Symmetric Root Locus. LQR Design
|
|
- Sybil Cain
- 6 years ago
- Views:
Transcription
1 Leture 5 Symmetri Root Lous LQR Design State Estimation Seletion of 'otimal' oles for SISO ole laement design: SRL LQR design examle Predition and urrent estimators L5:1
2 L5:2 Otimal ole laement for SISO systems For a single-inut system, we might selet one artiular outut (y = Cx to onstrain in a ost funtion: r = + u x = Ax + B u y J = ( 2 2 ρ y ( t + u ( t dt Cx y = Plant transfer funtion: x K Y ( s 1 N ( s = C ( s I A B =, say U ( s D ( s It an be shown that: J will be minimised by the ontrol law u = Kx the eigenvalues of the losed-loo system are the left half-lane roots of the 2n-degree olynomial equation α ( α ( s = D ( s D ( s + ρ N ( s N ( s = s Ref: Kailath, Linear Systems, 198
3 L5:3 Otimal ole laement for SISO systems α ( α ( s = D ( s D ( s + ρ N ( s N ( s = s Hene we an see the effets of the outut-weighting fator ρ on the losed-loo oles by lotting a root lous for N ( s N ( s 1 + ρ = D ( s D ( s This symmetri root lous (SRL will be a 18º (º lous if the oen-loo ole-zero exess is even (odd The roots of α (s = are guaranteed stable Hene if branhes of the 18º SRL lie on the imaginary axis, lot the º lous instead The SRL thus rovides a basis for seifying CLPs in a SISO ole-laement design
4 The SRL is lotted for the equation Examle: u SRL for disrete systems M y Oen-loo TF: D ( z.134( = U ( z ( z b z + 1 N D ( ( ρ 1 2 m d z z.7( z + ( z.91 N D ( ( z z =.82( z + ± j.39 Comliant struture: M = 1, m =.1 b =.36, =.91 States: x = [ d d y y ] T Samle eriod: T =.4 s 7.74 L5:4 See srit flex_srl.m and funtion srl.m
5 Disrete SRL for omliant struture Symmetri root lous Real Axis L5:5 Imag Axis
6 s A xi g a Im Use rlofind to selet trial CLPs L5:6» [rho,l]=rlofind(gol rho = l = i i i i i i i i Real Axis» dl=l(find(abs(l<1 dl = i i i i
7 SRL ole-laement design (see flex_srl.m G = ss(a, B, C, D,'InutName','fore u','oututname','dis d'; set(g, 'StateName', {'d', 'ddot', 'y', 'ydot'} T =.4; % samle eriod Gd = 2d(G, T; % disrete ss model L5:7 % Plot symmetri root lous and get desired CL oles [rho, dl] = srl(gd; % MCG-written funtion % State-feedba ontrol gains Phi = Gd.a; Gam = Gd.b; K = aer(phi, Gam, dl; % Closed-loo regulator system Gdu = [Gd; 1]; % get d and u as oututs Gdux = augstate(gdu; % augment lant oututs with states Gl = feedba(gdux, K, [1], [3:6]; % feed-ba 4 states to u Gl = Gl(1:2,1; % suress state oututs Gl.oututn={'dis d'; 'trl u'}; % Initial ondition resonse x = [1 ]'; % d( = 1 initial(gl, x
8 SRL ole-laement design Initial ondition resonse 1 d Time (se. L5:8 Amlitude To: dis d u.5 To: trl u
9 LQR design for omliant struture (see flex_lqr.m % Disrete model T =.4; Gd = 2d(G, T; Phi = Gd.a; Gam = Gd.b; % Otimal ontrol: trial and error R = 1; % Salar inut % Weight dislaements but not veloities % Get trial diagonal elements for Q Q11 = inut('enter ontroller Q11: '; Q22 = inut('enter ontroller Q22: '; Q = diag([q11 Q22 ]; K = dlqr(phi, Gam, Q, R L5:9
10 LQR design, Q11 = 1, Q22 = 1, R = 1 d y u Time (se. L5:1 Amlitude To: dis y To: dis d To: fore u
11 LQR with redition estimator u( m x( Γ + q 1 C y( L5:11 x y Control law: u ( = K x ˆ( Estimator: x ˆ( Plant: ( ( = Φ = Cx ( 1 x = Φ + ( x ˆ( L + Γ 1 u ( 1 + Γ Plant [ ( ˆ( 1 ] y C x K u ( Feedba omensator u( x ˆ ( 1 Φ Γ q 1 Φ C + y ˆ ( Estimator + L
12 Full-order redition estimator Plant: Estimator: x ( + 1 = Φ x ( + Γ u ( y ( = Cx ( L5:12 [ y ( C ˆ( 1 ] x ˆ ( + 1 = Φ x ˆ( 1 + Γ u ( + L x Estimation error: ~ x ( ˆ( 1 ( = x x ~ ~ Estimation error dynamis: x ( + 1 = [ Φ L C ] ( x Charateristi olynomial: α ( z = det [ Φ + C ] L zi L n oeffiients ontaining n unnowns Desired harateristi olynomial: α e ( z = ( z β ( z β 2 ( z β 1 n n hosen oeffiients For MIMO systems, Matlab s lae funtion uses the extra DoF to give a robust solution
13 Examle: Regulation of omliant struture with redition estimator u M b m Comliant struture: M = 1, m =.1 b =.36, =.91 States: x = [ d d y y ] T L5:13 y d Samle eriod: T =.4 s Sensed oututs: y = [d y] T A revious ontroller design K = [ ] to lae oles at z =.9 ± j.5,.8 ± j.4 (orresonding to [ζ, ω n ] = [.88,.29], [.23, 1.19] Try laing estimator oles 5-times faster: dls = 1/T*log(dlz; % ontroller s-oles des = 5*dls; dez = ex(t*des; % estimator z-oles
