimpour Associate Professor Ferdowsi University of Mashhad
LINEAR CONTROL SYSTEMS Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Lecture Stability analyi Topic to be covered include: Stability of linear control ytem. Bounded input bounded output tability
More informationCONTROL SYSTEMS. Chapter 5 : Root Locus Diagram. GATE Objective & Numerical Type Solutions. The transfer function of a closed loop system is
CONTROL SYSTEMS Chapter 5 : Root Locu Diagram GATE Objective & Numerical Type Solution Quetion 1 [Work Book] [GATE EC 199 IISc-Bangalore : Mark] The tranfer function of a cloed loop ytem i T () where i
More informationChapter 7. Root Locus Analysis
Chapter 7 Root Locu Analyi jw + KGH ( ) GH ( ) - K 0 z O 4 p 2 p 3 p Root Locu Analyi The root of the cloed-loop characteritic equation define the ytem characteritic repone. Their location in the complex
More informationRoot Locus Diagram. Root loci: The portion of root locus when k assume positive values: that is 0
Objective Root Locu Diagram Upon completion of thi chapter you will be able to: Plot the Root Locu for a given Tranfer Function by varying gain of the ytem, Analye the tability of the ytem from the root
More informationLecture 12: Examples of Root Locus Plots. Dr. Kalyana Veluvolu. Lecture 12: Examples of Root Locus Plots Dr. Kalyana Veluvolu
ROOT-LOCUS ANALYSIS Example: Given that G( ) ( + )( + ) Dr. alyana Veluvolu Sketch the root locu of 1 + G() and compute the value of that will yield a dominant econd order behavior with a damping ratio,
More informationMODERN CONTROL SYSTEMS
MODERN CONTROL SYSTEMS Lecture 1 Root Locu Emam Fathy Department of Electrical and Control Engineering email: emfmz@aat.edu http://www.aat.edu/cv.php?dip_unit=346&er=68525 1 Introduction What i root locu?
More informationAutomatic Control Systems. Part III: Root Locus Technique
www.pdhcenter.com PDH Coure E40 www.pdhonline.org Automatic Control Sytem Part III: Root Locu Technique By Shih-Min Hu, Ph.D., P.E. Page of 30 www.pdhcenter.com PDH Coure E40 www.pdhonline.org VI. Root
More informationFigure 1: Unity Feedback System
MEM 355 Sample Midterm Problem Stability 1 a) I the following ytem table? Solution: G() = Pole: -1, -2, -2, -1.5000 + 1.3229i, -1.5000-1.3229i 1 ( + 1)( 2 + 3 + 4)( + 2) 2 A you can ee, all pole are on
More informationEE Control Systems LECTURE 14
Updated: Tueday, March 3, 999 EE 434 - Control Sytem LECTURE 4 Copyright FL Lewi 999 All right reerved ROOT LOCUS DESIGN TECHNIQUE Suppoe the cloed-loop tranfer function depend on a deign parameter k We
More informationFinal Exam Sample Questions Signals and Systems Course Fall 91
1 1. Consider the signal x(t) with the Laplace transform region of convergence a < Real{s} < b where a < 0 < b. Determine the Laplace transform region of convergence for y(t) = x(t)u(t). 2. Given the following
More informationECE-320 Linear Control Systems. Spring 2014, Exam 1. No calculators or computers allowed, you may leave your answers as fractions.
ECE-0 Linear Control Sytem Spring 04, Exam No calculator or computer allowed, you may leave your anwer a fraction. All problem are worth point unle noted otherwie. Total /00 Problem - refer to the unit
More informationME2142/ME2142E Feedback Control Systems
Root Locu Analyi Root Locu Analyi Conider the cloed-loop ytem R + E - G C B H The tranient repone, and tability, of the cloed-loop ytem i determined by the value of the root of the characteritic equation
More informationDelhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:
Serial :. PT_EE_A+C_Control Sytem_798 Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubanewar olkata Patna Web: E-mail: info@madeeay.in Ph: -4546 CLASS TEST 8-9 ELECTRICAL ENGINEERING Subject
More informationControl Systems. Root locus.
