Control of industrial robots. Decentralized control
|
|
- Willis Hampton
- 5 years ago
- Views:
Transcription
1 Control of indutrial robot Decentralized control Prof Paolo Rocco Politecnico di Milano Dipartiento di Elettronica, Inforazione e Bioingegneria
2 Introduction Once the deired otion of the robot ha been coputed, a real tie controller enure that thi otion i tracked in the bet poible way All indutrial robot are in fact endowed with uch a real tie otion controller The indutrial robot control follow the independent joint control approach, ie it i a purely decentralized, non odel baed, control yte We will dicu the rationale behind thi approach and recognize it a the proble of controlling everal independent ervoechani Control of indutrial robot Decentralized control Paolo Rocco
3 Motion control interface The otion controller i one of the functional unit of a robot controller: external enor environent tak planner trajectory planner control robot internal enor We will now conider the lowet level part of the robot control yte, directly interacting with the robot internal enor and actuator Control of indutrial robot Decentralized control Paolo Rocco
4 Evaluation of control perforance What are poible criteria to evaluate the perforance of a otion control yte? Quality of otion in noinal condition accuracy/repeatability peed of tak execution energy aving Robutne of otion in perturbed condition adaptation to the environent high repeatability in pite of uncertaintie in odelling error Fro Robotic, Prof Aleandro De Luca, Univerity of Roe La Sapienza Control of indutrial robot Decentralized control Paolo Rocco
5 Decentralized odel Let u conider the dynaic odel of the anipulator: B ( q) q C( q, q ) q g( q) τ Aue that a otor act on each joint of the anipulator A iplified way to account for the dynaic of uch otor i to conider jut the effect related to the pinning of the otor around it own axi q i τ i q i τ i otor reduction n i : link Control of indutrial robot Decentralized control Paolo Rocco
6 Decentralized odel The dynaic odel of the otor i thu iply: J q i i Diq i τi τli i,, n where J i and D i are the oent of inertia and the coefficient of vicou friction of the otor, repectively, while τ li i the load torque at the axi of otor i, equal to: τ li τ i n i n i i the reduction ratio of the traniion between the i_th otor and the joint Auing that the traniion eleent are rigid, we alo have: q n i i q i Control of indutrial robot Decentralized control Paolo Rocco
7 Decentralized odel We now decopoe the inertia atrix into the u of a diagonal and contant ter ( average inertia) and a reidual ter: B ( q) B B( q) If we et: J { J }, D diag{ D }, N diag{ n }, B N B diag N i i i r re-organizing the equation we have: ( J Br ) q Dq d τ or: ( J b ) q D q d τ, i, n i rii i i i i i, where: d N B( q) N q N C( q, q ) N q N g( q) average inertia caled by the quare of the b traniion ratio: b rii n ii i Control of indutrial robot Decentralized control Paolo Rocco
8 Decentralized odel NON LINEAR COUPLED N g() N C(,)N N B()N d τ q (J B r ) q q The equation we have obtained can be interpreted a thoe of a linear and copletely decoupled yte, ubjected to a diturbance deriving fro the nonlinear and coupled ter of the dynaic odel The larger the reduction ratio n i, the le relevant i the diturbance ter D LINEAR DECOUPLED Control of indutrial robot Decentralized control Paolo Rocco
9 Independent joint control The decentralized odel of the robot dynaic i ued in the independent joint control, a widely ued approach in the indutrial robot controller q d R τ q The control yte i articulated in n SISO control loop, ignoring the dynaic coupling effect which are dealt with a diturbance The ingle control proble are aiilated to the control of a ervoechani q d R τ q dn q τ n The ethod heavily relie on the large value of the reduction ratio adopted in robotic Without thi effect, neglecting the variability of the inertia and the echanical coupling with the other joint would be poorly jutified R n q n Control of indutrial robot Decentralized control Paolo Rocco
10 The ervoechani traniion otor load A ervoechani i a paradigatic yte copoed of a otor, a echanical load and whatever traniion yte in between The proble i to control the otion of the load, uitably odulating the torque applied by the otor Different cenario can be given a far a the available enor are concerned: poition/peed at the otor and/or load ide However we uually have the otor current available a a eaure too: we will ee a clever way to ake ue of thi eaure, which greatly iplifie the otion control Control of indutrial robot Decentralized control Paolo Rocco
11 The electrical dynaic Aue that a DC otor i ued, whoe electrical chee can be iplified a follow: I R L V E A voltage V i applied which produce a current in the arature circuit through the dynaic induced by the reitance R and the inductance L A back ef E, proportional to the otor angular peed ω, i alo preent Thank to the electro-echanical converion ipleented by the bruhe-coutator yte, the otor deliver a torque τ which i proportional to the current I In indutrial robotic bruhle otor are ore coonly ued, for which however a iilar decription can be given, referred to the quadrature axi Control of indutrial robot Decentralized control Paolo Rocco
12 Electrical and echanical dynaic The yte i decribed by the following equation: I R L V ( t ) RI( t ) LI ( t ) E( t) V E τ τ q ( ) Kω ( t) E t ( t ) KI( t ) ( t ) J ω ( t ) ( t ) ω ( t ) which can be expreed by thi block diagra: V E LR I K K τ J ω q Notice that the back ef couple the electrical dynaic with the echanical dynaic Control of indutrial robot Decentralized control Paolo Rocco