14 L5:14 Predition estimator design Disretised lant model: T =.4; Gd = 2d(G,T; Phi = Gd.a; C = Gd.; Estimator gains: L = lae(phi',c',dez L = Regulator: H = reg(gd, K, L Feedba: Gl = feedba(gd, H, +1 Che resonse to initial ondition d( = 1 Exeriment with estimator ole seletion, et. (Matlab srit flex_redit.m
15 Resonse to initial ondition d = d( M u y Time (se. L5:15 Amlitude To: dis d.4.2 y( To: dis y u( To: fore u b m d
16 Atual states omared with redition estimates esonse of states and reditive estimates to x 1 ( = x 1 =d x 1 hat 5 x 2 =ddot x 2 hat Time (s 5 1 Time (s.4.2 x 3 =y x 3 hat 1.5 x 4 =ydot x 4 hat Time (s 5 1 Time (s L5:16
17 Current estimators L5:17 Using the revious redition estimator, the ontrol at instant is based on sensor data u to the revious samling instant: u ( = K x ˆ( 1 We now that delays (lateny in a feedba loo are de-stabilising Hene, if we were able to quily udate the state estimate at instant, based on the urrent measurement, it would be worthwhile: [ y ( C ˆ( 1 ] x ˆ ( = x ˆ( 1 + L x This measurement udate is erformed on the model redition (a time udate: x ˆ ( 1 = Φ x ˆ( Γ u ( We need to organise the alulations so that the measurement udate an be erformed raidly 1
18 LQR with urrent estimator u( m x( Γ + q 1 C Plant: x ( + 1 = Φ x ( + Γ u ( y ( = Cx ( Plant Φ Control law: u ( = K x ˆ( u( Γ + Estimator: Time udate: Φ x ˆ ( + 1 = Φ x ˆ( + Γ u ( x ˆ ( Measurement udate: K + L [ y ( C ˆ( 1 ] x ˆ ( = x ˆ( 1 + L x q 1 x ˆ ( 1 C L5:18 y( y ˆ ( +
19 Comarison between redition and urrent estimates For the urrent estimator we have x ˆ ( + 1 = Φ x ˆ( + Γ u ( and [ y ( C ˆ( 1 ] x ˆ ( = x ˆ( 1 + L x Hene x ˆ ( + 1 = Φ x ˆ( 1 + Γ u ( + Φ L y ( C x ˆ( [ 1 ] The redition estimation error is ~ x ( + 1 = x ˆ( + 1 x ( + 1 = Φ x ˆ( = Φ x 1 + Γ u ( + Φ L ( Γ [ Φ Φ L C ] ~ x ( u ( [ Cx ( Cx ˆ( 1 ] L5:19
20 Comarison between redition and urrent estimates... L5:2 For the urrent estimator we have the redition error ~ x ( + 1 = x ˆ( + 1 x ( + 1 = Φ Φ L C ~ x ( [ ] Similarly, we an show that the urrent estimate error is ~ x ( + 1 = x ˆ( x ( + 1 = Φ L C Φ ~ x ( [ ] The two error equations have the same eigenvalues (both are oututs from the same dynami system hene an use either as a basis for alulating L For the redition estimator: ~ x ( + 1 = L ~ [ Φ C ] ( x Hene for urrent estimator we an use: L = lae(phi, (C*Phi, dez
21 Imlementation of urrent estimator in Matlab Given x ˆ ( + 1 = Φ x ˆ( + Γ u ( and [ y ( C ˆ( 1 ] x ˆ ( = x ˆ( 1 + L x we an show that the state equations for the estimator, with inut y( and outut u(, are x ˆ( + 1 u ( = K I = [ Φ Γ K ][ I L C ] x ˆ( 1 + [ Φ Γ ] [ L C ] x ˆ( 1 KL y ( K L y ( Srit flex_urrent omares resonses of urrent and redition estimators L5:21
22 1.5 Initial Condition Results Time (se. L5:22 Amlitude To: dis d.4.2 To: dis y urrent estimator redition estimator To: fore u
Selection of 'optimal' poles for SISO pole placement design: SRL LQR design example Prediction and current estimators
L5: Leture 5 Symmetri Root Lous LQR Design State Estimation Seletion of 'otimal' oles for SISO ole laement design: SRL LQR design examle Predition and urrent estimators L5:2 Otimal ole laement for SISO
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 informationLecture 7 LQG Design. Linear Quadratic Gaussian regulator Control-estimation duality SRL for optimal estimator Example of LQG design for MIMO plant
L7: Lecture 7 LQG Design Linear Quadratic Gaussian regulator Control-estimation duality SRL for optimal estimator Example of LQG design for IO plant LQG regulator L7:2 If the process and measurement noises
More informationA General Approach for Analysis of Actuator Delay Compensation Methods for Real-Time Testing
The th World Conferene on Earthquake Engineering Otober -7, 8, Beijing, China A General Aroah for Analysis of Atuator Delay Comensation Methods for Real-Time Testing Cheng Chen and James M. Riles Post-dotoral
More informationOptimal control of inverted pendulum system using PID controller, LQR and MPC
IOP Conferene Series: aterials Siene and Engineering PAPER OPEN ACCESS Otimal ontrol of inverted endulum system using PID ontroller, LQR and PC To ite this artile: Elisa Sara Varghese et al 7 IOP Conf.