Control Sytem Root locu chibum@eoultech.ac.kr Outline Concet of Root Locu Contructing root locu Control Sytem Root Locu Stability and tranient reone i cloely related with the location of ole in -lane How
More informationRoot Locus Contents. Root locus, sketching algorithm. Root locus, examples. Root locus, proofs. Root locus, control examples
Root Locu Content Root locu, ketching algorithm Root locu, example Root locu, proof Root locu, control example Root locu, influence of zero and pole Root locu, lead lag controller deign 9 Spring ME45 -
More informationStability. ME 344/144L Prof. R.G. Longoria Dynamic Systems and Controls/Lab. Department of Mechanical Engineering The University of Texas at Austin
Stability The tability of a ytem refer to it ability or tendency to eek a condition of tatic equilibrium after it ha been diturbed. If given a mall perturbation from the equilibrium, it i table if it return.
More informationControl Systems. Root locus.
Control Sytem Root locu chibum@eoultech.ac.kr Outline Concet of Root Locu Contructing root locu Control Sytem Root Locu Stability and tranient reone i cloely related with the location of ole in -lane How
More informationCISE302: Linear Control Systems
Term 8 CISE: Linear Control Sytem Dr. Samir Al-Amer Chapter 7: Root locu CISE_ch 7 Al-Amer8 ١ Learning Objective Undertand the concept of root locu and it role in control ytem deign Be able to ketch root
More informationAnalysis of Stability &
INC 34 Feedback Control Sytem Analyi of Stability & Steady-State Error S Wonga arawan.won@kmutt.ac.th Summary from previou cla Firt-order & econd order ytem repone τ ωn ζω ω n n.8.6.4. ζ ζ. ζ.5 ζ ζ.5 ct.8.6.4...4.6.8..4.6.8
More informationME 375 FINAL EXAM SOLUTIONS Friday December 17, 2004
ME 375 FINAL EXAM SOLUTIONS Friday December 7, 004 Diviion Adam 0:30 / Yao :30 (circle one) Name Intruction () Thi i a cloed book eamination, but you are allowed three 8.5 crib heet. () You have two hour
More informationThe Root Locus Method
The Root Locu Method MEM 355 Performance Enhancement of Dynamical Sytem Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan
More informationECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances
ECE 350 Root Locu Deign Example Recall the imple crude ervo from lab G( ) 0 6.64 53.78 σ = = 3 23.473 PI To eliminate teady-tate error (for contant input) & perfect reection of contant diturbance Note:
More informationROOT LOCUS. Poles and Zeros
Automatic Control Sytem, 343 Deartment of Mechatronic Engineering, German Jordanian Univerity ROOT LOCUS The Root Locu i the ath of the root of the characteritic equation traced out in the - lane a a ytem
More informationMEM 355 Performance Enhancement of Dynamical Systems Root Locus Analysis
MEM 355 Performance Enhancement of Dynamical Sytem Root Locu Analyi Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan in
More informationFeedback Control Systems (FCS)
Feedback Control Sytem (FCS) Lecture19-20 Routh-Herwitz Stability Criterion Dr. Imtiaz Huain email: imtiaz.huain@faculty.muet.edu.pk URL :http://imtiazhuainkalwar.weebly.com/ Stability of Higher Order
More informationOrganic Compounds: Alkanes and Their Stereochemistry
3 Organic Compounds: Alkanes and Their Stereochemistry ترکیبات آلی: آلکان ها و استریوشیمی آنها Based on McMurry s Organic Chemistry, 7 th edition Why this Chapter Alkanes are unreactive, but provide useful
More informationبه نام خدا. Organic Chemistry 1. Dr Morteza Mehrdad University of Guilan, Department of Chemistry, Rasht, Iran
به نام خدا 3 Organic Chemistry 1 Dr Morteza Mehrdad University of Guilan, Department of Chemistry, Rasht, Iran m-mehrdad@guilan.ac.ir 3 Organic Compounds: Alkanes and Their Stereochemistry ترکیبات آلی:
More informationAdvanced Inorganic Chemistry. نیم سال اول Ferdowsi University of Mashhad
Advanced Inorganic Chemistry ماتریس matrix ماتریس آرایه ای مستطیلی از اعداد یا عالئم می باشد عضو های قطری 2 ماتریس واحد 3 جمع و تفریق ماتریس ها 4 جمع و تفریق ماتریس ها 5 نکته 6 تمرین جمع و تفریق ماتریس
More informationThe state variable description of an LTI system is given by 3 1O. Statement for Linked Answer Questions 3 and 4 :