13 Current control If a current eaure i available, we ight cloe a control loop around the current: I o R I () V E LR I K K τ J ω q ince the electrical dynaic i quite fat (copared with the echanical one) we will deign the current controller R I () o a to achieve a wide bandwidth (thouand rad/) in the deign of the current controller the ef can be conidered a a lowly varying diturbance, that the controller can effectively reject once the current control loop i cloed, it can be een a practically intantaneou fro the external poition/peed controller: τ o ( t ) KI( t ) KI ( t ) thi i why in the following we will aue that the otor torque τ i the control variable for the poition/peed control proble Control of indutrial robot Decentralized control Paolo Rocco
14 The rigid approxiation A firt way to approach the otion control proble i to conider the ervoechani (otor, load, and traniion) a a rigid yte In thi cae the equation of the yte are: otor load : : J J q l q l D nτ l q τ l τ τ l q τ J J l τ l q l traniion : q nq l (D : otor vicou friction coefficient; J l : load oent of inertia; n: traniion ratio; τ l : tranitted torque, otor ide; τ l : external torque, load ide) Eliinating q l and τ l fro thee equation, we obtain: ( J Jlr ) q Dq τ τlr with: J lr Jl, n τ lr τl n Control of indutrial robot Decentralized control Paolo Rocco
15 The rigid approxiation The rigid yte can be decribed in ter of tranfer function: with: τ τ lr G v () q q G v ( ) D ( J J ) lr If the friction coefficient D i neglected (which i the ot conervative ituation, ince the friction give a tabilizing effect but the value of thi coefficient i uncertain) we have: G v ( ) µ, µ J J lr Control of indutrial robot Decentralized control Paolo Rocco
16 P/PI control Let u cloe a PI controller on the peed and a proportional controller on the poition: q o K pp R PI () τ τ lr G v () q / q Thi control chee need two independent eaureent, one for the poition (encoder or reolver), the other one for the peed (tacho) It i a cacaded control chee: firt the internal peed loop i deigned for a large bandwidth, o a to enure a good diturbance rejection, too the external poition loop i then deigned for a retricted bandwidth in fact there are three neted loop: current, peed, and poition loop Control of indutrial robot Decentralized control Paolo Rocco
17 Deign of the PI peed controller PI controller q o R PI () τ τ lr G v () q R PI ( ) T K pv K pv T iv Tiv Loop tranfer function: K Lv ( ) RPI ( ) Gv ( ) If T iv i ufficiently large, ie if the zero of the PI i in a ufficiently low frequency range, the croover frequency ω cv i well approxiated by the high frequency approxiation of L: ( 0 0 ) ω cv 3 placeent of the PI zero Control of indutrial robot Decentralized control Paolo Rocco T iv pv µ T T iv iv iv db T iv ω cv w (rad/) L v ( ) ω cv ω cv K pv µ election of the PI gain
18 Deign of the P poition controller The poition controller ee the peed cloed loop, whoe tranfer function can be approxiated a: F v The loop tranfer function i thu: L ( ) p ω cv ( ) K F ( ) pp v q o It i enough to take K pp << ω cv in order to guarantee a croover frequency ω cp : K pp ( ω ) cv db K pp q o F v () ωcp q / w (rad/) ωcv q ωcp K pp election of the P gain Control of indutrial robot Decentralized control Paolo Rocco
19 Speed feedforward q o K pp R PI () τ τ lr G v () q / q In order to get a fater repone to the poition reference, it i poible to include a feedforward contribution, known a peed feedforward : the poition reference i differentiated and the contribution i added to the peed loop Uually the peed feedforward i weighted by a coefficient k ff copried between 0 and : q o k ff K pp R PI () τ τ lr G v () q / q Control of indutrial robot Decentralized control Paolo Rocco
20 Speed feedforward and PID If only a poition enor i ued and the peed i obtained differentiating the poition eaure, a chee which i fully equivalent to a PID controller i obtained: q o K pp R PI () τ τ lr G v () q / q q o R PID () τ τ lr G v () q / q R PID ( ) KP TD TI K T T P D I K pv K K pv K p K ptiv K K pp pv pp T iv Control of indutrial robot Decentralized control Paolo Rocco
21 Liitation of the rigid odel The rigid odel doe not entail any ignificant liitation to the bandwidth of the peed controller: in principle we ight obtain an arbitrarily fat cloed loop yte In practice liitation clearly eerge, in ter of vibration, noie, ocillation, etc Obviouly the rigid odel it i not adequate to explain how a ervoechani behave in cae the required perforance are increaed We need to coplicate the odel Control of indutrial robot Decentralized control Paolo Rocco
22 Two-a approxiation The iplet way to account for non-rigid behaviour of the yte i to include an elatic coupling between otor and load, which are till conidered rigid yte In thi cae the equation becoe: otor load : : traniion : J J q τ l l q l D nτ K el l q ( q nq ) D ( q nq ) τ l τ l τ l el l q, τ J D K el el J l q, τ l l Block diagra: q l J l τ l τ q J D q q l n D el K el τ l n now we have a 4 th order yte Control of indutrial robot Decentralized control Paolo Rocco
23 Liitation in the bandwidth If we revie the deign of the peed controller accounting for the flexibility in the joint, a it i done in baic robotic coure (ee background aterial), we coe up with liitation in the bandwidth of the peed controller Specifically, if we et: ω z K J el lr we have a a reaonable rule to tune the controller: ω 0 7 cv ω z The bandwidth of the poition controller ha to be reduced accordingly Control of indutrial robot Decentralized control Paolo Rocco
24 Background aterial Control of indutrial robot Decentralized control Paolo Rocco
25 A SITO yte Let u tudy the repone of the two-a yte to the torque coand τ (we then et τ l 0) The yte can be interpreted a a SITO (Single Input Two Output) yte: τ Solving the block diagra we have: G v ( ) J lr J 3 J lr D G v () G vl () el K q nq l / / q nq l ( JDel Jlr D ) ( JKel DDel ) DKel el the nuerator are different G vl ( ) J lr J 3 ( JD J D ) ( JK D Del ) DKel el lr D el K el el Jl J lr, J Jlr J n Control of indutrial robot Decentralized control Paolo Rocco
