Controller Design Based on Transient Response Criteria. Chapter 12 1
|
|
- Cordelia Horton
- 6 years ago
- Views:
Transcription
1 Controller Design Based on Transient Response Criteria Chapter 12 1
2 Desirable Controller Features 0. Stable 1. Quik responding 2. Adequate disturbane rejetion 3. Insensitive to model, measurement errors 4. Avoids exessive ontroller ation 5. Suitable over a wide range of operating onditions Impossible to satisfy all 5 unless self-tuning. Use optimum sloppiness" Chapter 12 2
3 Chapter 12 3
4 Alternatives for Controller Design 1.Tuning orrelations most limited to 1st order plus dead time 2.Closed-loop transfer funtion - analysis of stability or response harateristis. 3.Repetitive simulation (requires omputer software like MATLAB) 4.Frequeny response - stability and performane (requires omputer simulation and graphis) 5.On-line ontroller yling (field tuning) Chapter 12 4
5 Controller Synthesis - Time Domain Time-domain tehniques an be lassified into two groups: (a) Criteria based on a few points in the response (b) Criteria based on the entire response, or integral riteria Approah (a): settling time, % overshoot, rise time, deay ratio (Fig an be viewed as losed-loop response) θ s Ke Proess model Gs ( ) = (1st order) τ s + 1 Several methods based on 1/4 deay ratio have been proposed: Cohen-Coon, Ziegler-Nihols Chapter 12 5
6 Chapter 12 6
7 Comparison of Ziegler-Nihols and Cohen-Coon Equations for Controller Tuning (1940 s, 50 s) Controller Ziegler-Nihols Cohen-Coon Proportional KK = ( τ ) C KK = ( τ ) + 1 θ C θ 3 Proportional ( ) + KK = 0.9 τ KK ( τ C θ C = 0.9 ) θ Integral τ [ ( )] ( θ ) θ I τ θ I = 3.33 = τ τ ( θ ) τ τ τ Proportional ( ) + KK = 1.2 τ KK ( τ C θ C = 1.35 ) θ Integral ( ) + τ I = 2.0 θ [ ( θ τ θ )] I Derivative τ τ = ( ) τ τ θ τ τ ( θ ) D = 0.5 τ τ ( θ τ 0.37 ) D = τ τ ( θ ) τ Chapter 12 7
8 Approah (b) 1. Integral of square error (ISE) ISE = [ e(t) ] 2. Integral of absolute value of error (IAE) IAE = 3. Time-weighted IAE 0 0 ITAE = 0 e(t) dt 2 dt t e(t) dt Pik ontroller parameters to minimize integral. IAE allows larger deviation than ISE (smaller overshoots) ISE longer settling time ITAE weights errors ourring later more heavily Approximate optimum tuning parameters are orrelated with K, θ, τ (Table 12.3). Chapter 12 8
9 Chapter 12 9
10 Chapter 12 10
11 Chapter 12 11
12 Summary of Tuning Relationships 1. K C is inversely proportional to K P K V K M. 2. K C dereases as θ/τ inreases. 3. τ I and τ D inrease as θ/τ inreases (typially τ D = 0.25 τ I ). 4. Redue K, when adding more integral ation; inrease K, when adding derivative ation 5. To redue osillation, derease K C and inrease τ I. Chapter 12 12
13 Disadvantages of Tuning Correlations 1. Stability margin is not quantified. 2. Control laws an be vendor - speifi. 3. First order + time delay model an be inaurate. 4. K p, τ, and θ an vary. 5. Resolution, measurement errors derease stability margins. 6. ¼ deay ratio not onservative standard (too osillatory). Chapter 12 13
14 Diret Synthesis Y Y GCG = 1 G G sp + C ( G inludes G m, G v ) 1. Speify losed-loop response (transfer funtion) Y Y sp 2. Need proess model, G (= G P G M G V ) d 3. Solve for G, G C Y 1 Y sp d = G Y 1 Y sp d (12-3b) 14
15 Speify Closed Loop Transfer Funtion s Y θ e = (12 6) Y sp τ s+ 1 d (first order response, no offset) ( τ = speed of response, θ = proess time delay in G) But other variations of (12-6) an be used (e.g., replae time delay with polynomial approximation) 1 1 If θ = 0, then (12-3b) yields G = ) (12-5) G τ s K τs+1 τ 1 For G =, G = = + (PI) τs+1 Kτ s Kτ Kτ s 15
16 Derivation of PI Controller for FOPTD Proess Consider the standard first-order-plus-time-delay model, ( ) G s = θs Ke τs + 1 (12-10) Speify losed-loop response as FOPTD (12-6), but approximate - θ e s - 1-θs. Substituting and rearranging gives a PI ontroller, ( ) G = K 1+ 1/τ s, K I 1 τ =, τi = τ (12-11) K θ+ τ with the following ontroller settings: Chapter 12 16
17 Derivation of PID Controller for FOPTD Proess: let Y 1 θ s = 2 Y sp τ s+ 1 d θ s Ke K(1 θ s) Gs () = 2 τ s + 1 ( τ s + 1)(1 + θ s) 2 Y 1 Y sp d G = G Y 1- Y sp d 1-θ s ( )( ) 2 τs θ s 1 τs s 2 τs+ G 2 = = K( 1-θ s) 1-θ s K +τ s - 2 τ s+ 1 K τ θ θ τ = τ = + τ τ = K τ ( τ ) + 1 θ θ + I D ( )( θ ) ( θ ) (12-3b) (12-2a) (12-30) 17
18 Seond-Order-plus-Time-Delay (SOPTD) Model Consider a seond-order-plus-time-delay model, Use of FOPTD losed-loop response (12-6) and time delay approximation gives a PID ontroller in parallel form, where K 1 ( ) G s = Ke θs ( τ s+ 1)( τ s+ 1) G = K 1+ + τ Ds (12-13) τi s τ + τ τ τ, τ τ τ, τ (12-14) = I = 1+ 2 D = K τ + θ τ1+ τ2 (12-12) Chapter 12 18