CHAPTER 6 CONTROL SYSTEMS YEAR TO MARKS MCQ 6. The tate variable decription of an LTI ytem i given by Jxo N J a NJx N JN K O K OK O K O xo a x + u Kxo O K 3 a3 OKx O K 3 O L P L J PL P L P x N K O y _
More informationChapter #4 EEE Automatic Control
Spring 008 EEE 00 Chapter #4 EEE 00 Automatic Control Root Locu Chapter 4 /4 Spring 008 EEE 00 Introduction Repone depend on ytem and controller parameter > Cloed loop pole location depend on ytem and
More informationDynamic meteorology 1
Dynamic meteorology 1 Lecture Sahraei Physics Department Razi University http://www.razi.ac.ir/sahraei متغیرهای فیزیکی Physical Variables وابسته مستقل T - وابسته: )یا نرده ای است مانند فشار هوا P سرعت
More informationتحلیل و طراحی سیستم های کنترل چندمتغیره در حوزه فضای حالت
باسمه تعالی سیستم های کنترل چند متغیره Lecture 4 تحلیل و طراحی سیستم های کنترل چندمتغیره در حوزه فضای حالت مقدمه اهمیت استفاده از تحلیل و طراحی سیستم ها در فضای حالت دست یاقتن به توصیف دینامیک داخلی سیستم
More informationControl Systems Analysis and Design by the Root-Locus Method
6 Control Sytem Analyi and Deign by the Root-Locu Method 6 1 INTRODUCTION The baic characteritic of the tranient repone of a cloed-loop ytem i cloely related to the location of the cloed-loop pole. If
More informationAir pollution Sahraei Physics Department Razi University http://www.razi.ac.ir/sahraei پایداری قائم جو اگر بخواهیم پدیده های مهم جوی مانند آشفتگی را درک و پیش بینی کنیم باید برای پایداری حرکت قائم هوا
More informationStability Criterion Routh Hurwitz
EES404 Fundamental of Control Sytem Stability Criterion Routh Hurwitz DR. Ir. Wahidin Wahab M.Sc. Ir. Arie Subiantoro M.Sc. Stability A ytem i table if for a finite input the output i imilarly finite A
More information7.4 STEP BY STEP PROCEDURE TO DRAW THE ROOT LOCUS DIAGRAM
ROOT LOCUS TECHNIQUE. Values of on the root loci The value of at any point s on the root loci is determined from the following equation G( s) H( s) Product of lengths of vectors from poles of G( s)h( s)
More informationChapter 13. Root Locus Introduction
Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will
More informationNAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE
POLITONG SHANGHAI BASIC AUTOMATIC CONTROL June Academic Year / Exam grade NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE Ue only thee page (including the bac) for anwer. Do not ue additional
More informationMathematical modeling of control systems. Laith Batarseh. Mathematical modeling of control systems
Chapter two Laith Batareh Mathematical modeling The dynamic of many ytem, whether they are mechanical, electrical, thermal, economic, biological, and o on, may be decribed in term of differential equation
More informationAutomatic Control Systems, 9th Edition
Chapter 7: Root Locus Analysis Appendix E: Properties and Construction of the Root Loci Automatic Control Systems, 9th Edition Farid Golnaraghi, Simon Fraser University Benjamin C. Kuo, University of Illinois
More informationMultivariable Control Systems
Lecture Multivariable Control Sytem Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Lecture Reference are appeared in the lat lide. Dr. Ali Karimpour May 6 Uncertainty in Multivariable Sytem
More informationLecture 1 Root Locus
Root Locus ELEC304-Alper Erdogan 1 1 Lecture 1 Root Locus What is Root-Locus? : A graphical representation of closed loop poles as a system parameter varied. Based on Root-Locus graph we can choose the
More informationCHAPTER # 9 ROOT LOCUS ANALYSES
F K א CHAPTER # 9 ROOT LOCUS ANALYSES 1. Introduction The basic characteristic of the transient response of a closed-loop system is closely related to the location of the closed-loop poles. If the system
More informationControl Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:
Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the
More informationLinear System Fundamentals
Linear Sytem Fundamental MEM 355 Performance Enhancement of Dynamical Sytem Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Content Sytem Repreentation Stability Concept
More informationG(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec.