More informationControl Systems. Design of State Feedback Control.
Control Systems Design of State Feedback Control chibum@seoultech.ac.kr Outline Design of State feedback control Dominant pole design Symmetric root locus (linear quadratic regulation) 2 Selection of closed-loop
More informationIntroduction to MVC. least common denominator of all non-identical-zero minors of all order of G(s). Example: The minor of order 2: 1 2 ( s 1)
Introduction to MVC Definition---Proerness and strictly roerness A system G(s) is roer if all its elements { gij ( s)} are roer, and strictly roer if all its elements are strictly roer. Definition---Causal
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 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 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 informationA pressure output feedback control of turbo compressor surge with a thrust magnetic bearing actuator
Journal of Mehanial Siene and Tehnology 23 (2009) 1406~1414 Journal of Mehanial Siene and Tehnology www.sringerlin.om/ontent/1738-494x DOI 10.1007/s12206-008-1125-y A ressure outut feedba ontrol of turbo
More informationSimple Cyclic loading model based on Modified Cam Clay
Simle li loading model based on Modified am la Imlemented in RISP main rogram version 00. and higher B Amir Rahim, The RISP onsortium Ltd Introdution This reort resents a simle soil model whih rovides
More informationWe are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors
We are IntehOen the world s leading ublisher of Oen ess books Built by sientists for sientists 3350 108000 1.7 M Oen aess books available International authors and editors Downloads Our authors are among
More informationOn Fractional Predictive PID Controller Design Method Emmanuel Edet*. Reza Katebi.**
On Fractional Predictive PID Controller Design Method Emmanuel Edet*. Reza Katebi.** * echnology and Innovation Centre, Level 4, Deartment of Electronic and Electrical Engineering, University of Strathclyde,
More informationSubject: Modeling of Thermal Rocket Engines; Nozzle flow; Control of mass flow. p c. Thrust Chamber mixing and combustion
16.50 Leture 6 Subjet: Modeling of Thermal Roket Engines; Nozzle flow; Control of mass flow Though onetually simle, a roket engine is in fat hysially a very omlex devie and diffiult to reresent quantitatively
More informationSystem Modeling Concepts
1. E+2 1. E+1 1. E+4 1. E+3. 1 1.. 1 1. 2. 3. 4. 5. L i n e a r F r e q u e n y ( H z ) 2. 3. 4. 5. L i n e a r F r e q u e n y ( H z ) 2 1 1 2 2 1 2 1 Strutural Dynami odeling ehniques & odal nalysis
More informationAdvanced Control Theory
State Feedback Control Design chibum@seoultech.ac.kr Outline State feedback control design Benefits of CCF 2 Conceptual steps in controller design We begin by considering the regulation problem the task
More informationTuning of PID Controllers for Unstable Continuous Stirred Tank Reactors
nternational Journal of Alied Siene and Engineering 01. 10, 1: 1-18 Tuning of P Controllers for Unstable Continuous Stirred Tank Reators. rishna a,. Suryanarayana b, G. Aarna b, and R. Padma Sree b, *
More informationMechanical Systems Part A: State-Space Systems Lecture AL12
AL: 436-433 Mechanical Systems Part A: State-Space Systems Lecture AL Case study Case study AL: Design of a satellite attitude control system see Franklin, Powell & Emami-Naeini, Ch. 9. Requirements: accurate
More informationEconS 503 Homework #8. Answer Key
EonS 503 Homework #8 Answer Key Exerise #1 Damaged good strategy (Menu riing) 1. It is immediate that otimal rie is = 3 whih yields rofits of ππ = 3/ (the alternative being a rie of = 1, yielding ππ =
More informationCONSTRUCTION OF MIXED SAMPLING PLAN WITH DOUBLE SAMPLING PLAN AS ATTRIBUTE PLAN INDEXED THROUGH (MAPD, MAAOQ) AND (MAPD, AOQL)
Global J. of Arts & Mgmt., 0: () Researh Paer: Samath kumar et al., 0: P.07- CONSTRUCTION OF MIXED SAMPLING PLAN WITH DOUBLE SAMPLING PLAN AS ATTRIBUTE PLAN INDEXED THROUGH (MAPD, MAAOQ) AND (MAPD, AOQL)
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationV. Practical Optimization