19 Example 12.1 Use the DS design method to alulate PID ontroller settings for the proess: s 2e G = 10s+ 1 5s+ 1 ( )( ) Consider three values of the desired losed-loop time onstant: τ = 1, 3, and 10. Evaluate the ontrollers for unit step hanges in both the set point and the disturbane, assuming that G d = G. Perform the evaluation for two ases: a. The proess model is perfet ( G = G). b. The model gain is K = 0.9, instead of the atual value, K = 2. This model error ould ause a robustness problem in the ontroller for K = 2. s 0.9e G = 19 10s+ 1 5s+ 1 ( )( )
20 The ontroller settings for this example are: K K = ( 2) ( 0.9) K K = τ I τ D τ = 1 τ = 3 τ = Note only K is affeted by the hange in proess gain. Chapter 12 20
21 The values of K derease as τ inreases, but the values of and do not hange, as indiated by Eq τ D τ I Figure 12.3 Simulation results for Example 12.1 (a): orret model gain. 21
22 Figure 12.4 Simulation results for Example 12.1 (b): inorret model gain. 22
23 Chapter 12 23
24 Internal Model Control (IMC) It an be shown that G * * G = 1 GG GG GG Y = Y + D 1 G ( G G) 1 G ( G G ) * * 1 * sp * G = G Y = G GY + (1 G G ) D * * sp Chapter 12 24
25 IMC Design 1) G = G G + 2) * 1 1 G = f f G = ( τ s + 1) r Y = G fy + (1 fg ) D + sp + Chapter 12 25
26 Chapter 12 26
27 Controller Tuning Relations Model-based design methods suh as DS and IMC produe PI or PID ontrollers for ertain lasses of proess models, with one tuning parameter τ (see Table 12.1) How to Selet τ? Several IMC guidelines for τ have been published for the model in Eq : 1. τ / θ > 0.8 and τ > 0.1τ (Rivera et al., 1986) 2. τ> τ > θ (Chien and Fruehauf, 1990) 3. τ θ (Skogestad, 2003) = Chapter 12 27
28 Tuning for Lag-Dominant Models First- or seond-order models with relatively small time delays θ / τ<<1 are referred to as lag-dominant models. ( ) The IMC and DS methods provide satisfatory set-point responses, but very slow disturbane responses, beause the value of is very large. ( τ = τ ) τ I Fortunately, this problem an be solved in three different ways. Method 1: Integrator Approximation θs Ke K * e Approximate Gs ( ) = by Gs ( ) = τ s+ 1 s where K* = K/ τ. I θs Then an use the IMC tuning rules (Rule M or N) to speify the ontroller settings. 28
29 Method 2. Limit the Value of τ I Skogestad (2003) has proposed limiting the value of : ( ) { } τ = min τ,4 τ + θ (12-34) I 1 where τ 1 is the largest time onstant (if there are two). τ I Method 3. Design the Controller for Disturbanes, Rather Set-point Changes The desired CLTF is expressed in terms of (Y/D) d, rather than (Y/Y sp ) d Referene: Chen & Seborg (2002) Chapter 12 29
30 Example 12.4 Consider a lag-dominant model with θ / τ = 0.01: 100 G ( s) = e 100s + 1 Design three PI ontrollers: a) IMC ( τ = 1) ( ) b) IMC τ 2 based on the integrator approximation = ) IMC with Skogestad s modifiation (Eq ) τ 1 ( ) = s Chapter 12 30
31 Evaluate the three ontrollers by omparing their performane for unit step hanges in both set point and disturbane. Assume that the model is perfet and that G d (s) = G(s). Solution The PI ontroller settings are: Controller K τ I (a) IMC (b) Integrator approximation () Skogestad Chapter 12 31
32 Figure Comparison of set-point responses (top) and disturbane responses (bottom) for Example The responses for the integrator approximation and Chen and Seborg (disussed in textbook) methods are essentially idential. Chapter 12 32
33 On-Line Controller Tuning 1. Controller tuning inevitably involves a tradeoff between performane and robustness. 2. Controller settings do not have to be preisely determined. In general, a small hange in a ontroller setting from its best value (for example, ±10%) has little effet on losed-loop responses. 3. For most plants, it is not feasible to manually tune eah ontroller. Tuning is usually done by a ontrol speialist (engineer or tehniian) or by a plant operator. Beause eah person is typially responsible for 300 to 1000 ontrol loops, it is not feasible to tune every ontroller. 4. Diagnosti tehniques for monitoring ontrol system performane are available. Chapter 12 33
34 Controller Tuning and Troubleshooting Control Loops Chapter 12 34
35 Ziegler-Nihols Rules: These well-known tuning rules were published by Z-N in 1942: ontroller K τ I τ D P PI PID 0.5 K CU 0.45 K CU 0.6 K CU - P U /1.2 P U /2 - - P U /8 Z-N ontroller settings are widely onsidered to be an "industry standard". Z-N settings were developed to provide 1/4 deay ratio -- too osillatory? Chapter 12 35
