CONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. VIII Decoupling Control - M. Fikar

Size: px
Start display at page:

Download "CONTROL SYSTEMS, ROBOTICS AND AUTOMATION Vol. VIII Decoupling Control - M. Fikar"

Transcription

1 DECOUPLING CONTROL M. Fikar Department of Proce Control, Faculty of Chemical and Food Technology, Slovak Univerity of Technology in Bratilava, Radlinkého 9, SK Bratilava, Slovakia Keyword: Decoupling: dynamic, tatic, diagonal, block diagonal, triangular, in proce control; multivariable ytem Content 1. Introduction 1.1. Preliminarie Multivariable Sytem Decription Control Structure Ued for Decoupling Square and Non-quare Sytem Problem Formulation 2. Control of a Heat Exchanger 2.1. Model 2.2. Static Decoupling 2.3. Dynamic Decoupling 2.4. Proce Control Decoupling 2.5. Concluding Remark for the Heat Exchanger 3. Dynamic Decoupling 3.1. Linear State Feedback with Input Dynamic 3.2. Linear State Feedback 3.3. Square Sytem 3.4. Output Feedback Decoupling 3.5. Block Decoupling 3.6. Triangular Decoupling 3.7. Cot of Decoupling 4. Static decoupling 5. Proce Control Decoupling Deign 5.1. Ideal Decoupling 5.2. Simplified Decoupling 5.3. Inverted Decoupling 6. Other Topic Gloary Bibliography Biographical Sketch Summary Thi article tudie the problem of decoupling. Thi general term can be divided into two main ub-categorie: dynamic and tatic decoupling. Dynamic decoupling i more general and guarantee that under any operating condition, the manipulated variable influence independently the repective output. Static decoupling on the other hand i concerned only with the problem of teady-tate, hence decoupling i guaranteed only

2 for a pecial choice of input - tep change and in general operating regime interaction between output occur. The term decoupling generally mean diagonal decoupling, i.e. each input/output i independent. When certain input/output are grouped together, variou decoupling regime can be obtained: block decoupling when ome ubytem are independent, or triangular decoupling where ome output influence the other output but not vice vera. The lat part of the article i devoted to the decoupling iue in proce control deign where everal implification lead to pecialized control trategie. The quetion that will be anwered when invetigating decoupling control deign are: I it poible to decouple the given ytem? What kind of decoupling can be realized? What kind of controller i required? What are conequence and undeired effect of decoupling? 1. Introduction Multi-input multi-output control ytem occur very frequently in practice and contitute difficult control problem for the operating peronnel. Conider for example a ditillation column where control over concentration of multiple product i deired and the operator can change variou flow within the column. However, change of any manipulated variable influence all concentration and it i difficult to manipulate all flow imultaneouly to obtain the deired effect. Other common example may include control of flying object (aircraft, helicopter, landing module), electrical device (turbine), and many more, where in many ituation it i required to change everal variable imultaneouly to produce deired value of controlled variable. A uitable operating practice i to find pair of the input-output variable where the correponding manipulated variable ha the maximum effect on the output variable and to deign imple controller for each pair. In thi phae of control deign, technique of loop election are ued. If the choice of input-output pair i difficult to perform, it i poible to inert a precompenator that make the ytem diagonally dominant. Puruing thi idea further, a ome way of compenation can be ought that make the compenated cloed-loop ytem totally diagonal. Thi i called decoupling. In thi cae each output variable i influenced only by one manipulated variable and the problem of multivariable control i then reduced to a erie of inglevariable control problem that are more eaily olved. Thi article tudie variou categorie and pecial cae of decoupling. In the firt part multivariable ytem decription and ome elected compenation trategie are introduced that will be ued throughout the article. Next, motivation for decoupling control i hown on control of a heat exchanger. Next ection erve a theoretical foundation of the reult preented for the heat exchanger. Thee include dynamic, tatic decoupling and proce control decoupling trategie: The firt of them deal with

3 dynamic decoupling. It begin with the condition that are to be atified in order to achieve decoupled cloed-loop ytem. Selected choice of dynamic compenation are then dicued tarting from the mot veratile dynamic feedback with input dynamic and then howing which are condition that enable to ue le general compenation trategie a linear tate feedback and linear output feedback. The firt ubection treat diagonal decoupling, afterward alo block-diagonal and triangular decoupling trategie are propoed. Next ection deal with tatic decoupling and how again condition that aure it. Finally, the lat ection give an overview of proce control decoupling trategie Preliminarie See alo Chapter Control of Linear Multivariable Sytem for the definition of further ymbol and notation Multivariable Sytem Decription A linear time invariant determinitic continuou-time multivariable ytem with p output y, m input u, and n tate x can be decribed a (ee Decription and Claification.) State-pace ytem [ ABCD,,, ] (ee Canonical State Space Repreentation and Feedback.) x = Ax + Bu y = Cx + Du ABCDare matrice of dimenion A[ nn, ], B[ nm,, ] Cpn, [, ] and Dpm. [, ] where [,,, ] Tranfer function T( ) ( ) y = T u, (2) where T()[ p, m ] i a matrix with entrie tranfer function correponding to the appropriate input/output pair. Matrix fraction decription R(), P() with z being the partial tate (ee Polynomial and Matrix Fraction Decription.) (1) ( ) ( ) y = R z, u = P z, (3) where R(), P() are polynomial matrice of dimenion Pmm [, ], R[ pm, ] repectively, P() i column proper with column degree d, i = 1,... m. The relation between thee form i i