V. Practical Otimization Scaling Practical Otimality Parameterization Otimization Objectives Means Solutions ω c -otimization Observer based design V- Definition of Gain and Frequency Scales G ( s) kg
More informationTime Domain Method of Moments
Time Domain Method of Moments Massahusetts Institute of Tehnology 6.635 leture notes 1 Introdution The Method of Moments (MoM) introdued in the previous leture is widely used for solving integral equations
More informationHankel Optimal Model Order Reduction 1
Massahusetts Institute of Tehnology Department of Eletrial Engineering and Computer Siene 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Hankel Optimal Model Order Redution 1 This leture overs both
More informationTopic # Feedback Control
Topic #5 6.3 Feedback Control State-Space Systems Full-state Feedback Control How do we change the poles of the state-space system? Or,evenifwecanchangethepolelocations. Where do we put the poles? Linear
More informationA MULTIRATE APPROACH TO DDS ALGORITHM VERSUS TAYLOR-SERIES EXPANSION TECHNIQUE
A ULTIRATE APPROACH TO DDS ALGORITH VERSUS TAYLOR-SERIES EXPANSION TECHNIQUE Ewa Hermanowiz 1 and iroslaw Rojewski Faulty of Eletronis, Teleommuniations and Informatis, Gdansk University of Tehnology,
More informationdy dy 2 dy d Y 2 dx dx Substituting these into the given differential equation d 2 Y dy 2Y = 2x + 3 ( ) ( 1 + 2b)= 3
Solutions 14() 1 Coplete solutions to Eerise 14() 1. (a) Sine f()= 18 is a onstant so Y = C, differentiating this zero. Substituting for Y into Y = 18 C = 18, hene C = 9 The partiular integral Y = 9. (This
More informationMultivariable Generalized Predictive Scheme for Gas Turbine Control in Combined Cycle Power Plant
Multivariable Generalized Predictive Scheme for Gas urbine Control in Combined Cycle Power Plant L.X.Niu and X.J.Liu Deartment of Automation North China Electric Power University Beiing, China, 006 e-mail
More informationControl Systems. State Estimation.
State Estimation chibum@seoultech.ac.kr Outline Dominant pole design Symmetric root locus State estimation We are able to place the CLPs arbitrarily by feeding back all the states: u = Kx. But these may
More informationMicromechanics-based determination of effective. elastic properties of polymer bonded explosives
Miromehanis-based determination of effetive elasti roerties of olymer bonded exlosives Biswajit Banerjee and Daniel O. Adams Det. of Meh. Eng., Univ. of Utah, 50 S Central Camus Dr., Salt Lake City, UT
More informationsilicon wafers p b θ b IR heater θ h p h solution bath cleaning filter bellows pump
An Analysis of Cometitive Assoiative Net for Temerature Control of RCA Cleaning Solutions S Kurogi y, H Nobutomo y, T Nishida y, H Sakamoto y, Y Fuhikawa y, M Mimata z and K Itoh z ykyushu Institute of
More informationRouth-Hurwitz Lecture Routh-Hurwitz Stability test
ECE 35 Routh-Hurwitz Leture Routh-Hurwitz Staility test AStolp /3/6, //9, /6/ Denominator of transfer funtion or signal: s n s n s n 3 s n 3 a s a Usually of the Closed-loop transfer funtion denominator
More informationCDS 101/110: Lecture 2.1 System Modeling. Model-Based Analysis of Feedback Systems
CDS 11/11: Leture 21 System Modeling Rihard M Murray 5 Otober 215 Goals:! Define a model and its use in answering questions about a system! Introdue the onepts of state, dynamis, inputs and outputs! Review
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 informationFourier Series Tutorial
Fourier Series Tutorial INTRODUCTION This document is designed to overview the theory behind the Fourier series and its alications. It introduces the Fourier series and then demonstrates its use with a
More informationD(s) G(s) A control system design definition
R E Compensation D(s) U Plant G(s) Y Figure 7. A control system design definition x x x 2 x 2 U 2 s s 7 2 Y Figure 7.2 A block diagram representing Eq. (7.) in control form z U 2 s z Y 4 z 2 s z 2 3 Figure
More informationME 375 System Modeling and Analysis. Homework 11 Solution. Out: 18 November 2011 Due: 30 November 2011 = + +
Out: 8 November Due: 3 November Problem : You are given the following system: Gs () =. s + s+ a) Using Lalace and Inverse Lalace, calculate the unit ste resonse of this system (assume zero initial conditions).