36 Modified Z-N settings for PID ontrol ontroller K τ I τ D original Some overshoot No overshoot 0.6 K CU 0.33 K CU 0.2 K CU P U /2 P U /2 P U /3 P U /8 P U /3 P U /2 Chapter 12 36
37 Chapter 12 37
38 Chapter 12 38
39 Homework #9 (Due to 08/05/08) Exerises: 12.1, 12.2, 12.3, 12.5, Chapter 12 39
CHBE320 LECTURE X STABILITY OF CLOSED-LOOP CONTOL SYSTEMS. Professor Dae Ryook Yang
CHBE320 LECTURE X STABILITY OF CLOSED-LOOP CONTOL SYSTEMS Professor Dae Ryook Yang Spring 208 Dept. of Chemial and Biologial Engineering 0- Road Map of the Leture X Stability of losed-loop ontrol system
More informationUTC. Engineering 329. Proportional Controller Design. Speed System. John Beverly. Green Team. John Beverly Keith Skiles John Barker.
UTC Engineering 329 Proportional Controller Design for Speed System By John Beverly Green Team John Beverly Keith Skiles John Barker 24 Mar 2006 Introdution This experiment is intended test the variable
More information23.1 Tuning controllers, in the large view Quoting from Section 16.7:
Lesson 23. Tuning a real ontroller - modeling, proess identifiation, fine tuning 23.0 Context We have learned to view proesses as dynami systems, taking are to identify their input, intermediate, and output
More informationECE-320 Linear Control Systems. Winter 2013, Exam 1. No calculators or computers allowed, you may leave your answers as fractions.
ECE-320 Linear Control Systems Winter 2013, Exam 1 No alulators or omputers allowed, you may leave your answers as frations. All problems are worth 3 points unless noted otherwise. Total /100 1 Problems
More informationCHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang
CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 11-1 Road Map of the Lecture XI Controller Design and PID
More informationControl Theory association of mathematics and engineering
Control Theory assoiation of mathematis and engineering Wojieh Mitkowski Krzysztof Oprzedkiewiz Department of Automatis AGH Univ. of Siene & Tehnology, Craow, Poland, Abstrat In this paper a methodology
More informationDynamic Simulation and Composition Control in A 10 L Mixing Tank
roeeding of International Conferene on Chemial and Material Engineering ISBN : 978--97-8-7 SE.4 - Dynami Simulation and Composition Control in A L Mixing Tank Yulius Deddy Hermawan Chemial Engineering
More informationFeedback Control of Linear SISO systems. Process Dynamics and Control
Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals
More informationCHAPTER 3 TUNING METHODS OF CONTROLLER
57 CHAPTER 3 TUNING METHODS OF CONTROLLER 3.1 INTRODUCTION This chapter deals with a simple method of designing PI and PID controllers for first order plus time delay with integrator systems (FOPTDI).
More informationMillennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion
Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six
More informationA unified approach for proportional-integral-derivative controller design for time delay processes
Korean J. Chem. Eng., 32(4), 583-596 (2015) DOI: 10.1007/s11814-014-0237-6 INVITED REVIEW PAPER INVITED REVIEW PAPER pissn: 0256-1115 eissn: 1975-7220 A unified approach for proportional-integral-derivative
More informationAC : A GRAPHICAL USER INTERFACE (GUI) FOR A UNIFIED APPROACH FOR CONTINUOUS-TIME COMPENSATOR DESIGN
AC 28-1986: A GRAPHICAL USER INTERFACE (GUI) FOR A UNIFIED APPROACH FOR CONTINUOUS-TIME COMPENSATOR DESIGN Minh Cao, Wihita State University Minh Cao ompleted his Bahelor s of Siene degree at Wihita State
More informationAcoustic Waves in a Duct
Aousti Waves in a Dut 1 One-Dimensional Waves The one-dimensional wave approximation is valid when the wavelength λ is muh larger than the diameter of the dut D, λ D. The aousti pressure disturbane p is
More informationAn Integrated Architecture of Adaptive Neural Network Control for Dynamic Systems
An Integrated Arhiteture of Adaptive Neural Network Control for Dynami Systems Robert L. Tokar 2 Brian D.MVey2 'Center for Nonlinear Studies, 2Applied Theoretial Physis Division Los Alamos National Laboratory,
More informationA Tuning of the Nonlinear PI Controller and Its Experimental Application
Korean J. Chem. Eng., 18(4), 451-455 (2001) A Tuning of the Nonlinear PI Controller and Its Experimental Application Doe Gyoon Koo*, Jietae Lee*, Dong Kwon Lee**, Chonghun Han**, Lyu Sung Gyu, Jae Hak
More informationChapter 5 The SIMC Method for Smooth PID Controller Tuning
Chapter 5 The SIMC Method for Smooth PID Controller Tuning Sigurd Skogestad and Chriss Grimholt 5.1 Introduction Although the proportional-integral-derivative (PID) controller has only three parameters,
More informationControl Systems. Control Systems Design Lead-Lag Compensator.