4 ( ) ( ) ( ) ( ) 1 1 T = C I A B+ D = R P (4) Control Structure Ued for Decoupling The controller that will be ued for decoupling deign can be divided into four categorie (reference output denoted by r): Static feedforward (SFF) u = Gr Contant linear output feedback (LOF) u = Hy+ Gr Linear tate feedback (LSF) u = Fx+ Gr = H( ) y+ Gr Linear tate feedback with input dynamic (LSFID) Square and Non-quare Sytem Decoupling i mainly ued for quare ytem, i.e. ytem with equal number of input and output. In general, we can ditinguih three cae: m > p, m< p, and m = p. If there are more output than input ( m p) <, the fundamental problem i to define decoupling. A poible approach i to define ubytem where ome ubet of input influence only a ubet of output without affecting other output, hence to divide the, m, p ubytem. original ( mp ) ytem into maller ( ) i i The method given in the ubequent ection can then be applied to each ubytem. If it i poible to decouple all ubytem independently, then it i poible to decouple them imultaneouly. The ituation when there are more input than output ( m p) > i in fact a more ueful a with the equal number of input and output. Clearly, in the former cae there are more degree of freedom to obtain a decoupled cloed-loop ytem Problem Formulation The requirement for a variou verion of dynamic decoupling i cloely related to contraining the cloed-loop tranfer function to ome particular form. More pecifically, the ytem will be diagonally decoupled if it tranfer function matrix i diagonal and of full rank. The requirement of triangularly decoupled ytem i equivalent to the tranfer function matrix being (lower) triangular and full rank. Finally, a ytem i aid to be block decoupled if it tranfer function matrix i block diagonal and ha full rank. 2. Control of a Heat Exchanger 2.1. Model To explain the idea of decoupling, let u tart with an example of a heat exchanger

5 control. We conider a heat exchanger in form of a phere tank with the diameter r, upplied by input flow of cold liquid with temperature ϑ 0 and electrically heated. Within the exchanger, level h and temperature ϑ are to be controlled, the manipulated variable are input flowrate q 0 and heat powerω, and the diturbance i the inlet temperatureϑ 0. Output flowrate of the heated medium q 1 depend on the height of the liquid in the tank and i given a q 1 = k h. We aume for implicity that the height of the liquid i maller than r, the exchanger i well mixed and inulated, and that heat capacity cp and denity ρ are contant. With thee aumption, material and energy balance of the heat exchanger are a follow dv q0ρ = q1ρ + ρ (5) dt dvϑ q0ρcpϑ0 + ω = q1ρcpϑ + ρcp (6) dt where V i the volume of the liquid inide of the tank depending on actual liquid level h and for a phere it i given a 1 2 V( h) = π h (3 r h) (7) 3 After ome manipulation, the differential equation decribing dynamic behavior of controlled variable are given a ( q0 k h) dh 1 = (8) dt V '( h) dϑ 1 ω = + q0 0 dt V ( h) ρcp ( ϑ ϑ ) dv ( h) wherev '( h) =. The actual value of all parameter have been choen a r = 2 m, dh ρ = 1 kg / m, c = 4.2 J / kg/ K, k = 0.05 m /. The teady tate value of input ignal are p 3 q0 = 0.05 m /, ω = 1 J /, ϑ 0 = 300 K. (9) From the control point of view, the heat exchanger repreent nonlinear 2-input, 2- output ytem of a triangular tructure a the height h i not coupled with the heat powerω. Repone of the exchanger to tep change in manipulated variable i hown in Fig. 1. A expected, the height i not influenced by the tep change of the heat power at time t = 1000 wherea temperature i influenced by both input flowrate q 0 change

6 at time t = 20 and the heat power at time t = Steady tate of the exchanger i given a h q 0 = k 2 Figure 1: Step repone of the heat exchanger ω ϑ = ϑ0 + q 0 ρ c (11) p For the control deign purpoe, a linearized model in deviation variable will be developed. Let u denote the deviation from teady tate u 1 = q 0 q 0, u 2 = ω ω, x1 = h h, x2 = ϑ ϑ and aume that the inlet temperature i contant. After the Taylor expanion of the nonlinear element, the original nonlinear model can be approximated in the neighborhood of the teady tate by a linear tate pace model of the form (10) x a 0 x b 0 u y 1 0 x = +, = x2 0 a22 x2 b21 b22 u2 y x2 (12) or, in the tranfer function matrix a b11 0 a11 T() = b21 b22 a22 a 22 (13)

7 We can ee that the ytem tate are already decoupled and that the interaction are caued only by the matrix B. Moreover, a in the nonlinear cae, the tranfer function matrix Ti () triangular and the output y 1 i decoupled from the input u Static Decoupling Let u conider the implet decoupling trategy tatic decoupling. In thi cae we deire to have a ituation when a tep change in the tatic, teady tate level of each input i reflected by a correponding change in the teady-tate level of the correponding output and only that output. A imple feedforward olution a decribed in a more detail in ection 4 pecifie a contant precompenator matrix G that manipulate reference ignal and i given a the invere of the matrix T (0) 1 b11 a a 11 b 11 b21 b 22 a11b21 a 22 a22 a 22 b11b22 b 22 G = = (15) Figure 2: Static decoupling control deign for the heat exchanger Figure 2 compare behavior of the linear and nonlinear model. For the linear model, thi control deign reulted in full dynamic decoupling (not only in teady tate, but alo during tranient, ee ection 3) a the coupling effect are not caued by the ytem matrix A. The nonlinear model, however, differ from the linear model ignificantly at

8 time t = 300 and till exhibit ome mall coupling effect Dynamic Decoupling Even if we have een that dynamic decoupling i not neceary in thi cae, we can deign a controller that guarantee decoupling behavior all the time alo for more complex procee. The mot general procedure i linear tate feedback with input dynamic decribed by the algorithm 1 in ection 3.1. The cloed-loop pole have been pecified a Pˆ ( ) = diag ( , ) (16) and the reult are both for linear and nonlinear model are hown in Fig. 3. We can ee that repone peed i much improved. However, the problem with nonlinear model till remain. Figure 3: Dynamic decoupling deign for the heat exchanger Very often, the real input ignal are contrained in the magnitude. The effect of the contraint i much more important in the decoupled cloed-loop ytem. Fig. 4 how both manipulated and controlled variable when upper level contraint ha been impoed a u 1 < We can oberve, that even in the linear cae, the cloed-loop behavior exhibit coupling at time t = 300.