More informationSmoldering Combustion of Horizontally Oriented Polyurethane Foam with Controlled Air Supply
Smoldering Combustion of Horizontally Oriented Polyurethane Foam with Controlled Air Suly LEI PENG, CHANG LU, JIANJUN ZHOU, LINHE ZHANG, and FEI YOU State Key Laboratory of Fire Siene, USTC Hefei Anhui,
More informationControl System Design
ELEC4410 Control System Design Lecture 19: Feedback from Estimated States and Discrete-Time Control Design Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science
More informationI Poles & zeros. I First-order systems. I Second-order systems. I E ect of additional poles. I E ect of zeros. I E ect of nonlinearities
EE C28 / ME C34 Lecture Chater 4 Time Resonse Alexandre Bayen Deartment of Electrical Engineering & Comuter Science University of California Berkeley Lecture abstract Toics covered in this resentation
More informationCharge-Pump Phase-Locked Loops
Phase-Locked Loos Charge-Pum Phase-Locked Loos Ching-Yuan Yang National Chung-Hsing University Deartment of Electrical Engineering Concetual oeration of a hase-frequency detector (PFD) PFD 5- Ching-Yuan
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 informationDesign of NARMA L-2 Control of Nonlinear Inverted Pendulum
International Research Journal of Alied and Basic Sciences 016 Available online at www.irjabs.com ISSN 51-838X / Vol, 10 (6): 679-684 Science Exlorer Publications Design of NARMA L- Control of Nonlinear
More informationGEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING
GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING ECE 226 Summer 28 Quiz #2 July 6, 28 NAME: (FIRST) (LAST) GT username: (e.g., gtxyz23) To avoid losing 3 oints, circle your
More informationDetection and Estimation Theory
ESE 524 Detetion and Estimation heory Joseh A. O Sullivan Samuel C. Sahs Professor Eletroni Systems and Signals Researh Laboratory Eletrial and Systems Engineering Washington University 2 Urbauer Hall
More informationDownloaded on T02:40:49Z
Title Author(s) Primary wave energy onversions of osillating water olumns Sheng, Wanan; Alorn, Raymond; Lewis, Anthony Publiation date 213-9 Original itation Tye of ubliation Link to ublisher's version
More informationInternal Model Control
Internal Model Control Part o a et o leture note on Introdution to Robut Control by Ming T. Tham 2002 The Internal Model Prinile The Internal Model Control hiloohy relie on the Internal Model Prinile,
More informationTopic # /31 Feedback Control Systems
Topic #12 16.30/31 Feedback Control Systems State-Space Systems Full-state Feedback Control How do we change location of state-space eigenvalues/poles? Or, if we can change the pole locations where do
More informationA Method of Setting the Penalization Constants in the Suboptimal Linear Quadratic Tracking Method
XXVI. ASR '21 Seminar, Instruments and Control, Ostrava, Aril 26-27, 21 Paer 57 A Method of Setting the Penalization Constants in the Subotimal Linear Quadratic Tracking Method PERŮTKA, Karel Ing., Deartment
More informationDynamic System Eigenvalue Extraction using a Linear Echo State Network for Small-Signal Stability Analysis a Novel Application
Dynamic System Eigenvalue Extraction using a Linear Echo State Network for Small-Signal Stability Analysis a Novel Alication Jiaqi Liang, Jing Dai, Ganesh K. Venayagamoorthy, and Ronald G. Harley Abstract
More informationState Regulator. Advanced Control. design of controllers using pole placement and LQ design rules
Advanced Control State Regulator Scope design of controllers using pole placement and LQ design rules Keywords pole placement, optimal control, LQ regulator, weighting matrixes Prerequisites Contact state
More informationUNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: NOVEMBER 2013 COURSE, SUBJECT AND CODE: THEORY OF MACHINES ENME3TMH2 MECHANICAL ENGINEERING
UNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: NOVEMBER 2013 COURSE, SUBJECT AND CODE: THEORY OF MACHINES ENME3TMH2 DURATION: 3 Hours MARKS: 100 MECHANICAL ENGINEERING Internal Examiner: Dr. R.C. Loubser Indeendent
More informationNONLINEAR ADAPTIVE OBSERVER DESIGN IN COMBINED ERROR NONLINEAR ADAPTIVE CONTROL
ХРАНИТЕЛНА НАУКА ТЕХНИКА И ТЕХНОЛОГИИ 3 8-9 октомври 3 Пловдив SCIENIFIC WORKS FOOD SCIENCE ENGINEERING AND ECHNOLOGY 3 8-9 Otober 3 Plovdiv NONLINEAR ADAPIVE OBSERVER DESIGN IN COMBINED ERROR NONLINEAR