26 Relevant paraeter A in the rigid cae, we et D 0 The following paraeter are defined: ρ J J lr (inertia ratio) ω z Kel Del, ζ z J J K lr lr el (natural frequency and daping coefficient of the zero) µ ω ρ ω, ζ ρ ζ p z We then have: ζ z µ ωz ω Gv( ) ζ p J ω ω p p z rigid odel z p (natural frequency and daping coefficient of the pole) elatic effect G vl ( ) ζ z µ ωz ζ p ω ω p p Control of indutrial robot Decentralized control Paolo Rocco
27 Natural and locked frequencie The frequencie ω p and ω z have a very clear phyical interpretation: When the yte i uncontrained, it vibrate at the frequency of the pole of G v, ie ω p : thi i called natural frequency of the yte J D K el el J l When the otor i echanically contrained, the yte vibrate at the frequency of the zero of G v, ie ω z : thi i called locked frequency of the yte J D K el el J l Control of indutrial robot Decentralized control Paolo Rocco
28 Location of pole and zero Where are pole and zero of G v located in the coplex plane? G v ( ) µ ζ z ωz ζ p ω p I ω ω z p ω ω p z ζ ζ p z ρ > ω p ω z ζ p ω p ζ z ω z Re The pole are in a higher frequency range and are ore daped than the zero Control of indutrial robot Decentralized control Paolo Rocco
29 Frequency repone What i the hape of the frequency repone of G v? G v ( ) µ ζ z ωz ζ p ω p ω ω z p 40 ρ ζ z reonance G v ω/ω z antireonance Control of indutrial robot Decentralized control Paolo Rocco
30 A foral repreentation If τ l 0, we can conveniently repreent the yte with the following block diagra: q nq l τ G v () / q G l () where the otor poition and the load poition (referred to the otor haft) are forally linked by thi tranfer function: G l ( ) ζ z ω z z ζ z ω ω z Control of indutrial robot Decentralized control Paolo Rocco
31 P/PI control on the otor In indutrial robotic, enor are uually located only on otor ide Let u concentrate on the repone to change in the reference ignal (τ l 0): q o K pp R PI () τ G v () q / q G l () nq l If the peed i obtained a a derivative of poition: q o K pp R PI () τ G v () q / q G l () nq l Control of indutrial robot Decentralized control Paolo Rocco
32 P/PI control on the otor R PI () τ G v () q R v PI ( ) T K pv K pv T iv Tiv Loop tranfer function: L ( ) R ( ) G ( ) PI v K pv µ T T iv iv iv ζ z ωz ζ p ω p ω ω z p Let u introduce the following noralized deign paraeter: ω ~ cv K pv ω z µ it i the deign croover frequency, evaluated on the rigid odel (K pv µ), noralized to the frequency ω z : ~ large ω cv : aggreive deign all ω ~ cv : cautiou deign Control of indutrial robot Decentralized control Paolo Rocco
33 Frequency repone analyi Let u place the zero of the PI one decade before the antireonance frequency ω z : T iv 0 ωz We analyze Bode diagra of the loop tranfer function in two cae: ω~ cv 05 ~ ω cv ρ ζ z L v 0 L v 0 arg(l v ) ω/ω z arg(l v ) ω/ω z The phae argin i large in both cae ω/ω z ω/ω z Control of indutrial robot Decentralized control Paolo Rocco
34 Frequency repone analyi Fro the Bode tability criterion we cannot dicriinate between the two project They both ee to yield control yte with a high tability argin However if we take a look at the cloed loop frequency repone, fro otor and load ide, in the aggreive deign cae: ~ 5 ω cv otor load There i a clear reonance at the load ide, which i aociated to ocillation db ω/ω z Control of indutrial robot Decentralized control Paolo Rocco
35 Speed loop: root locu ~ Let draw the root locu at varying ω cv (equivalently K pv ): 5 Iaginary Axi 05 0 There are coplex pole whoe daping firt increae and then decreae The axiu daping i obtained when: ω~ cv ( ω 07ω ) cv 07 z deign guideline Real Axi Note: in thi locu and in the next one, the axe are noralized to ω z for increaed generality Control of indutrial robot Decentralized control Paolo Rocco
36 Proportional poition control q o K pp F v () q / q G l () nq l F v ( ) ( ) ( ) Lv peed cloed loop L v The loop tranfer function for the poition control i then: L ( ) p We introduce in thi cae, too, a noralized deign paraeter: K pp F v ( ) ω ~ cp K ω pp z it i the deign croover frequency, evaluated on the rigid odel (K pp ), noralized to the frequency ω z Control of indutrial robot Decentralized control Paolo Rocco
37 Poition loop: root locu ( ) Fv Lp ( ) K pp We draw the root locu at varying ω~ cp (equivalently K pp ) for different value of ~ ω cv : ω~ cv 05 ω~ cv ~ 5 ω cv Iag Axi 0 - Iag Axi 0 - Iag Axi Real Axi Real Axi Real Axi Larger bandwidth of the peed loop generate lightly daped pole, which in turn entail poor perforance of the poition loop Control of indutrial robot Decentralized control Paolo Rocco
38 Siulation We iulate in Siulink the coplete yte, including a tep on the external torque on the load ide (torque diturbance): Control of indutrial robot Decentralized control Paolo Rocco
39 Siulation Syte: ω z 00 rad/, ρ, ζ z 0 Speed PI: T iv 0/ω z Poition P: ω~ cp ω~ cv 05 ~ 5 otor load 5 ω cv otor load 04 0 torque diturbance t 05 torque diturbance t Control of indutrial robot Decentralized control Paolo Rocco
40 P control on the load and PI control on the otor In everal application, like with achine tool, the poition loop i cloed at the load ide: nq o l K pp R PI () τ G v () q / q G l () nq l In cae the otor peed i obtained differentiating the poition: nq o l K pp R PI () τ G v () q / q G l () nq l Control of indutrial robot Decentralized control Paolo Rocco
41 P poition control nq o l K pp F v () q / q G l () nq l F v ( ) ( ) ( ) Lv Nothing change a far a the peed loop i concerned L v The loop tranfer function for the poition control i now: L ( ) p K pp F v ( ) G l ( ), G l ζ z ωz ( ) ζ z ω ω z z Control of indutrial robot Decentralized control Paolo Rocco