9 Figure 4: Saturation effect from input clipping for the heat exchanger There are everal approache that can counteract thi ituation. In Fig. 5, the econd input i caled down by the ame amount a the firt input. We can ee that decoupled behaviour i again etablihed. Figure 5: Input caling in the preence of contraint for the heat exchanger

10 - - - TO ACCESS ALL THE 35 PAGES OF THIS CHAPTER, Click here Bibliography Deoer C. and Günde A. (1986). Decoupling linear mulitinput multioutput plant by dynamic output feedback. IEEE Tran. Automatic Control 31, [Dicuion about the cot of decoupling - when the requirement of diagonal tranfer function may increae multiplicity of non-minimum phae zero]. Furuta K. and Kamiyama S. (1977). State feedback and invere ytem. Int. J. Control 25, [State tate feedback approach to decoupling]. Mikleš J. and Mézáro A. (1991). A decoupling pole placement controller for a cla of multivariable ytem. Problem of Control and Information Theory 20(4), [Deign of a diagonal decoupling controller uitable alo for non-minimum phae ytem with decoupling action in feedforward term]. Sinha P.K. (1984). Multivariable Control. An Introduction. New York and Bael: Marcel Dekker, Inc. [State pace approach to diagonal decoupling. Conider tate and output feedback decoupling]. Wade H.L. (1997). Inverted decoupling: a neglected technique. ISA Tranaction 36(1), [Dicuion of variou decoupling technique in proce control deign]. Wang S.H. and Davion E.J. (1975). Deign of decoupled control ytem: a frequency domain approach. Int. J. Control 21, [Linear output feedback deign in frequency domain for diagonal decoupling]. William T.W.C. and Antakli P.J. (1986). A unifying approach to the decoupling of linear multivariable ytem. Int. J. Control 44(1), [General approach to dynamic decoupling. All pecial cae are dicued: diagonal, triangular, and block decoupling baed in the interactor matrix]. Wolovich W.A. (1974). Linear Multivariable Sytem. Springer-Verlag, New York. [A good introduction to tatic and dynamic diagonal decoupling of ytem decribed by matrix fraction decription]. Wolowich W.A. and Falb P.L. (1976). Invariant and canonical form under dynamic compenation. SIAM J. Control and Optimization 14(6), [The fundamental role of the interactor matrix in decoupling]. Wonham W.M. (1979). Linear Multivariable Control: A Geometric Approach. New York: Springer- Verlag. [An introduction to geometric approach and it approach to decoupling control]. Biographical Sketch Mirolav Fikar received the Ing. degree from the Faculty of Chemical Technology (CHTF), Slovak Univerity of Technology in Bratilava in 1989, Dr. in 1994, and Doc. (Aociate Profeor) in Since 1989 he ha been with the Department of Proce Control CHTF STU. In 1999 he wa awarded the Alexander von Humboldt fellowhip. He alo worked at Technical Univerity Lyngby, Techniche Univeritaet Dortmund, CRNS-ENSIC Nancy, Ruhr Univeritaet Bochum, and other. The publication activity of Dr. Fikar include more than 70 work and he i co-author of three book. In hi cientific work, he deal with predictive control, contraint handling, ytem identification, optimization, and proce control.

CHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL

CHAPTER 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 information

CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS

CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS CHAPTER 8 OBSERVER BASED REDUCED ORDER CONTROLLER DESIGN FOR LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.1 INTRODUCTION 8.2 REDUCED ORDER MODEL DESIGN FOR LINEAR DISCRETE-TIME CONTROL SYSTEMS 8.3

More information

NONLINEAR CONTROLLER DESIGN FOR A SHELL AND TUBE HEAT EXCHANGER AN EXPERIMENTATION APPROACH

NONLINEAR CONTROLLER DESIGN FOR A SHELL AND TUBE HEAT EXCHANGER AN EXPERIMENTATION APPROACH International Journal of Electrical, Electronic and Data Communication, ISSN: 232-284 Volume-3, Iue-8, Aug.-25 NONLINEAR CONTROLLER DESIGN FOR A SHELL AND TUBE HEAT EXCHANGER AN EXPERIMENTATION APPROACH

More information

EE Control Systems LECTURE 6

EE 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

Digital Control System

Digital 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 information

ME 375 FINAL EXAM Wednesday, May 6, 2009

ME 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 information

A Simplified Methodology for the Synthesis of Adaptive Flight Control Systems

A Simplified Methodology for the Synthesis of Adaptive Flight Control Systems A Simplified Methodology for the Synthei of Adaptive Flight Control Sytem J.ROUSHANIAN, F.NADJAFI Department of Mechanical Engineering KNT Univerity of Technology 3Mirdamad St. Tehran IRAN Abtract- A implified

More information

The Hassenpflug Matrix Tensor Notation

The Hassenpflug Matrix Tensor Notation The Haenpflug Matrix Tenor Notation D.N.J. El Dept of Mech Mechatron Eng Univ of Stellenboch, South Africa e-mail: dnjel@un.ac.za 2009/09/01 Abtract Thi i a ample document to illutrate the typeetting of

More information

7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281

7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 281 72 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 28 and i 2 Show how Euler formula (page 33) can then be ued to deduce the reult a ( a) 2 b 2 {e at co bt} {e at in bt} b ( a) 2 b 2 5 Under what condition

More information

Bogoliubov Transformation in Classical Mechanics

Bogoliubov Transformation in Classical Mechanics Bogoliubov Tranformation in Claical Mechanic Canonical Tranformation Suppoe we have a et of complex canonical variable, {a j }, and would like to conider another et of variable, {b }, b b ({a j }). How

More information

State Space: Observer Design Lecture 11

State Space: Observer Design Lecture 11 State Space: Oberver Deign Lecture Advanced Control Sytem Dr Eyad Radwan Dr Eyad Radwan/ACS/ State Space-L Controller deign relie upon acce to the tate variable for feedback through adjutable gain. Thi