Design Lead-Lag Compensator hibum@seoulteh.a.kr Outline Lead ompensator design in frequeny domain Lead ompensator design steps. Example on lead ompensator design. Frequeny Domain Design Frequeny response
More informationProportional-Integral-Derivative PID Controls
Proortional-Integral-Derivative PID Controls Dr M.J. Willis Det. of Chemial and Proess Engineering University of Newastle e-mail: mark.willis@nl.a.uk Written: 7 th November, 998 Udated: 6 th Otober, 999
More informationCombined Electric and Magnetic Dipoles for Mesoband Radiation, Part 2
Sensor and Simulation Notes Note 53 3 May 8 Combined Eletri and Magneti Dipoles for Mesoband Radiation, Part Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque
More informationDIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS
CHAPTER 4 DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS 4.1 INTRODUCTION Around the world, environmental and ost onsiousness are foring utilities to install
More informationAn Adaptive Optimization Approach to Active Cancellation of Repeated Transient Vibration Disturbances
An aptive Optimization Approah to Ative Canellation of Repeated Transient Vibration Disturbanes David L. Bowen RH Lyon Corp / Aenteh, 33 Moulton St., Cambridge, MA 138, U.S.A., owen@lyonorp.om J. Gregory
More informationA Spatiotemporal Approach to Passive Sound Source Localization
A Spatiotemporal Approah Passive Sound Soure Loalization Pasi Pertilä, Mikko Parviainen, Teemu Korhonen and Ari Visa Institute of Signal Proessing Tampere University of Tehnology, P.O.Box 553, FIN-330,
More informationIan G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and Richard D. Braatz*
Ind. Eng. Chem. Res. 996, 35, 3437-344 3437 PROCESS DESIGN AND CONTROL Improved Filter Design in Internal Model Control Ian G. Horn, Jeffery R. Arulandu, Christopher J. Gombas, Jeremy G. VanAntwerp, and
More informationAdditional Closed-Loop Frequency Response Material (Second edition, Chapter 14)
Appendix J Additional Closed-Loop Frequency Response Material (Second edition, Chapter 4) APPENDIX CONTENTS J. Closed-Loop Behavior J.2 Bode Stability Criterion J.3 Nyquist Stability Criterion J.4 Gain
More informationSpeed-feedback Direct-drive Control of a Low-speed Transverse Flux-type Motor with Large Number of Poles for Ship Propulsion
Speed-feedbak Diret-drive Control of a Low-speed Transverse Flux-type Motor with Large Number of Poles for Ship Propulsion Y. Yamamoto, T. Nakamura 2, Y. Takada, T. Koseki, Y. Aoyama 3, and Y. Iwaji 3
More informationRobust Flight Control Design for a Turn Coordination System with Parameter Uncertainties
Amerian Journal of Applied Sienes 4 (7): 496-501, 007 ISSN 1546-939 007 Siene Publiations Robust Flight ontrol Design for a urn oordination System with Parameter Unertainties 1 Ari Legowo and Hiroshi Okubo
More informationIMPEDANCE EFFECTS OF LEFT TURNERS FROM THE MAJOR STREET AT A TWSC INTERSECTION
09-1289 Citation: Brilon, W. (2009): Impedane Effets of Left Turners from the Major Street at A TWSC Intersetion. Transportation Researh Reord Nr. 2130, pp. 2-8 IMPEDANCE EFFECTS OF LEFT TURNERS FROM THE
More informationComplexity of Regularization RBF Networks
Complexity of Regularization RBF Networks Mark A Kon Department of Mathematis and Statistis Boston University Boston, MA 02215 mkon@buedu Leszek Plaskota Institute of Applied Mathematis University of Warsaw
More informationFREQUENCY DOMAIN FEEDFORWARD COMPENSATION. F.J. Pérez Castelo and R. Ferreiro Garcia
FREQUENCY DOMAIN FEEDFORWARD COMPENSATION F.J. Pérez Castelo and R. Ferreiro Garia Dept. Ingeniería Industrial. Universidad de La Coruña javierp@ud.es, Phone: 98 7.Fax: -98-7 ferreiro@ud.es, Phone: 98
More informationMethods of evaluating tests
Methods of evaluating tests Let X,, 1 Xn be i.i.d. Bernoulli( p ). Then 5 j= 1 j ( 5, ) T = X Binomial p. We test 1 H : p vs. 1 1 H : p>. We saw that a LRT is 1 if t k* φ ( x ) =. otherwise (t is the observed
More informationAverage Rate Speed Scaling
Average Rate Speed Saling Nikhil Bansal David P. Bunde Ho-Leung Chan Kirk Pruhs May 2, 2008 Abstrat Speed saling is a power management tehnique that involves dynamially hanging the speed of a proessor.