42 Root locu L ( ) p K pp Fv ( ) G l ( ) We draw the root locu at varying ω~ cp (equivalently K pp ) for different value of ~ ω cv : ω~ cv 05 ω~ cv ~ 5 ω cv 3 ~ ax 07 ω cp 3 3 ω~ cp ax 063 ~ ax 0 5 ω cp Iag Axi 0 Iag Axi 0 Iag Axi Real Axi Real Axi Real Axi At increaing bandwidth of the peed loop the deign of the poition loop becoe ore coplicated Even for all value of K pp the yte can get untable Control of indutrial robot Decentralized control Paolo Rocco
43 Siulation We iulate again in Siulink the coplete yte, including a tep on the external torque on the load ide (torque diturbance): Control of indutrial robot Decentralized control Paolo Rocco
44 Siulation Syte: ω z 00 rad/, ρ, ζ z 0 Speed PI: T iv 0/ω z Poition P: ω cp 0 ~ ω~ cv 05 ~ 5 otor load 5 ω cv otor load 04 0 torque diturbance 05 torque diturbance t t Control of indutrial robot Decentralized control Paolo Rocco
45 Siulation Syte: ω z 00 rad/, ρ, ζ z 0 Speed PI: T iv 0/ω z Poition P: ω~ cp 07 ~ 5 ω cv 3 x otor load The yte i untable t Control of indutrial robot Decentralized control Paolo Rocco
CHAPTER 13 FILTERS AND TUNED AMPLIFIERS
HAPTE FILTES AND TUNED AMPLIFIES hapter Outline. Filter Traniion, Type and Specification. The Filter Tranfer Function. Butterworth and hebyhev Filter. Firt Order and Second Order Filter Function.5 The
More informationLecture 8. PID control. Industrial process control ( today) PID control. Insights about PID actions
Lecture 8. PID control. The role of P, I, and D action 2. PID tuning Indutrial proce control (92... today) Feedback control i ued to improve the proce performance: tatic performance: for contant reference,
More informationADAPTIVE CONTROL DESIGN FOR A SYNCHRONOUS GENERATOR
ADAPTIVE CONTROL DESIGN FOR A SYNCHRONOUS GENERATOR SAEED ABAZARI MOHSEN HEIDARI NAVID REZA ABJADI Key word: Adaptive control Lyapunov tability Tranient tability Mechanical power. The operating point of
More informationLecture 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 informationThe Extended Balanced Truncation Algorithm
International Journal of Coputing and Optiization Vol. 3, 2016, no. 1, 71-82 HIKARI Ltd, www.-hikari.co http://dx.doi.org/10.12988/ijco.2016.635 The Extended Balanced Truncation Algorith Cong Huu Nguyen
More informationCh. 6 Single Variable Control ES159/259
Ch. 6 Single Variable Control Single variable control How o we eterine the otor/actuator inut o a to coan the en effector in a eire otion? In general, the inut voltage/current oe not create intantaneou
More informationLecture 8 - SISO Loop Design
Lecture 8 - SISO Loop Deign Deign approache, given pec Loophaping: in-band and out-of-band pec Fundamental deign limitation for the loop Gorinevky Control Engineering 8-1 Modern Control Theory Appy reult
More informationDigital Control System
Digital Control Sytem - A D D A Micro ADC DAC Proceor Correction Element Proce Clock Meaurement A: Analog D: Digital Continuou Controller and Digital Control Rt - c Plant yt Continuou Controller Digital
More informationANALOG REALIZATIONS OF FRACTIONAL-ORDER INTEGRATORS/DIFFERENTIATORS A Comparison
AALOG REALIZATIOS OF FRACTIOAL-ORDER ITEGRATORS/DIFFERETIATORS A Coparion Guido DEESD, Technical Univerity of Bari, Via de Gaperi, nc, I-7, Taranto, Italy gaione@poliba.it Keyword: Abtract: on-integer-order
More informationIndependent Joint Control
ME135 ADANCED OBOICS Independent oint Contro ee-hwan yu Schoo of Mechanica Engineering Introduction to Contro Contro: deterining the tie hitory of joint input to do a coanded otion Contro ethod are depend
More informationIN SUPERVISING the correct operation of dynamic plants,
1158 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 14, NO. 6, NOVEMBER 2006 Nonlinear Fault Detection and Iolation in a Three-Tank Heating Syte Raffaella Mattone and Aleandro De Luca, Senior Meber,
More informationConservation of Energy
Add Iportant Conervation of Energy Page: 340 Note/Cue Here NGSS Standard: HS-PS3- Conervation of Energy MA Curriculu Fraework (006):.,.,.3 AP Phyic Learning Objective: 3.E.., 3.E.., 3.E..3, 3.E..4, 4.C..,
More informationLecture 17: Frequency Response of Amplifiers
ecture 7: Frequency epone of Aplifier Gu-Yeon Wei Diiion of Engineering and Applied Science Harard Unierity guyeon@eec.harard.edu Wei Oeriew eading S&S: Chapter 7 Ski ection ince otly decribed uing BJT
More informationGain and Phase Margins Based Delay Dependent Stability Analysis of Two- Area LFC System with Communication Delays
Gain and Phae Margin Baed Delay Dependent Stability Analyi of Two- Area LFC Sytem with Communication Delay Şahin Sönmez and Saffet Ayaun Department of Electrical Engineering, Niğde Ömer Halidemir Univerity,
More informationLecture 5 Introduction to control
Lecture 5 Introduction to control Tranfer function reviited (Laplace tranform notation: ~jω) () i the Laplace tranform of v(t). Some rule: ) Proportionality: ()/ in () 0log log() v (t) *v in (t) () * in
More informationTopic 7 Fuzzy expert systems: Fuzzy inference
Topic 7 Fuzzy expert yte: Fuzzy inference adani fuzzy inference ugeno fuzzy inference Cae tudy uary Fuzzy inference The ot coonly ued fuzzy inference technique i the o-called adani ethod. In 975, Profeor
More informationECE 3510 Root Locus Design Examples. PI To eliminate steady-state error (for constant inputs) & perfect rejection of constant disturbances
ECE 350 Root Locu Deign Example Recall the imple crude ervo from lab G( ) 0 6.64 53.78 σ = = 3 23.473 PI To eliminate teady-tate error (for contant input) & perfect reection of contant diturbance Note:
More informationSliding-Mode Bilateral Teleoperation Control Design for Master-Slave Pneumatic Servo Systems
Thi paper appear in Control Engineering Practice, 212. http://dx.doi.org/1.116/j.conengprac.212.2.3 Sliding-Mode Bilateral Teleoperation Control Deign for Mater-Slave Pneuatic Servo Syte R. Moreau 1, M.T.