More information

Gain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays

Gain 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 information

EE 4443/5329. LAB 3: Control of Industrial Systems. Simulation and Hardware Control (PID Design) The Inverted Pendulum. (ECP Systems-Model: 505)

EE 4443/5329. LAB 3: Control of Industrial Systems. Simulation and Hardware Control (PID Design) The Inverted Pendulum. (ECP Systems-Model: 505) EE 4443/5329 LAB 3: Control of Indutrial Sytem Simulation and Hardware Control (PID Deign) The Inverted Pendulum (ECP Sytem-Model: 505) Compiled by: Nitin Swamy Email: nwamy@lakehore.uta.edu Email: okuljaca@lakehore.uta.edu

More information

Control of Delayed Integrating Processes Using Two Feedback Controllers R MS Approach

Control of Delayed Integrating Processes Using Two Feedback Controllers R MS Approach Proceeding of the 7th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING (ICOSSSE '8) Control of Delayed Integrating Procee Uing Two Feedback Controller R MS Approach LIBOR

More information

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS

S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS S_LOOP: SINGLE-LOOP FEEDBACK CONTROL SYSTEM ANALYSIS by Michelle Gretzinger, Daniel Zyngier and Thoma Marlin INTRODUCTION One of the challenge to the engineer learning proce control i relating theoretical

More information

EE Control Systems LECTURE 14

EE 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 information

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get

into a discrete time function. Recall that the table of Laplace/z-transforms is constructed by (i) selecting to get Lecture 25 Introduction to Some Matlab c2d Code in Relation to Sampled Sytem here are many way to convert a continuou time function, { h( t) ; t [0, )} into a dicrete time function { h ( k) ; k {0,,, }}

More information

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking

A Simple Approach to Synthesizing Naïve Quantized Control for Reference Tracking A Simple Approach to Syntheizing Naïve Quantized Control for Reference Tracking SHIANG-HUA YU Department of Electrical Engineering National Sun Yat-Sen Univerity 70 Lien-Hai Road, Kaohiung 804 TAIAN Abtract:

More information

Analysis of Step Response, Impulse and Ramp Response in the Continuous Stirred Tank Reactor System

Analysis of Step Response, Impulse and Ramp Response in the Continuous Stirred Tank Reactor System ISSN: 454-50 Volume 0 - Iue 05 May 07 PP. 7-78 Analyi of Step Repone, Impule and Ramp Repone in the ontinuou Stirred Tank Reactor Sytem * Zohreh Khohraftar, Pirouz Derakhhi, (Department of hemitry, Science

More information

Control Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:

Control 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 information

Evolutionary Algorithms Based Fixed Order Robust Controller Design and Robustness Performance Analysis

Evolutionary Algorithms Based Fixed Order Robust Controller Design and Robustness Performance Analysis Proceeding of 01 4th International Conference on Machine Learning and Computing IPCSIT vol. 5 (01) (01) IACSIT Pre, Singapore Evolutionary Algorithm Baed Fixed Order Robut Controller Deign and Robutne

More information

Social Studies 201 Notes for November 14, 2003

Social Studies 201 Notes for November 14, 2003 1 Social Studie 201 Note for November 14, 2003 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the

More information

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty IOSR Journal of Electrical and Electronic Engineering (IOSR-JEEE) ISSN: 78-676Volume, Iue 6 (Nov. - Dec. 0), PP 4-0 Simple Oberver Baed Synchronization of Lorenz Sytem with Parametric Uncertainty Manih

More information

OBSERVER-BASED REDUCED ORDER CONTROLLER DESIGN FOR THE STABILIZATION OF LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS

OBSERVER-BASED REDUCED ORDER CONTROLLER DESIGN FOR THE STABILIZATION OF LARGE SCALE LINEAR DISCRETE-TIME CONTROL SYSTEMS International Journal o Computer Science, Engineering and Inormation Technology (IJCSEIT, Vol.1, No.5, December 2011 OBSERVER-BASED REDUCED ORDER CONTROLLER DESIGN FOR THE STABILIZATION OF LARGE SCALE

More information

THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY STABILIZING CONTROLLERS. Tatsuya Hoshikawa, Kou Yamada and Yuko Tatsumi

THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY STABILIZING CONTROLLERS. Tatsuya Hoshikawa, Kou Yamada and Yuko Tatsumi International Journal of Innovative Computing, Information Control ICIC International c 206 ISSN 349-498 Volume 2, Number 2, April 206 pp. 357 370 THE PARAMETERIZATION OF ALL TWO-DEGREES-OF-FREEDOM SEMISTRONGLY

More information

Module 4: Time Response of discrete time systems Lecture Note 1

Module 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 information

Chapter 13. Root Locus Introduction

Chapter 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 information

Mathematical modeling of control systems. Laith Batarseh. Mathematical modeling of control systems

Mathematical 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 information

ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION. Xiaoqun Wang

ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION. Xiaoqun Wang Proceeding of the 2008 Winter Simulation Conference S. J. Maon, R. R. Hill, L. Mönch, O. Roe, T. Jefferon, J. W. Fowler ed. ON THE APPROXIMATION ERROR IN HIGH DIMENSIONAL MODEL REPRESENTATION Xiaoqun Wang

More information

A Comparative Study on Control Techniques of Non-square Matrix Distillation Column

A Comparative Study on Control Techniques of Non-square Matrix Distillation Column IJCTA, 8(3), 215, pp 1129-1136 International Science Pre A Comparative Study on Control Technique of Non-quare Matrix Ditillation Column 1 S Bhat Vinayambika, 2 S Shanmuga Priya, and 3 I Thirunavukkarau*

More information

A Constraint Propagation Algorithm for Determining the Stability Margin. The paper addresses the stability margin assessment for linear systems

A Constraint Propagation Algorithm for Determining the Stability Margin. The paper addresses the stability margin assessment for linear systems A Contraint Propagation Algorithm for Determining the Stability Margin of Linear Parameter Circuit and Sytem Lubomir Kolev and Simona Filipova-Petrakieva Abtract The paper addree the tability margin aement