More informationSupporting Information
Supporting Information Olsman and Goentoro 10.1073/pnas.1601791113 SI Materials Analysis of the Sensitivity and Error Funtions. We now define the sensitivity funtion Sð, «0 Þ, whih summarizes the steepness
More informationSubject: Introduction to Component Matching and Off-Design Operation % % ( (1) R T % (
16.50 Leture 0 Subjet: Introdution to Component Mathing and Off-Design Operation At this point it is well to reflet on whih of the many parameters we have introdued (like M, τ, τ t, ϑ t, f, et.) are free
More informationHeat exchangers: Heat exchanger types:
Heat exhangers: he proess of heat exhange between two fluids that are at different temperatures and separated by a solid wall ours in many engineering appliations. he devie used to implement this exhange
More informationNon-Markovian study of the relativistic magnetic-dipole spontaneous emission process of hydrogen-like atoms
NSTTUTE OF PHYSCS PUBLSHNG JOURNAL OF PHYSCS B: ATOMC, MOLECULAR AND OPTCAL PHYSCS J. Phys. B: At. Mol. Opt. Phys. 39 ) 7 85 doi:.88/953-75/39/8/ Non-Markovian study of the relativisti magneti-dipole spontaneous
More informationEE 321 Project Spring 2018
EE 21 Projet Spring 2018 This ourse projet is intended to be an individual effort projet. The student is required to omplete the work individually, without help from anyone else. (The student may, however,
More informationA model for measurement of the states in a coupled-dot qubit
A model for measurement of the states in a oupled-dot qubit H B Sun and H M Wiseman Centre for Quantum Computer Tehnology Centre for Quantum Dynamis Griffith University Brisbane 4 QLD Australia E-mail:
More informationCalculation of Desorption Parameters for Mg/Si(111) System
e-journal of Surfae Siene and Nanotehnology 29 August 2009 e-j. Surf. Si. Nanoteh. Vol. 7 (2009) 816-820 Conferene - JSSS-8 - Calulation of Desorption Parameters for Mg/Si(111) System S. A. Dotsenko, N.
More informationTaste for variety and optimum product diversity in an open economy
Taste for variety and optimum produt diversity in an open eonomy Javier Coto-Martínez City University Paul Levine University of Surrey Otober 0, 005 María D.C. Garía-Alonso University of Kent Abstrat We
More informationmax min z i i=1 x j k s.t. j=1 x j j:i T j
AM 221: Advaned Optimization Spring 2016 Prof. Yaron Singer Leture 22 April 18th 1 Overview In this leture, we will study the pipage rounding tehnique whih is a deterministi rounding proedure that an be
More informationMath 151 Introduction to Eigenvectors
Math 151 Introdution to Eigenvetors The motivating example we used to desrie matrixes was landsape hange and vegetation suession. We hose the simple example of Bare Soil (B), eing replaed y Grasses (G)
More informationON-LINE ESTIMATION OF THE VENTILATION RATE OF GREENHOUSES
ON-LINE ESTIMATION OF THE VENTILATION RATE OF GREENHOUSES J. Bontsema *, E.J. van Henten *, J.G. Kornet *, J. Budding ** and T. Rieswijk ** * Agrotehnology and Food Innovations B.V., Greenhouse Tehnology
More informationCRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS
Russian Physis Journal, Vol. 48, No. 8, 5 CRITICAL EXPONENTS TAKING INTO ACCOUNT DYNAMIC SCALING FOR ADSORPTION ON SMALL-SIZE ONE-DIMENSIONAL CLUSTERS A. N. Taskin, V. N. Udodov, and A. I. Potekaev UDC
More informationCase I: 2 users In case of 2 users, the probability of error for user 1 was earlier derived to be 2 A1
MUTLIUSER DETECTION (Letures 9 and 0) 6:33:546 Wireless Communiations Tehnologies Instrutor: Dr. Narayan Mandayam Summary By Shweta Shrivastava (shwetash@winlab.rutgers.edu) bstrat This artile ontinues
More informationUPPER-TRUNCATED POWER LAW DISTRIBUTIONS
Fratals, Vol. 9, No. (00) 09 World Sientifi Publishing Company UPPER-TRUNCATED POWER LAW DISTRIBUTIONS STEPHEN M. BURROUGHS and SARAH F. TEBBENS College of Marine Siene, University of South Florida, St.