6003 where A = jg(j!)j ; = tan Im [G(j!)] Re [G(j!)] = \G(j!) 2. (a) Calculate the magnitude and phae of G() = + 0 by hand for! =, 2, 5, 0, 20, 50, and 00 rad/ec. (b) ketch the aymptote for G() according
More informationIn the Name of God. Welcome to Chem. 100 General Chemistry I
In the Name of God Welcome to Chem. 100 General Chemistry I General Chemistry I Autumn Semester 96-97 Ahmad Amiri Assistant Professor of Inorganic Chemistry Chemistry Department University of Tehran ahmadamiri@ut.ac.ir
More informationFigure 1 Siemens PSSE Web Site
Stability Analyi of Dynamic Sytem. In the lat few lecture we have een how mall ignal Lalace domain model may be contructed of the dynamic erformance of ower ytem. The tability of uch ytem i a matter of
More information6.302 Feedback Systems Recitation 6: Steady-State Errors Prof. Joel L. Dawson S -
6302 Feedback ytem Recitation 6: teadytate Error Prof Joel L Dawon A valid performance metric for any control ytem center around the final error when the ytem reache teadytate That i, after all initial
More informationCALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems
Control and Dynamical Sytem CDS 0 Problem Set #5 Iued: 3 Nov 08 Due: 0 Nov 08 Note: In the upper left hand corner of the econd page of your homework et, pleae put the number of hour that you pent on thi
More informationRoot locus Analysis. P.S. Gandhi Mechanical Engineering IIT Bombay. Acknowledgements: Mr Chaitanya, SYSCON 07
Root locus Analysis P.S. Gandhi Mechanical Engineering IIT Bombay Acknowledgements: Mr Chaitanya, SYSCON 07 Recap R(t) + _ k p + k s d 1 s( s+ a) C(t) For the above system the closed loop transfer function
More informationFunction and Impulse Response
Tranfer Function and Impule Repone Solution of Selected Unolved Example. Tranfer Function Q.8 Solution : The -domain network i hown in the Fig... Applying VL to the two loop, R R R I () I () L I () L V()
More informationNonlinear Equations in One Variable
Chapter 3 Nonlinear Equations in One Variable فهرست مطالب این جلسه حل معادله تک متغیره غیر خطی بروشهای نصف کردن نقطه ثابت نیوتن و سکانت آشنایی مقدماتی با مینیمم سازی تک متغیره فرض می شود تابع مورد نظر
More informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationECE-202 FINAL December 13, 2016 CIRCLE YOUR DIVISION
ECE-202 Final, Fall 16 1 ECE-202 FINAL December 13, 2016 Name: (Pleae print clearly.) Student Email: CIRCLE YOUR DIVISION DeCarlo- 8:30-9:30 Talavage-9:30-10:30 2021 2022 INSTRUCTIONS There are 35 multiple
More informationآنالیز واریانس : ANOVA )ANALYSIS OF VARIANCE(
آنالیز واریانس : ANOVA )ANALYSIS OF VARIANCE( این روش آماری در کجا کاربرد دارد تاکنون استنباط آماری برای پارامتر های یک جامعه آماری و نهایتا برای پارامترهای دو جامعه آماری مطالبی برای شما گفته شده اما
More informationModule 4: Time Response of discrete time systems Lecture Note 1
Digital Control Module 4 Lecture Module 4: ime Repone of dicrete time ytem Lecture Note ime Repone of dicrete time ytem Abolute tability i a baic requirement of all control ytem. Apart from that, good
More informationCHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL
98 CHAPTER DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL INTRODUCTION The deign of ytem uing tate pace model for the deign i called a modern control deign and it i
More informationتحلیل و طراحی سیستم های کنترل چندمتغیره علی خاکی صدیق گروه کنترل- شهریور
بسم الل ه الر حمن الر حیم تحلیل و طراحی سیستم های کنترل چندمتغیره 1393 علی خاکی صدیق گروه کنترل- شهریور 1 سیستم های کنترل چندمتغیره: طرح مساله سیستم های چند ورودی-چند خروجی: سیستم های کنترل چندمتغیره دیدگاه
More informationمعادلات دیفرانسیل معمولی و جزي ی دسته بندي معادلات دیفرانسیل خاص معادله 0 معادلات دیفرانسیل اغلب از مدل کردن پدیده های فیزیکی حاصل می شوند.