More information

Massachusetts Institute of Technology Dynamics and Control II

Massachusetts Institute of Technology Dynamics and Control II I E Maachuett Intitute of Technology Department of Mechanical Engineering 2.004 Dynamic and Control II Laboratory Seion 5: Elimination of Steady-State Error Uing Integral Control Action 1 Laboratory Objective:

More information

Robust Decentralized Design of H -based Frequency Stabilizer of SMES

Robust Decentralized Design of H -based Frequency Stabilizer of SMES International Energy Journal: Vol. 6, No., Part, June 005-59 Robut Decentralized Deign of H -baed Frequency Stabilizer of SMES www.erd.ait.ac.th/reric C. Vorakulpipat *, M. Leelajindakrirerk *, and I.

More information

SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD

SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD SMALL-SIGNAL STABILITY ASSESSMENT OF THE EUROPEAN POWER SYSTEM BASED ON ADVANCED NEURAL NETWORK METHOD S.P. Teeuwen, I. Erlich U. Bachmann Univerity of Duiburg, Germany Department of Electrical Power Sytem

More information

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004

Lecture 4. Chapter 11 Nise. Controller Design via Frequency Response. G. Hovland 2004 METR4200 Advanced Control Lecture 4 Chapter Nie Controller Deign via Frequency Repone G. Hovland 2004 Deign Goal Tranient repone via imple gain adjutment Cacade compenator to improve teady-tate error Cacade

More information

Lecture 10 Filtering: Applied Concepts

Lecture 10 Filtering: Applied Concepts Lecture Filtering: Applied Concept In the previou two lecture, you have learned about finite-impule-repone (FIR) and infinite-impule-repone (IIR) filter. In thee lecture, we introduced the concept of filtering

More information

March 18, 2014 Academic Year 2013/14

March 18, 2014 Academic Year 2013/14 POLITONG - SHANGHAI BASIC AUTOMATIC CONTROL Exam grade March 8, 4 Academic Year 3/4 NAME (Pinyin/Italian)... STUDENT ID Ue only thee page (including the back) for anwer. Do not ue additional heet. Ue of

More information

Chapter #4 EEE8013. Linear Controller Design and State Space Analysis. Design of control system in state space using Matlab

Chapter #4 EEE8013. Linear Controller Design and State Space Analysis. Design of control system in state space using Matlab EEE83 hapter #4 EEE83 Linear ontroller Deign and State Space nalyi Deign of control ytem in tate pace uing Matlab. ontrollabilty and Obervability.... State Feedback ontrol... 5 3. Linear Quadratic Regulator

More information

EXTENDED STABILITY MARGINS ON CONTROLLER DESIGN FOR NONLINEAR INPUT DELAY SYSTEMS. Otto J. Roesch, Hubert Roth, Asif Iqbal

EXTENDED STABILITY MARGINS ON CONTROLLER DESIGN FOR NONLINEAR INPUT DELAY SYSTEMS. Otto J. Roesch, Hubert Roth, Asif Iqbal EXTENDED STABILITY MARGINS ON CONTROLLER DESIGN FOR NONLINEAR INPUT DELAY SYSTEMS Otto J. Roech, Hubert Roth, Aif Iqbal Intitute of Automatic Control Engineering Univerity Siegen, Germany {otto.roech,

More information

Efficient Methods of Doppler Processing for Coexisting Land and Weather Clutter

Efficient Methods of Doppler Processing for Coexisting Land and Weather Clutter Efficient Method of Doppler Proceing for Coexiting Land and Weather Clutter Ça gatay Candan and A Özgür Yılmaz Middle Eat Technical Univerity METU) Ankara, Turkey ccandan@metuedutr, aoyilmaz@metuedutr

More information

IEOR 3106: Fall 2013, Professor Whitt Topics for Discussion: Tuesday, November 19 Alternating Renewal Processes and The Renewal Equation

IEOR 3106: Fall 2013, Professor Whitt Topics for Discussion: Tuesday, November 19 Alternating Renewal Processes and The Renewal Equation IEOR 316: Fall 213, Profeor Whitt Topic for Dicuion: Tueday, November 19 Alternating Renewal Procee and The Renewal Equation 1 Alternating Renewal Procee An alternating renewal proce alternate between

More information

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam

Solutions. Digital Control Systems ( ) 120 minutes examination time + 15 minutes reading time at the beginning of the exam BSc - Sample Examination Digital Control Sytem (5-588-) Prof. L. Guzzella Solution Exam Duration: Number of Quetion: Rating: Permitted aid: minute examination time + 5 minute reading time at the beginning

More information

Social Studies 201 Notes for March 18, 2005

Social Studies 201 Notes for March 18, 2005 1 Social Studie 201 Note for March 18, 2005 Etimation of a mean, mall ample ize Section 8.4, p. 501. When a reearcher ha only a mall ample ize available, the central limit theorem doe not apply to the

More information

To appear in International Journal of Numerical Methods in Fluids in Stability analysis of numerical interface conditions in uid-structure therm

To appear in International Journal of Numerical Methods in Fluids in Stability analysis of numerical interface conditions in uid-structure therm To appear in International Journal of Numerical Method in Fluid in 997. Stability analyi of numerical interface condition in uid-tructure thermal analyi M. B. Gile Oxford Univerity Computing Laboratory

More information

Digital Control System

Digital Control System Digital Control Sytem Summary # he -tranform play an important role in digital control and dicrete ignal proceing. he -tranform i defined a F () f(k) k () A. Example Conider the following equence: f(k)

More information

UNIT 15 RELIABILITY EVALUATION OF k-out-of-n AND STANDBY SYSTEMS

UNIT 15 RELIABILITY EVALUATION OF k-out-of-n AND STANDBY SYSTEMS UNIT 1 RELIABILITY EVALUATION OF k-out-of-n AND STANDBY SYSTEMS Structure 1.1 Introduction Objective 1.2 Redundancy 1.3 Reliability of k-out-of-n Sytem 1.4 Reliability of Standby Sytem 1. Summary 1.6 Solution/Anwer