More informationDesign of an Adaptive Neural Network Controller for Effective Position Control of Linear Pneumatic Actuators
Researh Artile International Journal of Current Engineering and Tehnology E-ISSN 77 406, P-ISSN 347-56 04 INPRESSCO, All Rights Reserved Available at http://inpresso.om/ategory/ijet Design of an Adaptive
More informationEE451/551: Digital Control. Relationship Between s and z Planes. The Relationship Between s and z Planes 11/10/2011
/0/0 EE45/55: Digital Control Chater 6: Digital Control System Design he Relationshi Between s and Planes As noted reviously: s j e e e e r s j where r e and If an analog system has oles at: s n jn a jd
More informationMeasuring & Inducing Neural Activity Using Extracellular Fields I: Inverse systems approach
Measuring & Induing Neural Ativity Using Extraellular Fields I: Inverse systems approah Keith Dillon Department of Eletrial and Computer Engineering University of California San Diego 9500 Gilman Dr. La
More informationCHAPTER 10: STABILITY &TUNING
When I complete this chapter, I want to be able to do the following. Determine the stability of a process without control Determine the stability of a closed-loop feedback control system Use these approaches
More informationEvaluation of effect of blade internal modes on sensitivity of Advanced LIGO
Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple
More informationVerka Prolović Chair of Civil Engineering Geotechnics, Faculty of Civil Engineering and Architecture, Niš, R. Serbia
3 r d International Conferene on New Developments in Soil Mehanis and Geotehnial Engineering, 8-30 June 01, Near East University, Niosia, North Cyprus Values of of partial fators for for EC EC 7 7 slope
More informationThe Complete Energy Translations in the Detailed. Decay Process of Baryonic Sub-Atomic Particles. P.G.Bass.
The Complete Energy Translations in the Detailed Deay Proess of Baryoni Su-Atomi Partiles. [4] P.G.Bass. PGBass P12 Version 1..3 www.relativitydomains.om August 218 Astrat. This is the final paper on the
More informationSingular Event Detection
Singular Event Detetion Rafael S. Garía Eletrial Engineering University of Puerto Rio at Mayagüez Rafael.Garia@ee.uprm.edu Faulty Mentor: S. Shankar Sastry Researh Supervisor: Jonathan Sprinkle Graduate
More informationStabilization of the Precision Positioning Stage Working in the Vacuum Environment by Using the Disturbance Observer
Proeedings of the 4th IIAE International Conferene on Industrial Appliation Engineering 216 Stabilization of the Preision Positioning Stage Working in the Vauum Environment by Using the Disturbane Observer
More informationOptimization of Statistical Decisions for Age Replacement Problems via a New Pivotal Quantity Averaging Approach
Amerian Journal of heoretial and Applied tatistis 6; 5(-): -8 Published online January 7, 6 (http://www.sienepublishinggroup.om/j/ajtas) doi:.648/j.ajtas.s.65.4 IN: 36-8999 (Print); IN: 36-96 (Online)
More informationAn iterative least-square method suitable for solving large sparse matrices
An iteratie least-square method suitable for soling large sparse matries By I. M. Khabaza The purpose of this paper is to report on the results of numerial experiments with an iteratie least-square method
More informationLecture 3 - Lorentz Transformations
Leture - Lorentz Transformations A Puzzle... Example A ruler is positioned perpendiular to a wall. A stik of length L flies by at speed v. It travels in front of the ruler, so that it obsures part of the
More informationA NETWORK SIMPLEX ALGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM
NETWORK SIMPLEX LGORITHM FOR THE MINIMUM COST-BENEFIT NETWORK FLOW PROBLEM Cen Çalışan, Utah Valley University, 800 W. University Parway, Orem, UT 84058, 801-863-6487, en.alisan@uvu.edu BSTRCT The minimum
More informationThe Laws of Acceleration
The Laws of Aeleration The Relationships between Time, Veloity, and Rate of Aeleration Copyright 2001 Joseph A. Rybzyk Abstrat Presented is a theory in fundamental theoretial physis that establishes the
More informationEarlier Lecture. This gas tube is called as Pulse Tube and this phenomenon is called as Pulse Tube action.
31 1 Earlier Leture In te earlier leture, we ave seen a Pulse Tube (PT) ryoooler in wi te meanial displaer is removed and an osillating gas flow in te tin walled tube produes ooling. Tis gas tube is alled
More information3 Tidal systems modelling: ASMITA model
3 Tidal systems modelling: ASMITA model 3.1 Introdution For many pratial appliations, simulation and predition of oastal behaviour (morphologial development of shorefae, beahes and dunes) at a ertain level
More informationSimple Considerations on the Cosmological Redshift
Apeiron, Vol. 5, No. 3, July 8 35 Simple Considerations on the Cosmologial Redshift José Franiso Garía Juliá C/ Dr. Maro Mereniano, 65, 5. 465 Valenia (Spain) E-mail: jose.garia@dival.es Generally, the
More informationTheory. Coupled Rooms
Theory of Coupled Rooms For: nternal only Report No.: R/50/TCR Prepared by:. N. taey B.., MO Otober 00 .00 Objet.. The objet of this doument is present the theory alulations to estimate the reverberant
More informationPhysics of Relaxation. Outline
Physis of Relaxation Weiguo Li Outline Fundamental relaxation Mehanisms Magneti dipole-dipole oupling» Stati oupling» Dynami oupling Frequeny dependene of relaxation Rate Temperature dependene of relaxation
More informationThe Effectiveness of the Linear Hull Effect
The Effetiveness of the Linear Hull Effet S. Murphy Tehnial Report RHUL MA 009 9 6 Otober 009 Department of Mathematis Royal Holloway, University of London Egham, Surrey TW0 0EX, England http://www.rhul.a.uk/mathematis/tehreports
More informationDetermination of the reaction order
5/7/07 A quote of the wee (or amel of the wee): Apply yourself. Get all the eduation you an, but then... do something. Don't just stand there, mae it happen. Lee Iaoa Physial Chemistry GTM/5 reation order
More informationAnswers to Coursebook questions Chapter J2
Answers to Courseook questions Chapter J 1 a Partiles are produed in ollisions one example out of many is: a ollision of an eletron with a positron in a synhrotron. If we produe a pair of a partile and
More informationGeneral Equilibrium. What happens to cause a reaction to come to equilibrium?