More informationAcceleration Feedback in a Stage Having Paired Reluctance Linear Actuator with Hysteresis. Qing-sheng CHEN, Xiao-feng YANG and Li-wei WU
06 International Conference on Electrical Engineering and Autoation (ICEEA 06) ISBN: 978--60595-407-3 Acceleration eedback in a Stage Having Paired Reluctance Linear Actuator with Hyterei Qing-heng CHEN,
More informationFractional-Order PI Speed Control of a Two-Mass Drive System with Elastic Coupling
Fractional-Order PI Speed Control of a Two-Ma Drive Sytem with Elatic Coupling Mohammad Amin Rahimian, Mohammad Saleh Tavazoei, and Farzad Tahami Electrical Engineering Department, Sharif Univerity of
More informationPhysics 20 Lesson 28 Simple Harmonic Motion Dynamics & Energy
Phyic 0 Leon 8 Siple Haronic Motion Dynaic & Energy Now that we hae learned about work and the Law of Coneration of Energy, we are able to look at how thee can be applied to the ae phenoena. In general,
More information( ) Zp THE VIBRATION ABSORBER. Preamble - A NEED arises: lbf in. sec. X p () t = Z p. cos Ω t. Z p () r. ω np. F o. cos Ω t. X p. δ s.
THE VIBRATION ABSORBER Preable - A NEED arie: Lui San Andre (c) 8 MEEN 363-617 Conider the periodic forced repone of a yte (Kp-Mp) defined by : 1 1 5 lbf in : 1 3 lb (t) It natural frequency i: : ec F(t)
More informationFRTN10 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 informationG(s) = 1 s by hand for! = 1, 2, 5, 10, 20, 50, and 100 rad/sec.
6003 where A = jg(j!)j ; = tan Im [G(j!)] Re [G(j!)] = \G(j!) 2. (a) Calculate the magnitude and phae of G() = + 0 by hand for! =, 2, 5, 0, 20, 50, and 00 rad/ec. (b) ketch the aymptote for G() according
More informationScale Efficiency in DEA and DEA-R with Weight Restrictions
Available online at http://ijdea.rbiau.ac.ir Int. J. Data Envelopent Analyi (ISSN 2345-458X) Vol.2, No.2, Year 2014 Article ID IJDEA-00226, 5 page Reearch Article International Journal of Data Envelopent
More informationModeling & Analysis of the International Space Station
Modeling & Analysis of the International Space Station 1 Physical Syste Solar Alpha Rotary Joints Physical Syste Rotor Stator Gear Train Solar Array Inboard Body Outboard Body +x Solar Array 3 Physical
More informationPHYSICS 211 MIDTERM II 12 May 2004
PHYSIS IDTER II ay 004 Exa i cloed boo, cloed note. Ue only your forula heet. Write all wor and anwer in exa boolet. The bac of page will not be graded unle you o requet on the front of the page. Show
More informationFrequency Response Analysis of Linear Active Disturbance Rejection Control
Senor & Tranducer, Vol. 57, Iue, October 3, pp. 346-354 Senor & Tranducer 3 by IFSA http://www.enorportal.co Freuency Repone Analyi of Linear Active Diturbance Reection Control Congzhi HUANG, Qing ZHENG
More informationSIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuits II. Solutions to Assignment 3 February 2005.