More information

Advanced D-Partitioning Analysis and its Comparison with the Kharitonov s Theorem Assessment

Advanced 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 information

Question 1 Equivalent Circuits

Question 1 Equivalent Circuits MAE 40 inear ircuit Fall 2007 Final Intruction ) Thi exam i open book You may ue whatever written material you chooe, including your cla note and textbook You may ue a hand calculator with no communication

More information

1 Basic Equations of the PLLs

1 Basic Equations of the PLLs 1 Baic Equation of the PLL 1.1 INTRODUCTION Phae lock loop (PLL) belong to a larger et of regulation ytem. A an independent reearch and deign field it tarted in the 1950 [1] and gained major practical

More information

FRTN10 Exercise 3. Specifications and Disturbance Models

FRTN10 Exercise 3. Specifications and Disturbance Models FRTN0 Exercie 3. Specification and Diturbance Model 3. A feedback ytem i hown in Figure 3., in which a firt-order proce if controlled by an I controller. d v r u 2 z C() P() y n Figure 3. Sytem in Problem

More information

Design of Robust PI Controller for Counter-Current Tubular Heat Exchangers

Design of Robust PI Controller for Counter-Current Tubular Heat Exchangers Deign of Robut PI Controller for Counter-Current Tubular Heat Excanger Jana Závacká Monika Bakošová Intitute of Information Engineering Automation Matematic Faculty of Cemical Food Tecnology STU in Bratilava

More information

Linear System Fundamentals

Linear 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 information

CHEAP CONTROL PERFORMANCE LIMITATIONS OF INPUT CONSTRAINED LINEAR SYSTEMS

CHEAP 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 information

What lies between Δx E, which represents the steam valve, and ΔP M, which is the mechanical power into the synchronous machine?

What lies between Δx E, which represents the steam valve, and ΔP M, which is the mechanical power into the synchronous machine? A 2.0 Introduction In the lat et of note, we developed a model of the peed governing mechanim, which i given below: xˆ K ( Pˆ ˆ) E () In thee note, we want to extend thi model o that it relate the actual

More information

Design of Digital Filters

Design of Digital Filters Deign of Digital Filter Paley-Wiener Theorem [ ] ( ) If h n i a caual energy ignal, then ln H e dω< B where B i a finite upper bound. One implication of the Paley-Wiener theorem i that a tranfer function

More information

Hybrid Projective Dislocated Synchronization of Liu Chaotic System Based on Parameters Identification

Hybrid Projective Dislocated Synchronization of Liu Chaotic System Based on Parameters Identification www.ccenet.org/ma Modern Applied Science Vol. 6, No. ; February Hybrid Projective Dilocated Synchronization of Liu Chaotic Sytem Baed on Parameter Identification Yanfei Chen College of Science, Guilin

More information

A PLC BASED MIMO PID CONTROLLER FOR MULTIVARIABLE INDUSTRIAL PROCESSES

A PLC BASED MIMO PID CONTROLLER FOR MULTIVARIABLE INDUSTRIAL PROCESSES ABCM Sympoium Serie in Mechatronic - Vol. 3 - pp.87-96 Copyright c 8 by ABCM A PLC BASE MIMO PI CONOLLE FO MULIVAIABLE INUSIAL POCESSES Joé Maria Galvez, jmgalvez@ufmg.br epartment of Mechanical Engineering

More information

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog

Chapter 2 Sampling and Quantization. In order to investigate sampling and quantization, the difference between analog Chapter Sampling and Quantization.1 Analog and Digital Signal In order to invetigate ampling and quantization, the difference between analog and digital ignal mut be undertood. Analog ignal conit of continuou

More information

Reliability Analysis of Embedded System with Different Modes of Failure Emphasizing Reboot Delay

Reliability Analysis of Embedded System with Different Modes of Failure Emphasizing Reboot Delay International Journal of Applied Science and Engineering 3., 4: 449-47 Reliability Analyi of Embedded Sytem with Different Mode of Failure Emphaizing Reboot Delay Deepak Kumar* and S. B. Singh Department

More information

Convex Hulls of Curves Sam Burton

Convex Hulls of Curves Sam Burton Convex Hull of Curve Sam Burton 1 Introduction Thi paper will primarily be concerned with determining the face of convex hull of curve of the form C = {(t, t a, t b ) t [ 1, 1]}, a < b N in R 3. We hall

More information

The Laplace Transform , Haynes Miller and Jeremy Orloff

The Laplace Transform , Haynes Miller and Jeremy Orloff The Laplace Tranform 8.3, Hayne Miller and Jeremy Orloff Laplace tranform baic: introduction An operator take a function a input and output another function. A tranform doe the ame thing with the added

More information

An estimation approach for autotuning of event-based PI control systems

An estimation approach for autotuning of event-based PI control systems Acta de la XXXIX Jornada de Automática, Badajoz, 5-7 de Septiembre de 08 An etimation approach for autotuning of event-baed PI control ytem Joé Sánchez Moreno, María Guinaldo Loada, Sebatián Dormido Departamento

More information

LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM. P.Dickinson, A.T.Shenton

LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM. P.Dickinson, A.T.Shenton LOW ORDER MIMO CONTROLLER DESIGN FOR AN ENGINE DISTURBANCE REJECTION PROBLEM P.Dickinon, A.T.Shenton Department of Engineering, The Univerity of Liverpool, Liverpool L69 3GH, UK Abtract: Thi paper compare

More information

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder

R. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder R. W. Erickon Department of Electrical, Computer, and Energy Engineering Univerity of Colorado, Boulder Cloed-loop buck converter example: Section 9.5.4 In ECEN 5797, we ued the CCM mall ignal model to

More information

Chapter 1 Basic Description of Laser Diode Dynamics by Spatially Averaged Rate Equations: Conditions of Validity

Chapter 1 Basic Description of Laser Diode Dynamics by Spatially Averaged Rate Equations: Conditions of Validity Chapter 1 Baic Decription of Laer Diode Dynamic by Spatially Averaged Rate Equation: Condition of Validity A laer diode i a device in which an electric current input i converted to an output of photon.