یادآری مجمل از معادلات دیفرانسیل دسته بندی معادلات معادلات دیفرانسیل معملی دیفرانسیل...١ جزي ی...١ معادلات دیفرانسیل مرتبه یک مرتبه د مراتب بالاتر...٢ معادلات دیفرانسیل خطی غیرخطی... ٢ حل معادلات دیفرانسیل...
More informationAdvanced D-Partitioning Analysis and its Comparison with the Kharitonov s Theorem Assessment
Journal of Multidiciplinary Engineering Science and Technology (JMEST) ISSN: 59- Vol. Iue, January - 5 Advanced D-Partitioning Analyi and it Comparion with the haritonov Theorem Aement amen M. Yanev Profeor,
More informationTest 2 SOLUTIONS. ENGI 5821: Control Systems I. March 15, 2010
Test 2 SOLUTIONS ENGI 5821: Control Systems I March 15, 2010 Total marks: 20 Name: Student #: Answer each question in the space provided or on the back of a page with an indication of where to find the
More informationGain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays
Gain and Phae Margin Baed Delay Dependent Stability Analyi of Two- Area LFC Sytem with Communication Delay Şahin Sönmez and Saffet Ayaun Department of Electrical Engineering, Niğde Ömer Halidemir Univerity,
More information1 Routh Array: 15 points
EE C28 / ME34 Problem Set 3 Solution Fall 2 Routh Array: 5 point Conider the ytem below, with D() k(+), w(t), G() +2, and H y() 2 ++2 2(+). Find the cloed loop tranfer function Y () R(), and range of k
More informationECE-202 Exam 1 January 31, Name: (Please print clearly.) CIRCLE YOUR DIVISION DeCarlo DeCarlo 7:30 MWF 1:30 TTH
ECE-0 Exam January 3, 08 Name: (Pleae print clearly.) CIRCLE YOUR DIVISION 0 0 DeCarlo DeCarlo 7:30 MWF :30 TTH INSTRUCTIONS There are multiple choice worth 5 point each and workout problem worth 40 point.
More informationSchool of Mechanical Engineering Purdue University. DC Motor Position Control The block diagram for position control of the servo table is given by:
Root Locus Motivation Sketching Root Locus Examples ME375 Root Locus - 1 Servo Table Example DC Motor Position Control The block diagram for position control of the servo table is given by: θ D 0.09 See
More informationAutomatic Control Systems
Automatic Control Sytem Lecture- Block Diagram Reduction Emam Fathy Department of Electrical and Control Engineering email: emfmz@yahoo.com Introduction A Block Diagram i a horthand pictorial repreentation
More informationDYNAMIC REDESIGN OF A FLOW CONTROL SERVO-VALVE USING A PRESSURE CONTROL PILOT
Proceeding of IMECE ASME International Mechanical Engineering Congre & Exhibition November -6,, New York, New York, USA IMECE/DSC-B- DYNAMIC REDESIGN OF A FLOW CONTROL SERVO-VALVE USING A PRESSURE CONTROL
More informationMechanics. Free rotational oscillations. LD Physics Leaflets P Measuring with a hand-held stop-clock. Oscillations Torsion pendulum
Mechanic Ocillation Torion pendulum LD Phyic Leaflet P.5.. Free rotational ocillation Meauring with a hand-held top-clock Object of the experiment g Meauring the amplitude of rotational ocillation a function
More informationتنش محوری فصل هفتم بخش دوم - مقاومت مصالح PROBLEMS. 6.1 through 6.18 Using. Fig. Fig. P6.4. Fig. P ft 8 ft. 2.4 m 2.4 m lb. 48 kn.