SIMON FRASER UNIVERSITY School of Engineering Science ENSC 320 Electric Circuit II Solution to Aignment 3 February 2005. Initial Condition Source 0 V battery witch flip at t 0 find i 3 (t) Component value:
More informationSection J8b: FET Low Frequency Response
ection J8b: FET ow Frequency epone In thi ection of our tudie, we re o to reiit the baic FET aplifier confiuration but with an additional twit The baic confiuration are the ae a we etiated ection J6 of
More informationMultivariable Control Systems
Lecture Multivariable Control Sytem Ali Karimpour Aociate Profeor Ferdowi Univerity of Mahhad Lecture Reference are appeared in the lat lide. Dr. Ali Karimpour May 6 Uncertainty in Multivariable Sytem
More informationR. 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 informationLOW 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 informationSolutions. 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 informationS E V E N. Steady-State Errors SOLUTIONS TO CASE STUDIES CHALLENGES
S E V E N Steady-State Error SOLUTIONS TO CASE STUDIES CHALLENGES Antenna Control: Steady-State Error Deign via Gain 76.39 a. G( (50)(.3). Syte i Type. Step input: e( ) 0; Rap input: e( ) v 76.39.59 ;
More informationMassachusetts 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 informationModeling and Simulation of a Two-Mass Resonant System with Speed Controller
International ournal of Information and Electronic Engineering, Vol. 3, No. 5, eptember 203 odeling and imulation of a Two-a Reonant ytem with peed ontroller Ghazanfar hahgholian, ember, IAIT Abtract The
More informationRobust 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 informationBogoliubov 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 informationOn the Use of High-Order Moment Matching to Approximate the Generalized-K Distribution by a Gamma Distribution
On the Ue of High-Order Moent Matching to Approxiate the Generalized- Ditribution by a Gaa Ditribution Saad Al-Ahadi Departent of Syte & Coputer Engineering Carleton Univerity Ottawa Canada aahadi@ce.carleton.ca
More informationMODE SHAPE EXPANSION FROM DATA-BASED SYSTEM IDENTIFICATION PROCEDURES
Mecánica Coputacional Vol XXV, pp. 1593-1602 Alberto Cardona, Norberto Nigro, Victorio Sonzogni, Mario Storti. (Ed.) Santa Fe, Argentina, Noviebre 2006 MODE SHAPE EXPANSION FROM DATA-BASED SYSTEM IDENTIFICATION
More informationForce Reflecting Bilateral Control of Master-Slave Systems in Teleoperation
Force Reflecting Bilateral Control of Mater Syte in Teleoperation A. ALFI, M. FARROKHI Departent of Electrical Engineering, Center of Excellence for Power Syte Autoation and Operation Iran Univerity of
More informationTrajectory Planning and Feedforward Design for High Performance Motion Systems
Trajectory Planning and Feedforward Deign for High Performance Motion Sytem Paul Lambrecht, Matthij Boerlage, Maarten Steinbuch Faculty of Mechanical Engineering, Control Sytem Technology Group Eindhoven
More informationS_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 informationWolfgang Hofle. CERN CAS Darmstadt, October W. Hofle feedback systems
Wolfgang Hofle Wolfgang.Hofle@cern.ch CERN CAS Darmtadt, October 9 Feedback i a mechanim that influence a ytem by looping back an output to the input a concept which i found in abundance in nature and
More informationImage Denoising Based on Non-Local Low-Rank Dictionary Learning
Advanced cience and Technology Letter Vol.11 (AT 16) pp.85-89 http://dx.doi.org/1.1457/atl.16. Iage Denoiing Baed on Non-Local Low-Rank Dictionary Learning Zhang Bo 1 1 Electronic and Inforation Engineering
More informationControl Issues for Velocity Sourced Series Elastic Actuators
Control Iue for Velocity Sourced Serie Elatic Actuator Gordon Wyeth School of Information Technology and Electrical Engineering Univerity of Queenland wyeth@itee.uq.edu.au Abtract The Serie Elaic Actuator
More informationSMALL-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 informationME 375 FINAL EXAM Wednesday, May 6, 2009
ME 375 FINAL EXAM Wedneday, May 6, 9 Diviion Meckl :3 / Adam :3 (circle one) Name_ Intruction () Thi i a cloed book examination, but you are allowed three ingle-ided 8.5 crib heet. A calculator i NOT allowed.
More informationEnergy Shaping Nonlinear Acceleration Control for a Mobile Inverted Pendulum with a Slider Mechanism Utilizing Instability
Proceeding of the World Congre on Engineering and Coputer Science Vol I WCECS, October 4-6,, San Francico, USA Energy Shaping Nonlinear Acceleration Control for a obile Inverted Pendulu ith a Slider echani
More informationControl Systems Engineering ( Chapter 7. Steady-State Errors ) Prof. Kwang-Chun Ho Tel: Fax:
Control Sytem Engineering ( Chapter 7. Steady-State Error Prof. Kwang-Chun Ho kwangho@hanung.ac.kr Tel: 0-760-453 Fax:0-760-4435 Introduction In thi leon, you will learn the following : How to find the
More informationLecture 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 informationControl and simulation of doubly fed induction generator for variable speed wind turbine systems based on an integrated finite element approach
Control and iulation of doubly fed induction generator for variable peed wind turbine yte baed on an integrated finite eleent approach Qiong-zhong Chen*, Michel Defourny #, Olivier Brül* * Univerity of
More information376 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 informationCHAPTER 4 DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL
98 CHAPTER DESIGN OF STATE FEEDBACK CONTROLLERS AND STATE OBSERVERS USING REDUCED ORDER MODEL INTRODUCTION The deign of ytem uing tate pace model for the deign i called a modern control deign and it i
More informationQuestion 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 informationNAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE
POLITONG SHANGHAI BASIC AUTOMATIC CONTROL June Academic Year / Exam grade NAME (pinyin/italian)... MATRICULATION NUMBER... SIGNATURE Ue only thee page (including the bac) for anwer. Do not ue additional
More information15 N 5 N. Chapter 4 Forces and Newton s Laws of Motion. The net force on an object is the vector sum of all forces acting on that object.