More information

Lecture Notes II. As the reactor is well-mixed, the outlet stream concentration and temperature are identical with those in the tank.

Lecture Notes II. As the reactor is well-mixed, the outlet stream concentration and temperature are identical with those in the tank. Lecture Note II Example 6 Continuou Stirred-Tank Reactor (CSTR) Chemical reactor together with ma tranfer procee contitute an important part of chemical technologie. From a control point of view, reactor

More information

Lecture #9 Continuous time filter

Lecture #9 Continuous time filter Lecture #9 Continuou time filter Oliver Faut December 5, 2006 Content Review. Motivation......................................... 2 2 Filter pecification 2 2. Low pa..........................................

More information

CONTROL OF INTEGRATING PROCESS WITH DEAD TIME USING AUTO-TUNING APPROACH

CONTROL OF INTEGRATING PROCESS WITH DEAD TIME USING AUTO-TUNING APPROACH Brazilian Journal of Chemical Engineering ISSN 004-6632 Printed in Brazil www.abeq.org.br/bjche Vol. 26, No. 0, pp. 89-98, January - March, 2009 CONROL OF INEGRAING PROCESS WIH DEAD IME USING AUO-UNING

More information

SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lectures 41-48)

SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lectures 41-48) Chapter 5 SERIES COMPENSATION: VOLTAGE COMPENSATION USING DVR (Lecture 41-48) 5.1 Introduction Power ytem hould enure good quality of electric power upply, which mean voltage and current waveform hould

More information

HOMEWORK ASSIGNMENT #2

HOMEWORK ASSIGNMENT #2 Texa A&M Univerity Electrical Engineering Department ELEN Integrated Active Filter Deign Methodologie Alberto Valde-Garcia TAMU ID# 000 17 September 0, 001 HOMEWORK ASSIGNMENT # PROBLEM 1 Obtain at leat

More information

ROBUST CONTROLLER DESIGN WITH HARD INPUT CONSTRAINTS. TIME DOMAIN APPROACH. Received August 2015; revised November 2015

ROBUST CONTROLLER DESIGN WITH HARD INPUT CONSTRAINTS. TIME DOMAIN APPROACH. Received August 2015; revised November 2015 International Journal of Innovative Computing, Information and Control ICIC International c 2016 ISSN 1349-4198 Volume 12, Number 1, February 2016 pp. 161 170 ROBUST CONTROLLER DESIGN WITH HARD INPUT CONSTRAINTS.

More information

Codes Correcting Two Deletions

Codes Correcting Two Deletions 1 Code Correcting Two Deletion Ryan Gabry and Frederic Sala Spawar Sytem Center Univerity of California, Lo Angele ryan.gabry@navy.mil fredala@ucla.edu Abtract In thi work, we invetigate the problem of

More information

THE IDENTIFICATION OF THE OPERATING REGIMES OF THE CONTROLLERS BY THE HELP OF THE PHASE TRAJECTORY

THE IDENTIFICATION OF THE OPERATING REGIMES OF THE CONTROLLERS BY THE HELP OF THE PHASE TRAJECTORY Mariu M. B LA Aurel Vlaicu Univerity of Arad, Engineering Faculty Bd. Revolu iei nr. 77, 3030, Arad, Romania, E-mail: mariu.bala@ieee.org THE IDENTIFICATION OF THE OPERATING REGIMES OF THE CONTROLLERS

More information

Optimal Coordination of Samples in Business Surveys

Optimal Coordination of Samples in Business Surveys Paper preented at the ICES-III, June 8-, 007, Montreal, Quebec, Canada Optimal Coordination of Sample in Buine Survey enka Mach, Ioana Şchiopu-Kratina, Philip T Rei, Jean-Marc Fillion Statitic Canada New

More information

Preemptive scheduling on a small number of hierarchical machines

Preemptive scheduling on a small number of hierarchical machines Available online at www.ciencedirect.com Information and Computation 06 (008) 60 619 www.elevier.com/locate/ic Preemptive cheduling on a mall number of hierarchical machine György Dóa a, Leah Eptein b,

More information

Multivariable Control Systems

Multivariable 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 information

Lecture 21. The Lovasz splitting-off lemma Topics in Combinatorial Optimization April 29th, 2004

Lecture 21. The Lovasz splitting-off lemma Topics in Combinatorial Optimization April 29th, 2004 18.997 Topic in Combinatorial Optimization April 29th, 2004 Lecture 21 Lecturer: Michel X. Goeman Scribe: Mohammad Mahdian 1 The Lovaz plitting-off lemma Lovaz plitting-off lemma tate the following. Theorem

More information

Chapter 4 Interconnection of LTI Systems

Chapter 4 Interconnection of LTI Systems Chapter 4 Interconnection of LTI Sytem 4. INTRODUCTION Block diagram and ignal flow graph are commonly ued to decribe a large feedback control ytem. Each block in the ytem i repreented by a tranfer function,

More information

Chapter 7. Root Locus Analysis

Chapter 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 information

MODELING OF A SYSTEM WITH HYBRID DYNAMICS

MODELING OF A SYSTEM WITH HYBRID DYNAMICS 4 Acta Electrotechnica et Informatica, Vol., No., 0, 4 9, DOI: 0.478/v098-0-000- MODELING OF A SYSTEM WITH HYBRID DYNAMICS Vratilav HLADKÝ, Ľuboš POPOVIČ, Ján SARNOVSKÝ Department of Cybernetic and Artificial