General Equilibrium Chemial Equilibrium Most hemial reations that are enountered are reversible. In other words, they go fairly easily in either the forward or reverse diretions. The thing to remember
More informationSlenderness Effects for Concrete Columns in Sway Frame - Moment Magnification Method
Slenderness Effets for Conrete Columns in Sway Frame - Moment Magnifiation Method Slender Conrete Column Design in Sway Frame Buildings Evaluate slenderness effet for olumns in a sway frame multistory
More informationMODELLING THE POSTPEAK STRESS DISPLACEMENT RELATIONSHIP OF CONCRETE IN UNIAXIAL COMPRESSION
VIII International Conferene on Frature Mehanis of Conrete and Conrete Strutures FraMCoS-8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang Eds) MODELLING THE POSTPEAK STRESS DISPLACEMENT RELATIONSHIP
More informationExperiment 03: Work and Energy
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physis Department Physis 8.01 Purpose of the Experiment: Experiment 03: Work and Energy In this experiment you allow a art to roll down an inlined ramp and run into
More informationInter-fibre contacts in random fibrous materials: experimental verification of theoretical dependence on porosity and fibre width
J Mater Si (2006) 41:8377 8381 DOI 10.1007/s10853-006-0889-7 LETTER Inter-fibre ontats in random fibrous materials: experimental verifiation of theoretial dependene on porosity and fibre width W. J. Bathelor
More informationMaximum Entropy and Exponential Families
Maximum Entropy and Exponential Families April 9, 209 Abstrat The goal of this note is to derive the exponential form of probability distribution from more basi onsiderations, in partiular Entropy. It
More informationA Queueing Model for Call Blending in Call Centers
A Queueing Model for Call Blending in Call Centers Sandjai Bhulai and Ger Koole Vrije Universiteit Amsterdam Faulty of Sienes De Boelelaan 1081a 1081 HV Amsterdam The Netherlands E-mail: {sbhulai, koole}@s.vu.nl
More informationDevelopment of Fuzzy Extreme Value Theory. Populations
Applied Mathematial Sienes, Vol. 6, 0, no. 7, 58 5834 Development of Fuzzy Extreme Value Theory Control Charts Using α -uts for Sewed Populations Rungsarit Intaramo Department of Mathematis, Faulty of
More information( ) ( ) Volumetric Properties of Pure Fluids, part 4. The generic cubic equation of state:
CE304, Spring 2004 Leture 6 Volumetri roperties of ure Fluids, part 4 The generi ubi equation of state: There are many possible equations of state (and many have been proposed) that have the same general
More informationWood Design. = theoretical allowed buckling stress
Wood Design Notation: a = name for width dimension A = name for area A req d-adj = area required at allowable stress when shear is adjusted to inlude self weight b = width of a retangle = name for height
More information11.1 Polynomial Least-Squares Curve Fit
11.1 Polynomial Least-Squares Curve Fit A. Purpose This subroutine determines a univariate polynomial that fits a given disrete set of data in the sense of minimizing the weighted sum of squares of residuals.
More informationMean Activity Coefficients of Peroxodisulfates in Saturated Solutions of the Conversion System 2NH 4. H 2 O at 20 C and 30 C
Mean Ativity Coeffiients of Peroxodisulfates in Saturated Solutions of the Conversion System NH 4 Na S O 8 H O at 0 C and 0 C Jan Balej Heřmanova 5, 170 00 Prague 7, Czeh Republi balejan@seznam.z Abstrat:
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 6 (2/24/04) Energy Transfer Kernel F(E E')
22.54 Neutron Interations and Appliations (Spring 2004) Chapter 6 (2/24/04) Energy Transfer Kernel F(E E') Referenes -- J. R. Lamarsh, Introdution to Nulear Reator Theory (Addison-Wesley, Reading, 1966),
More informationNormative and descriptive approaches to multiattribute decision making
De. 009, Volume 8, No. (Serial No.78) China-USA Business Review, ISSN 57-54, USA Normative and desriptive approahes to multiattribute deision making Milan Terek (Department of Statistis, University of
More informationBINARY RANKINE CYCLE OPTIMIZATION Golub, M., Koscak-Kolin, S., Kurevija, T.