Chapter 4 orce and ewton Law of Motion Goal for Chapter 4 to undertand what i force to tudy and apply ewton irt Law to tudy and apply the concept of a and acceleration a coponent of ewton Second Law to
More informationGiven the following circuit with unknown initial capacitor voltage v(0): X(s) Immediately, we know that the transfer function H(s) is
EE 4G Note: Chapter 6 Intructor: Cheung More about ZSR and ZIR. Finding unknown initial condition: Given the following circuit with unknown initial capacitor voltage v0: F v0/ / Input xt 0Ω Output yt -
More informationThe Measurement of DC Voltage Signal Using the UTI
he Meaurement of DC Voltage Signal Uing the. INRODUCION can er an interface for many paive ening element, uch a, capacitor, reitor, reitive bridge and reitive potentiometer. By uing ome eternal component,
More informationMarch 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 informationSection Induction motor drives
Section 5.1 - nduction motor drive Electric Drive Sytem 5.1.1. ntroduction he AC induction motor i by far the mot widely ued motor in the indutry. raditionally, it ha been ued in contant and lowly variable-peed
More informationA New Predictive Approach for Bilateral Teleoperation With Applications to Drive-by-Wire Systems
1 A New Predictive Approach for Bilateral Teleoperation With Application to Drive-by-Wire Syte Ya-Jun Pan, Carlo Canuda-de-Wit and Olivier Senae Departent of Mechanical Engineering, Dalhouie Univerity
More informationChapter 13. Root Locus Introduction
Chapter 13 Root Locu 13.1 Introduction In the previou chapter we had a glimpe of controller deign iue through ome imple example. Obviouly when we have higher order ytem, uch imple deign technique will
More informationA 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 informationThree Phase Induction Motors
Chapter (8) hree Phae Induction Motor Introduction he three-phae induction otor are the ot widely ued electric otor in indutry. hey run at eentially contant peed fro no-load to full-load. However, the
More informationResonant Load Control Methods for Industrial Servo Drives
IEEE Indutry Application Society Annual Meeting Rome, Italy, October 8 2, 2000 Reonant Load Control Method for Indutrial Servo Drive George Elli Kollmorgen Corporation 20 Rock Road Radford, VA 24060 T:
More informationThrottle Actuator Swapping Modularity Design for Idle Speed Control
9 merican ontrol onference Hyatt Regency Riverfront, St. Loui, MO, US June -, 9 ThB.4 Throttle ctuator Swapping Modularity Deign for Idle Speed ontrol Shifang Li, Melih akmakci, Ilya V. Kolmanovky and.
More informationDesign By Emulation (Indirect Method)
Deign By Emulation (Indirect Method he baic trategy here i, that Given a continuou tranfer function, it i required to find the bet dicrete equivalent uch that the ignal produced by paing an input ignal
More informationLecture 2 Phys 798S Spring 2016 Steven Anlage. The heart and soul of superconductivity is the Meissner Effect. This feature uniquely distinguishes
ecture Phy 798S Spring 6 Steven Anlage The heart and oul of uperconductivity i the Meiner Effect. Thi feature uniquely ditinguihe uperconductivity fro any other tate of atter. Here we dicu oe iple phenoenological
More informationControl Theory and Congestion
Control Theor and Congetion Glenn Vinnicombe and Fernando Paganini Cambridge/Caltech and UCLA IPAM Tutorial March 2002. Outline of econd part: 1. Performance in feedback loop: tracking, diturbance rejection,
More informationECEN620: Network Theory Broadband Circuit Design Fall 2018
ECEN60: Network Theory Broadband Circuit Deign Fall 08 Lecture 6: Loop Filter Circuit Sam Palermo Analog & Mixed-Signal Center Texa A&M Univerity Announcement HW i due Oct Require tranitor-level deign
More informationEE 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 information16.30/31 September 24, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: October 15, 2010 T.A. B. Luders /31 Lab #1
16.30/31 Septeber 24, 2010 Prof. J. P. How and Prof. E. Frazzoli Due: October 15, 2010 T.A. B. Luders 16.30/31 Lab #1 1 Introduction The Quanser helicopter is a echanical device that eulates the flight
More informationStability regions in controller parameter space of DC motor speed control system with communication delays
Stability region in controller parameter pace of DC motor peed control ytem with communication delay Şahin Sönmez, Saffet Ayaun Department of Electrical and Electronic Engineering, Nigde Univerity, 5124,
More informationEE/ME/AE324: Dynamical Systems. Chapter 8: Transfer Function Analysis
EE/ME/AE34: Dynamical Sytem Chapter 8: Tranfer Function Analyi The Sytem Tranfer Function Conider the ytem decribed by the nth-order I/O eqn.: ( n) ( n 1) ( m) y + a y + + a y = b u + + bu n 1 0 m 0 Taking
More informationFeedback Control System Fundamentals
unam online continuing education coure Feedback ontrol ytem Fundamental by eter ennedy Feedback ontrol ytem Fundamental unam online continuing education coure Feedback ontrol ytem Fundamental. Introduction:
More informationTuning of High-Power Antenna Resonances by Appropriately Reactive Sources
Senor and Simulation Note Note 50 Augut 005 Tuning of High-Power Antenna Reonance by Appropriately Reactive Source Carl E. Baum Univerity of New Mexico Department of Electrical and Computer Engineering
More informationAll Division 01 students, START HERE. All Division 02 students skip the first 10 questions, begin on # (D)
ATTENTION: All Diviion 01 tudent, START HERE. All Diviion 0 tudent kip the firt 10 quetion, begin on # 11. 1. Approxiately how any econd i it until the PhyicBowl take place in the year 109? 10 (B) 7 10