More informationA NONLILEAR CONTROLLER FOR SHIP AUTOPILOTS
Vietnam Journal of Mehanis, VAST, Vol. 4, No. (), pp. A NONLILEAR CONTROLLER FOR SHIP AUTOPILOTS Le Thanh Tung Hanoi University of Siene and Tehnology, Vietnam Abstrat. Conventional ship autopilots are
More informationSYNTHESIS AND OPTIMIZATION OF EPICYCLIC-TYPE AUTOMATIC TRANSMISSIONS BASED ON NOMOGRAPHS
Al-Qadisiya Journal For Engineering Sienes Vol. 4 o. 3 Year 0 SYTHESIS AD OPTIMIZATIO OF EPICYCLIC-TYPE AUTOMATIC TASMISSIOS BASED O OMOGAPHS E. L. Esmail K. H. Salih Leturer Assistant Leturer Deartment
More informationRobust Performance Design of PID Controllers with Inverse Multiplicative Uncertainty
American Control Conference on O'Farrell Street San Francisco CA USA June 9 - July Robust Performance Design of PID Controllers with Inverse Multilicative Uncertainty Tooran Emami John M Watkins Senior
More informationLINEAR SYSTEMS WITH POLYNOMIAL UNCERTAINTY STRUCTURE: STABILITY MARGINS AND CONTROL
LINEAR SYSTEMS WITH POLYNOMIAL UNCERTAINTY STRUCTURE: STABILITY MARGINS AND CONTROL Mohammad Bozorg Deatment of Mechanical Engineering University of Yazd P. O. Box 89195-741 Yazd Iran Fax: +98-351-750110
More informationState Feedback and State Estimators Linear System Theory and Design, Chapter 8.
1 Linear System Theory and Design, http://zitompul.wordpress.com 2 0 1 4 2 Homework 7: State Estimators (a) For the same system as discussed in previous slides, design another closed-loop state estimator,
More informationIterative Methods for Designing Orthogonal and Biorthogonal Two-channel FIR Filter Banks with Regularities
R. Bregović and T. Saramäi, Iterative methods for designing orthogonal and biorthogonal two-channel FIR filter bans with regularities, Proc. Of Int. Worsho on Sectral Transforms and Logic Design for Future
More informationLag-Lead Compensator Design
Lag-Lead Compenator Deign ELEC 3 Spring 08 Lag or Lead Struture A bai ompenator onit of a gain, one real pole and one real zero Two type: phae-lead and phae-lag Phae-lead: provide poitive phae hift and
More informationInvestigating the Performance of a Hydraulic Power Take-Off
Investigating the Performane of a Hydrauli Power Take-Off A.R. Plummer and M. Shlotter Centre for Power Transmission and Control, University of Bath, Bath, BA 7AY, UK E-mail: A.R.Plummer@bath.a.uk E-mail:
More information1. Tc from BCS 2. Ginzburg-Landau theory 3. Josephson effect
Condensed Matter Physis 6 Leture 6/: More on superondutiity.. T from BCS. Ginzburg-Landau theory 3. Josephson effet Referenes: Ashroft & Mermin 34 Taylor & Heinonen 7.-7.5 7.7 blaboard Reall from last
More informationEE451/551: Digital Control. Chapter 7: State Space Representations
EE45/55: Digital Control Chapter 7: State Spae Representations State Variables Definition 7.: The system state is a minimal set of { variables x ( t ), i =, 2,, n needed together with the i input ut, and
More informationCourse Outline. Higher Order Poles: Example. Higher Order Poles. Amme 3500 : System Dynamics & Control. State Space Design. 1 G(s) = s(s + 2)(s +10)
Amme 35 : System Dynamics Control State Space Design Course Outline Week Date Content Assignment Notes 1 1 Mar Introduction 2 8 Mar Frequency Domain Modelling 3 15 Mar Transient Performance and the s-plane
More informationRUN-TO-RUN CONTROL AND PERFORMANCE MONITORING OF OVERLAY IN SEMICONDUCTOR MANUFACTURING. 3 Department of Chemical Engineering
Coyright 2002 IFAC 15th Triennial World Congress, Barcelona, Sain RUN-TO-RUN CONTROL AND PERFORMANCE MONITORING OF OVERLAY IN SEMICONDUCTOR MANUFACTURING C.A. Bode 1, B.S. Ko 2, and T.F. Edgar 3 1 Advanced
More informationTOWARD THE DEVELOPMENT OF A METHODOLOGY FOR DESIGNING HELICOPTER FLIGHT CONTROL LAWS BY INTEGRATING HANDLING QUALITIES REQUIREMENTS
TOWARD THE DEVELOPMENT OF A METHODOLOGY FOR DESIGNING HELICOPTER FLIGHT CONTROL LAWS BY INTEGRATING HANDLING QUALITIES REQUIREMENTS Jean-Charles Antonioli ONERA Air Base 70 366 Salon de Provene Frane Armin
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 informationNeural Network Predictive Control of a Chemical Reactor
Ata Chimia Slovaa, ol., No., 009, 1-36 Neural Network Preditive Control of a Chemial Reator Anna asičkaninová*, Monika Bakošová Institute of Information Engineering, Automation and Mathematis, Faulty of
More informationRemark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the function V ( x ) to be positive definite.