More information

USING NONLINEAR CONTROL ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS

USING NONLINEAR CONTROL ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS October 12-17, 28, Beijing, China USING NONLINEAR CONTR ALGORITHMS TO IMPROVE THE QUALITY OF SHAKING TABLE TESTS T.Y. Yang 1 and A. Schellenberg 2 1 Pot Doctoral Scholar, Dept. of Civil and Env. Eng.,

More information

Control Systems Analysis and Design by the Root-Locus Method

Control 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 information

ECE382/ME482 Spring 2004 Homework 4 Solution November 14,

ECE382/ME482 Spring 2004 Homework 4 Solution November 14, ECE382/ME482 Spring 2004 Homework 4 Solution November 14, 2005 1 Solution to HW4 AP4.3 Intead of a contant or tep reference input, we are given, in thi problem, a more complicated reference path, r(t)

More information

NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flow Reactor

NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flow Reactor NONISOTHERMAL OPERATION OF IDEAL REACTORS Plug Flow Reactor T o T T o T F o, Q o F T m,q m T m T m T mo Aumption: 1. Homogeneou Sytem 2. Single Reaction 3. Steady State Two type of problem: 1. Given deired

More information

online learning Unit Workbook 4 RLC Transients

online learning Unit Workbook 4 RLC Transients online learning Pearon BTC Higher National in lectrical and lectronic ngineering (QCF) Unit 5: lectrical & lectronic Principle Unit Workbook 4 in a erie of 4 for thi unit Learning Outcome: RLC Tranient

More information

The Root Locus Method

The 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 information

Multi-dimensional Fuzzy Euler Approximation

Multi-dimensional Fuzzy Euler Approximation Mathematica Aeterna, Vol 7, 2017, no 2, 163-176 Multi-dimenional Fuzzy Euler Approximation Yangyang Hao College of Mathematic and Information Science Hebei Univerity, Baoding 071002, China hdhyywa@163com

More information

ECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances

ECE 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 information

Unavoidable Cycles in Polynomial-Based Time-Invariant LDPC Convolutional Codes

Unavoidable Cycles in Polynomial-Based Time-Invariant LDPC Convolutional Codes European Wirele, April 7-9,, Vienna, Autria ISBN 978--87-4-9 VE VERLAG GMBH Unavoidable Cycle in Polynomial-Baed Time-Invariant LPC Convolutional Code Hua Zhou and Norbert Goertz Intitute of Telecommunication

More information

Integration of RTO with MPC through the gradient of a convex function

Integration of RTO with MPC through the gradient of a convex function Preprint of the 8th IFAC Sympoium on Advanced Control of Chemical Procee he International Federation of Automatic Control Furama Riverfront, Singapore, July 1-13, 1 Integration of RO with MPC through the

More information

Then C pid (s) S h -stabilizes G(s) if and only if Ĉpid(ŝ) S 0 - stabilizes Ĝ(ŝ). For any ρ R +, an RCF of Ĉ pid (ŝ) is given by

Then C pid (s) S h -stabilizes G(s) if and only if Ĉpid(ŝ) S 0 - stabilizes Ĝ(ŝ). For any ρ R +, an RCF of Ĉ pid (ŝ) is given by 9 American Control Conference Hyatt Regency Riverfront, St. Loui, MO, USA June -, 9 WeC5.5 PID Controller Synthei with Shifted Axi Pole Aignment for a Cla of MIMO Sytem A. N. Gündeş and T. S. Chang Abtract

More information

Automatic Control Systems. Part III: Root Locus Technique

Automatic 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 information

Calculation of the temperature of boundary layer beside wall with time-dependent heat transfer coefficient

Calculation of the temperature of boundary layer beside wall with time-dependent heat transfer coefficient Ŕ periodica polytechnica Mechanical Engineering 54/1 21 15 2 doi: 1.3311/pp.me.21-1.3 web: http:// www.pp.bme.hu/ me c Periodica Polytechnica 21 RESERCH RTICLE Calculation of the temperature of boundary

More information

Copyright 1967, by the author(s). All rights reserved.

Copyright 1967, by the author(s). All rights reserved. Copyright 1967, by the author(). All right reerved. Permiion to make digital or hard copie of all or part of thi work for peronal or claroom ue i granted without fee provided that copie are not made or

More information

5.5 Application of Frequency Response: Signal Filters

5.5 Application of Frequency Response: Signal Filters 44 Dynamic Sytem Second order lowpa filter having tranfer function H()=H ()H () u H () H () y Firt order lowpa filter Figure 5.5: Contruction of a econd order low-pa filter by combining two firt order

More information

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with :

376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD. D(s) = we get the compensated system with : 376 CHAPTER 6. THE FREQUENCY-RESPONSE DESIGN METHOD Therefore by applying the lead compenator with ome gain adjutment : D() =.12 4.5 +1 9 +1 we get the compenated ytem with : PM =65, ω c = 22 rad/ec, o

More information

Chapter 10. Closed-Loop Control Systems

Chapter 10. Closed-Loop Control Systems hapter 0 loed-loop ontrol Sytem ontrol Diagram of a Typical ontrol Loop Actuator Sytem F F 2 T T 2 ontroller T Senor Sytem T TT omponent and Signal of a Typical ontrol Loop F F 2 T Air 3-5 pig 4-20 ma

More information

CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems

CALIFORNIA 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 information

MAE 101A. Homework 3 Solutions 2/5/2018

MAE 101A. Homework 3 Solutions 2/5/2018 MAE 101A Homework 3 Solution /5/018 Munon 3.6: What preure gradient along the treamline, /d, i required to accelerate water upward in a vertical pipe at a rate of 30 ft/? What i the anwer if the flow i

More information

Sliding Mode Control of a Dual-Fuel System Internal Combustion Engine

Sliding Mode Control of a Dual-Fuel System Internal Combustion Engine Proceeding of the ASME 9 Dynamic Sytem and Control Conference DSCC9 October -4, 9, Hollywood, California, USA DSCC9-59 Control of a Dual-Fuel Sytem Internal Combution Engine Stephen Pace Department of

More information