و نیرو فصل هفتم تنش محوری بخش دوم - مقاومت مصالح 4 4 F 64 F 6 7 48 4 6 F 6 8 F 6 F 4 8 4 84 6 68 U OEMS 86_6_6-7 8 /6/9 ::46 M -7 F 64 F 6 8 4 8 4 4 48 7 F 6 4 F 6 4 84 6 68 U OEMS 86_6_6-7 8 /6/9 ::46
More informationStability Analysis Techniques
Stability Analysis Techniques In this section the stability analysis techniques for the Linear Time-Invarient (LTI) discrete system are emphasized. In general the stability techniques applicable to LTI
More informationAnalysis and Design of a Third Order Phase-Lock Loop
Analyi Deign of a Third Order Phae-Lock Loop DANIEL Y. ABRAMOVITCH Ford Aeropace Corporation 3939 Fabian Way, MS: X- Palo Alto, CA 94303 Abtract Typical implementation of a phae-lock loop (PLL) are econd
More informationECE 345 / ME 380 Introduction to Control Systems Lecture Notes 8
Learning Objectives ECE 345 / ME 380 Introduction to Control Systems Lecture Notes 8 Dr. Oishi oishi@unm.edu November 2, 203 State the phase and gain properties of a root locus Sketch a root locus, by
More informationCHAPTER 1 Basic Concepts of Control System. CHAPTER 6 Hydraulic Control System
CHAPTER 1 Basic Concepts of Control System 1. What is open loop control systems and closed loop control systems? Compare open loop control system with closed loop control system. Write down major advantages
More informationAlkenes: Structure and Reactivity
6 Alkenes: Structure and Reactivity آلکن ها: ساختار و واکنش پذیری Dr Morteza Mehrdad University of Guilan, Department of Chemistry, Rasht, Iran m-mehrdad@guilan.ac.ir Based on McMurry s Organic Chemistry,
More informationLecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions
Lecture 8. PID control. The role of P, I, and D action 2. PID tuning Indutrial proce control (92... today) Feedback control i ued to improve the proce performance: tatic performance: for contant reference,
More informationNODIA AND COMPANY. GATE SOLVED PAPER Chemical Engineering Instrumentation and Process Control. Copyright By NODIA & COMPANY
No part of thi publication may be reproduced or ditributed in any form or any mean, electronic, mechanical, photocopying, or otherwie without the prior permiion of the author. GATE SOLVED PAPER Chemical
More informationDigital Control System
Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital
More informationModule 07 Control Systems Design & Analysis via Root-Locus Method
Module 07 Control Systems Design & Analysis via Root-Locus Method Ahmad F. Taha EE 3413: Analysis and Desgin of Control Systems Email: ahmad.taha@utsa.edu Webpage: http://engineering.utsa.edu/ taha March
More informationآخرین نسخه نرم افزارهای نرم افزارهای
فروش ویژه آخرین نسخه نرم افزارهای نرم افزارهای BIOVIA Discovery Studio 4.5 (2016) Molecular Operating Environment (MOE) 2015.10 شرکت زیست آروین تنها شرکت فعال در زمینه تهیه و توزیع نرم افزارهای بیوانفورماتیک
More informationAnalysing panel flutter in supersonic flow by Hopf bifurcation
Iranian Journal of Numerical Analysis and Optimization Vol 4, No. 2, (2014), pp 1-14 Analysing panel flutter in supersonic flow by Hopf bifurcation Z. Monfared and Z. Dadi Abstract This paper is devoted
More informationCHEAP CONTROL PERFORMANCE LIMITATIONS OF INPUT CONSTRAINED LINEAR SYSTEMS
Copyright 22 IFAC 5th Triennial World Congre, Barcelona, Spain CHEAP CONTROL PERFORMANCE LIMITATIONS OF INPUT CONSTRAINED LINEAR SYSTEMS Tritan Pérez Graham C. Goodwin Maria M. Serón Department of Electrical
More informationRoot Locus Techniques
Root Locu Technque ELEC 32 Cloed-Loop Control The control nput u t ynthezed baed on the a pror knowledge of the ytem plant, the reference nput r t, and the error gnal, e t The control ytem meaure the output,
More informationDynamical Meteorology 1
Dynamical Meteorology 1 Lecture 5 Sahraei Physics Department, Razi University http://www.razi.ac.ir/sahraei Structure of the Static Atmosphere جو ایستا: در صورتی که در جو هیچگونه ناپایداری وجود نداشته
More informationSKEE 3143 CONTROL SYSTEM DESIGN. CHAPTER 3 Compensator Design Using the Bode Plot
SKEE 3143 CONTROL SYSTEM DESIGN CHAPTER 3 Compenator Deign Uing the Bode Plot 1 Chapter Outline 3.1 Introduc4on Re- viit to Frequency Repone, ploang frequency repone, bode plot tability analyi. 3.2 Gain
More informationGiven the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is
EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -
More informationThese are practice problems for the final exam. You should attempt all of them, but turn in only the even-numbered problems!