Leture Remark 4.1 Unlike Lyapunov theorems, LaSalle s theorem does not require the funtion V ( x ) to be positive definite. ost often, our interest will be to show that x( t) as t. For that we will need
More informationCSC321: 2011 Introduction to Neural Networks and Machine Learning. Lecture 11: Bayesian learning continued. Geoffrey Hinton
CSC31: 011 Introdution to Neural Networks and Mahine Learning Leture 11: Bayesian learning ontinued Geoffrey Hinton Bayes Theorem, Prior robability of weight vetor Posterior robability of weight vetor
More informationParticipation Factors. However, it does not give the influence of each state on the mode.
Particiation Factors he mode shae, as indicated by the right eigenvector, gives the relative hase of each state in a articular mode. However, it does not give the influence of each state on the mode. We
More informationA Comparison between Biased and Unbiased Estimators in Ordinary Least Squares Regression
Journal of Modern Alied Statistical Methods Volume Issue Article 7 --03 A Comarison between Biased and Unbiased Estimators in Ordinary Least Squares Regression Ghadban Khalaf King Khalid University, Saudi
More informationRobust Predictive Control of Input Constraints and Interference Suppression for Semi-Trailer System
Vol.7, No.7 (4),.37-38 htt://dx.doi.org/.457/ica.4.7.7.3 Robust Predictive Control of Inut Constraints and Interference Suression for Semi-Trailer System Zhao, Yang Electronic and Information Technology
More informationWave Propagation through Random Media
Chapter 3. Wave Propagation through Random Media 3. Charateristis of Wave Behavior Sound propagation through random media is the entral part of this investigation. This hapter presents a frame of referene
More informationCSC321: 2011 Introduction to Neural Networks and Machine Learning. Lecture 10: The Bayesian way to fit models. Geoffrey Hinton
CSC31: 011 Introdution to Neural Networks and Mahine Learning Leture 10: The Bayesian way to fit models Geoffrey Hinton The Bayesian framework The Bayesian framework assumes that we always have a rior
More informationControl Systems Design
ELEC4410 Control Systems Design Lecture 18: State Feedback Tracking and State Estimation Julio H. Braslavsky julio@ee.newcastle.edu.au School of Electrical Engineering and Computer Science Lecture 18:
More informationCompressor Surge Control Design Using Linear Matrix Inequality Approach
Comressor Surge Control Design Using Linear Matrix Inequality Aroach Nur Uddin Det. of Electrical Engineering Universitas Pertamina Jakarta, Indonesia Email: nur.uddin@universitasertamina.ac.id Jan Tommy
More informationApplication of Drucker-Prager Plasticity Model for Stress- Strain Modeling of FRP Confined Concrete Columns
Available online at www.sienediret.om Proedia Engineering 14 (211) 687 694 The Twelfth East Asia-Paifi Conferene on Strutural Engineering and Constrution Aliation of Druker-Prager Plastiity Model for Stress-
More informationExperimental study with analytical validation of thermo-hydraulic performance of plate heat exchanger with different chevron angles
Exerimental study with analytial validation of thermo-hydrauli erformane of late heat exhanger with different hevron angles Arunahala U C, Ajay R K and Sandee H M Abstrat The Plate heat exhanger is rominent
More informationLecture «Robot Dynamics»: Dynamics 1
Leture «Robot Dynamis»: Dynamis 1 151-0851-00 V leture: CAB G11 uesday 10:15 12:00, every week exerise: HG E1.2 Wednesday 8:15 10:00, aording to shedule (about every 2nd week) offie hour: LEE H303 Friday
More informationObserver/Kalman Filter Time Varying System Identification
Observer/Kalman Filter Time Varying System Identification Manoranjan Majji Texas A&M University, College Station, Texas, USA Jer-Nan Juang 2 National Cheng Kung University, Tainan, Taiwan and John L. Junins
More informationNAME section. BANNER ID N00 MAT 102 LAST EXAM Fall Complete each problem using the answer key general forms file provided.