More informationConditions for equilibrium (both translational and rotational): 0 and 0
Leon : Equilibriu, Newton econd law, Rolling, Angular Moentu (Section 8.3- Lat tie we began dicuing rotational dynaic. We howed that the rotational inertia depend on the hape o the object and the location
More informationinto 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 informationH DESIGN OF ROTOR FLUX ORIENTED CONTROLLED INDUCTION
H DESIGN OF ROTOR FLUX ORIENTED CONTROLLED INDUCTION MOTOR DRIVES: SPEED CONTROL, STABILITY ROBUSTNESS AND NOISE ATTENUATION João C. Bailio,, Joé A. Silva Jr.,, Jr., and Lui G. B. Rolim, Member, IEEE,
More informationMEM 355 Performance Enhancement of Dynamical Systems Root Locus Analysis
MEM 355 Performance Enhancement of Dynamical Sytem Root Locu Analyi Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan in
More informationA Robust RF-MRAS based Speed Estimator using Neural Network as a Reference Model for Sensor-less Vector Controlled IM Drives
Control Theory and Inforatic Vol, No.3, 0.iite.org A Robut RF-MRAS baed Speed Etiator uing Neural Netork a a Reference Model for Senor-le Vector Controlled IM Drive A. Venkadean, Reearch Scholar Departent
More informationµ-analysis OF INDIRECT SELF CONTROL OF AN INDUCTION MACHINE Henrik Mosskull
-ANALYSIS OF INDIRECT SELF CONTROL OF AN INDUCTION MACHINE Henrik Mokull Bombardier Tranportation, SE-7 7 Väterå, Sweden S, Automatic Control, KTH, SE- Stockholm, Sweden Abtract: Robut tability and performance
More informationBasic parts of an AC motor : rotor, stator, The stator and the rotor are electrical
INDUCTION MOTO 1 CONSTUCTION Baic part of an AC motor : rotor, tator, encloure The tator and the rotor are electrical circuit that perform a electromagnet. CONSTUCTION (tator) The tator - tationary part
More informationEvolutionary 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 informationTP A.30 The effect of cue tip offset, cue weight, and cue speed on cue ball speed and spin
technical proof TP A.30 The effect of cue tip offet, cue weight, and cue peed on cue all peed and pin technical proof upporting: The Illutrated Principle of Pool and Billiard http://illiard.colotate.edu
More informationThe Root Locus Method
The Root Locu Method MEM 355 Performance Enhancement of Dynamical Sytem Harry G. Kwatny Department of Mechanical Engineering & Mechanic Drexel Univerity Outline The root locu method wa introduced by Evan
More informationAutomatic Control Systems. Part III: Root Locus Technique
www.pdhcenter.com PDH Coure E40 www.pdhonline.org Automatic Control Sytem Part III: Root Locu Technique By Shih-Min Hu, Ph.D., P.E. Page of 30 www.pdhcenter.com PDH Coure E40 www.pdhonline.org VI. Root
More informationMobile Communications TCS 455
Mobile Counication TCS 455 Dr. Prapun Sukopong prapun@iit.tu.ac.th Lecture 24 1 Office Hour: BKD 3601-7 Tueday 14:00-16:00 Thurday 9:30-11:30 Announceent Read Chapter 9: 9.1 9.5 Section 1.2 fro [Bahai,
More informationRanking DEA Efficient Units with the Most Compromising Common Weights
The Sixth International Sypoiu on Operation Reearch and It Application ISORA 06 Xiniang, China, Augut 8 12, 2006 Copyright 2006 ORSC & APORC pp. 219 234 Ranking DEA Efficient Unit with the Mot Coproiing
More informationPerformance Analysis of a Three-Channel Control Architecture for Bilateral Teleoperation with Time Delay
Extended Suary pp.1224 1230 Perforance Analyi of a Three-Channel Control Architecture for Bilateral Teleoperation with Tie Delay Ryogo Kubo Meber (Keio Univerity, kubo@u.d.keio.ac.jp) Noriko Iiyaa Student
More informationName: Answer Key Date: Regents Physics. Energy
Nae: Anwer Key Date: Regent Phyic Tet # 9 Review Energy 1. Ue GUESS ethod and indicate all vector direction.. Ter to know: work, power, energy, conervation of energy, work-energy theore, elatic potential
More informationConvergence of a Fixed-Point Minimum Error Entropy Algorithm
Entropy 05, 7, 5549-5560; doi:0.3390/e7085549 Article OPE ACCESS entropy ISS 099-4300 www.dpi.co/journal/entropy Convergence of a Fixed-Point Miniu Error Entropy Algorith Yu Zhang, Badong Chen, *, Xi Liu,
More informationABSTRACT- In this paper, a Shunt active power filter (SAPF) is developed without considering any harmonic detection
Special Iue of International Journal of Advance in Applied Science and Engineering (IJAEAS) ISSN (P): 2348-1811; ISSN (E): 2348-182X Vol. 4, Iue 1,2, March 2017, 34-39 IIST SHUNT ACTIVE POWER FILTER PERFORMANCE
More informationThe Influence of the Load Condition upon the Radial Distribution of Electromagnetic Vibration and Noise in a Three-Phase Squirrel-Cage Induction Motor
The Influence of the Load Condition upon the Radial Ditribution of Electromagnetic Vibration and Noie in a Three-Phae Squirrel-Cage Induction Motor Yuta Sato 1, Iao Hirotuka 1, Kazuo Tuboi 1, Maanori Nakamura
More informationUfuk Demirci* and Feza Kerestecioglu**
1 INDIRECT ADAPTIVE CONTROL OF MISSILES Ufuk Deirci* and Feza Kerestecioglu** *Turkish Navy Guided Missile Test Station, Beykoz, Istanbul, TURKEY **Departent of Electrical and Electronics Engineering,
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.010: Systems Modeling and Dynamics III. Final Examination Review Problems
ASSACHUSETTS INSTITUTE OF TECHNOLOGY Departent of echanical Engineering 2.010: Systes odeling and Dynaics III Final Eaination Review Probles Fall 2000 Good Luck And have a great winter break! page 1 Proble
More informationHomework 12 Solution - AME30315, Spring 2013
Homework 2 Solution - AME335, Spring 23 Problem :[2 pt] The Aerotech AGS 5 i a linear motor driven XY poitioning ytem (ee attached product heet). A friend of mine, through careful experimentation, identified
More information