Math 33 - ODE Due: 7 December 208 Written Problem Set # 4 Thee are practice problem for the final exam. You hould attempt all of them, but turn in only the even-numbered problem! Exercie Solve the initial
More informationAli Karimpour Associate Professor Ferdowsi University of Mashhad
LINEAR CONTROL SYSTEMS Ali Karimour Aoiate Profeor Ferdowi Univerity of Mahhad Leture 0 Leture 0 Frequeny domain hart Toi to be overed inlude: Relative tability meaure for minimum hae ytem. ain margin.
More informationسنگ بنای جهان چیست سعید پاک طینت مهدی آبادی پژوهشگاه دانش های بنیادی 8 اردیبهشت 1395
سنگ بنای جهان چیست سعید پاک طینت مهدی آبادی پژوهشگاه دانش های بنیادی 8 اردیبهشت 1395 جهان وما از چه ساخته شده ایم آب )اکسیدها ) ماده جهان ناشناخته است! مقدار زیادی اکسیژن %96 C H O unknown slide 2 1. Are
More informationLecture 3: The Root Locus Method
Lecture 3: The Root Locus Method Venkata Sonti Department of Mechanical Engineering Indian Institute of Science Bangalore, India, 56001 This draft: March 1, 008 1 The Root Locus method The Root Locus method,
More informationLecture 5 Introduction to control
Lecture 5 Introduction to control Tranfer function reviited (Laplace tranform notation: ~jω) () i the Laplace tranform of v(t). Some rule: ) Proportionality: ()/ in () 0log log() v (t) *v in (t) () * in
More informationMA 266 FINAL EXAM INSTRUCTIONS May 2, 2005
MA 66 FINAL EXAM INSTRUCTIONS May, 5 NAME INSTRUCTOR. You mut ue a # pencil on the mark ene heet anwer heet.. If the cover of your quetion booklet i GREEN, write in the TEST/QUIZ NUMBER boxe and blacken
More informationMM1: Basic Concept (I): System and its Variables
MM1: Baic Concept (I): Sytem and it Variable A ytem i a collection of component which are coordinated together to perform a function Sytem interact with their environment. The interaction i defined in
More informationROUTH HURWITZ ANALYSIS
ROUTH HURWITZ ANALYSIS The Routh Hurwitz analyi tell you how many root are located in the a) let-hand plane, ) right-hand plane, and c) on the jω-axi. The technique i illutrated here with an example. The
More informationRESULTS ON ALMOST COHEN-MACAULAY MODULES
Journal of Algebraic Systems Vol. 3, No. 2, (2016), pp 147-150 RESULTS ON ALMOST COHEN-MACAULAY MODULES A. MAFI AND S. TABEJAMAAT Abstract. Let (R, m) be a commutative Noetherian local ring, and M be a
More informationEE Control Systems LECTURE 6
Copyright FL Lewi 999 All right reerved EE - Control Sytem LECTURE 6 Updated: Sunday, February, 999 BLOCK DIAGRAM AND MASON'S FORMULA A linear time-invariant (LTI) ytem can be repreented in many way, including:
More information