NAME setion BANNER ID N00 MAT 0 LAST EXAM Fall 0 Comlete eah roblem using the answer key general forms file rovided. Chek-list for eah roblem: ) State the Model used: samling distribution of the means,
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 informationFlow Characteristics of High-Pressure Hydrogen Gas in the Critical Nozzle
Flow Charateristis of High-Pressure Hydrogen Gas in the Critial Nozzle Shigeru MATSUO *1, Soihiro KOYAMA *2, Junji NAGAO *3 and Toshiaki SETOGUCHI *4 *1 Saga University, Det. of Mehanial Engineering, 1
More informationTopic # Feedback Control Systems
Topic #17 16.31 Feedback Control Systems Deterministic LQR Optimal control and the Riccati equation Weight Selection Fall 2007 16.31 17 1 Linear Quadratic Regulator (LQR) Have seen the solutions to the
More informationarxiv: v2 [astro-ph] 1 Oct 2007
Mon. Not. R. Astron. So. 000, 1 25 (2007) Printed 20 June 2018 (MN LATEX style file v2.2) Long-term tidal evolution of short-eriod lanets with omanions arxiv:0706.0224v2 [astro-h] 1 Ot 2007 Rosemary A.
More informationFundamental Theorem of Calculus
Chater 6 Fundamental Theorem of Calulus 6. Definition (Nie funtions.) I will say that a real valued funtion f defined on an interval [a, b] is a nie funtion on [a, b], if f is ontinuous on [a, b] and integrable
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 informationThe simulation analysis of the bridge rectifier continuous operation in AC circuit
Computer Appliations in Eletrial Engineering Vol. 4 6 DOI 8/j.8-448.6. The simulation analysis of the bridge retifier ontinuous operation in AC iruit Mirosław Wiślik, Paweł Strząbała Kiele University of
More informationEvent-triggering stabilization of complex linear systems with disturbances over digital channels
Event-triggering stabilization of comlex linear systems with disturbances over digital channels Mohammad Javad Khojasteh, Mojtaba Hedayatour, Jorge Cortés, Massimo Franceschetti Abstract As stos and auses
More informationMost results in this section are stated without proof.
Leture 8 Level 4 v2 he Expliit formula. Most results in this setion are stated without proof. Reall that we have shown that ζ (s has only one pole, a simple one at s =. It has trivial zeros at the negative
More informationSolutions to Problem Set 1
Eon602: Maro Theory Eonomis, HKU Instrutor: Dr. Yulei Luo September 208 Solutions to Problem Set. [0 points] Consider the following lifetime optimal onsumption-saving problem: v (a 0 ) max f;a t+ g t t
More informationController Design Based on Transient Response Criteria. Chapter 12 1
Controller Design Based on Transient Response Criteria Chapter 12 1 Desirable Controller Features 0. Stable 1. Quik responding 2. Adequate disturbane rejetion 3. Insensitive to model, measurement errors
More informationarxiv: v2 [cs.ai] 16 Feb 2016
Cells in Multidimensional Reurrent Neural Networks arxiv:42.2620v2 [s.ai] 6 Feb 206 Gundram Leifert Tobias Sauß Tobias Grüning Welf Wustlih Roger Labahn University of Rostok Institute of Mathematis 805
More informationFeedback-Based Iterative Learning Control for MIMO LTI Systems
International Journal of Control, Feedback-Based Automation, Iterative and Systems, Learning vol. Control 6, no., for. MIMO 69-77, LTI Systems Aril 8 69 Feedback-Based Iterative Learning Control for MIMO
More informationDEVELOPMENT OF A MULTI-FEED P-T WELLBORE MODEL FOR GEOTHERMAL WELLS
PROCEEDINGS, Thirty-First Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, California, January 3-February 1, 6 SGP-TR-179 DEVELOPMENT OF MULTI-FEED P-T WELLBORE MODEL FOR GEOTHERML
More informationImproved Extended Kalman Filter for Parameters Identification
Improved Extended Kalman Filter for Parameters Identifiation Peipei Zhao. Zhenyu Wang. ao Lu. Yulin Lu Institute of Disaster Prevention, Langfang,Hebei Provine, China SUMMARY: he extended Kalman filter
More informationtwenty steel construction: columns & tension members ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS FALL 2018 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS Cor-Ten Steel Sulpture By Rihard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Strutures of the Everyday) FALL 2018 leture
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More information