BINARY RANKINE CYCLE OPTIMIZATION Golub, M., Kosak-Kolin, S., Kurevija, T. Faulty of Mining, Geology and Petroleum Engineering Department of Petroleum Engineering Pierottijeva 6, Zagreb 0 000, Croatia
More informationName Solutions to Test 1 September 23, 2016
Name Solutions to Test 1 September 3, 016 This test onsists of three parts. Please note that in parts II and III, you an skip one question of those offered. Possibly useful formulas: F qequb x xvt E Evpx
More informationEffects of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interaction Broadband Noise
Effets of Vane Sweep on Fan-Wake/Outlet-Guide-Vane Interation Broadband Noise Hongbin Ju* GE Global Researh Center, One Researh Cirle, Niskayuna, NY. 09 A method is developed for prediting broadband noise
More informationFINITE WORD LENGTH EFFECTS IN DSP
FINITE WORD LENGTH EFFECTS IN DSP PREPARED BY GUIDED BY Snehal Gor Dr. Srianth T. ABSTRACT We now that omputers store numbers not with infinite preision but rather in some approximation that an be paed
More informationComparison of PD and LQR Methods for Spacecraft Attitude Control Using Star Trackers
Comparison of PD and LQ Methods for Spaeraft Attitude Control Using Star raers Sott Beatt, Universit of New Meio, United States, sott.beatt@pangeateh.om ABSAC he wor ontained herein is a omparison of spaeraft
More information9 Geophysics and Radio-Astronomy: VLBI VeryLongBaseInterferometry
9 Geophysis and Radio-Astronomy: VLBI VeryLongBaseInterferometry VLBI is an interferometry tehnique used in radio astronomy, in whih two or more signals, oming from the same astronomial objet, are reeived
More informationAdaptive neuro-fuzzy inference system-based controllers for smart material actuator modelling
Adaptive neuro-fuzzy inferene system-based ontrollers for smart material atuator modelling T L Grigorie and R M Botez Éole de Tehnologie Supérieure, Montréal, Quebe, Canada The manusript was reeived on
More informationPhysical Laws, Absolutes, Relative Absolutes and Relativistic Time Phenomena
Page 1 of 10 Physial Laws, Absolutes, Relative Absolutes and Relativisti Time Phenomena Antonio Ruggeri modexp@iafria.om Sine in the field of knowledge we deal with absolutes, there are absolute laws that
More informationFORCE DISTRIBUTION OF REINFORCED CONCRETE COUPLING BEAMS WITH DIAGONAL REINFORCEMENT
FORCE DISTRIBUTION OF REINFORCED CONCRETE COULING BEAMS WITH DIAGONAL REINFORCEMENT Yenny Nurhasanah Jurusan Teknik Sipil, Fakultas Teknik, Universitas Muhammadiyah Surakarta Jl. A. Yani Tromol os 1 abelan
More informationDetermination of the Aerodynamic Characteristics of Flying Vehicles Using Method Large Eddy Simulation with Software ANSYS
Automation, Control and Intelligent Systems 15; 3(6): 118-13 Published online Deember, 15 (http://www.sienepublishinggroup.om//ais) doi: 1.11648/.ais.1536.14 ISSN: 38-5583 (Print); ISSN: 38-5591 (Online)
More informationGeneral Closed-form Analytical Expressions of Air-gap Inductances for Surfacemounted Permanent Magnet and Induction Machines
General Closed-form Analytial Expressions of Air-gap Indutanes for Surfaemounted Permanent Magnet and Indution Mahines Ronghai Qu, Member, IEEE Eletroni & Photoni Systems Tehnologies General Eletri Company
More informationSupplementary information for: All-optical signal processing using dynamic Brillouin gratings
Supplementary information for: All-optial signal proessing using dynami Brillouin gratings Maro Santagiustina, Sanghoon Chin 2, Niolay Primerov 2, Leonora Ursini, Lu Thévena 2 Department of Information
More informationWavetech, LLC. Ultrafast Pulses and GVD. John O Hara Created: Dec. 6, 2013
Ultrafast Pulses and GVD John O Hara Created: De. 6, 3 Introdution This doument overs the basi onepts of group veloity dispersion (GVD) and ultrafast pulse propagation in an optial fiber. Neessarily, it
More informationCHAPTER 26 The Special Theory of Relativity
CHAPTER 6 The Speial Theory of Relativity Units Galilean-Newtonian Relativity Postulates of the Speial Theory of Relativity Simultaneity Time Dilation and the Twin Paradox Length Contration Four-Dimensional
More informationImproved cascade control structure for enhanced performance
Improved cascade control structure for enhanced performance Article (Unspecified) Kaya, İbrahim, Tan, Nusret and Atherton, Derek P. (7) Improved cascade control structure for enhanced performance. Journal
More informationDirectional Coupler. 4-port Network
Diretional Coupler 4-port Network 3 4 A diretional oupler is a 4-port network exhibiting: All ports mathed on the referene load (i.e. S =S =S 33 =S 44 =0) Two pair of ports unoupled (i.e. the orresponding
More information10.5 Unsupervised Bayesian Learning
The Bayes Classifier Maximum-likelihood methods: Li Yu Hongda Mao Joan Wang parameter vetor is a fixed but unknown value Bayes methods: parameter vetor is a random variable with known prior distribution
More informationINFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION
Proeedings of ICFDP 8: 8 th International Congress of Fluid Dynamis & Propulsion Deember 14-17, 006, Sharm El-Shiekh, Sinai, Egypt ICFDP8-EG-154 INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE
More informationThe Lorenz Transform
The Lorenz Transform Flameno Chuk Keyser Part I The Einstein/Bergmann deriation of the Lorentz Transform I follow the deriation of the Lorentz Transform, following Peter S Bergmann in Introdution to the
More information