Bending Magnetic Levitation Control Applying the Continuous Model of Flexible Steel Plate
|
|
- Kelley Webb
- 5 years ago
- Views:
Transcription
1 Proc. Schl. Eng. okai okai Univ., Univ., Ser. ESer. E 4(15 - ( Bending Magnetic Levitation Control Appling the Continuous Model of Fleile Steel Plate Hikaru YONEZAWA *1, Hiroki MARUMORI *1, akaoshi NARIA * and Hideaki KAO *3 (Received on Mar. 31, 15 and accepted on Jul. 15, 15 Astract We have proposed the levitation of an ultrathin steel plate that has een ent to an etent that has not induced plastic deformation. It has een confirmed that virations are suppressed and levitation performance is improved. However, when the steel plate is ent and levitated, the elastic viration occurs. In practice, since the steel plate is ver thin, elastic viration cannot e sufficientl suppressed using onl a limited numer of electromagnets, and levitation performance is not alwas impeccale. o model a fleile thin steel plate, we appl a continuous model which epresses the motion of the plate. Appling the optimal control theor to the continuous model, the ending levitation eperiments were carried out. It was concluded ased upon the applied continuous model, that levitation performance ecome stale and desirale ending levitation performance was achieved. Kewords: Fleile steel plate, Electromagnetic levitation sstem, Elastic viration, Bending levitation control, Continuous model 1. Introduction hin steel plates are widel used as materials for automoiles, electric appliances, cans and other products in current industries. With various industrial demands, the surface qualit of steel plates continues to e enhanced. However, ecause a contact conveance using rollers is mainl adopted in the process of a thin-steel-plate production line, the prolem of surface qualit deterioration arises. In recent ears, as a countermeasure for this prolem, researches on the noncontact conveance sstem with the application of electromagnetic levitation technolog have ecome active 1-4. In the past, our research group have constructed an electromagnetic levitation control sstem with which the relative distance etween electromagnets and a steel plate are constantl maintained, aiming to prevent the steel plate from falling from the conveer or coming into contact with the electromagnet during electromagnetic levitation conveance 5. However, as the steel plate ecomes thinner, the viration caused minute unpredictale factors, including the *1 Graduate Student, Course of Mechanical Engineering * Assistant Professor, Department of Electrical and Electronic Engineering, oko Universit of Science, Suwa, Japan *3 Assistant Professor, Department of Prime Mover Engineering nonlinearit of the attractive force of the electromagnet and the change in resistance due to heat generation the electromagnet, makes it difficult to maintain the levitation state. Furthermore, when an ultrathin steel plate with a thickness of less than.3 mm is targeted for levitation, the levitation control ecomes difficult ecause the thin plate undergoes increased fleure. o overcome these prolems, we propose a levitation of an ultrathin-steel-plate that is ent to an etent that does not induce plastic deformation 6. It has een confirmed that virations with mainl low frequencies are generated when a steel plate is ent and levitated. In addition, the levitation performance of steel plate is markedl improved 7. However, when the steel plate is ent and levitated, the elastic viration arises. In practice, since the steel plate is ver thin, the elastic viration cannot e sufficientl suppressed using onl a limited numer of electromagnets, and hence it is essential to eliminate the elastic viration appling the control theor as much as possile. he control method used in the past studies of the authors had the advantage that the control sstem can e designed in a simple. However, specific virations that occur from eing a fleile steel plate were not ale to e considered this control method. In other words, it was a model for independentl feeding ack the status of each of Vol., 15 77
2 Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO Resistance Amplifier AMP5 AMP4 AMP3 AMP AMP1 D/A converter DSP (MS3C31 4MH A/D converter Steel plate (8 mm 6 mm.7 mm Gap sensor i 1 i i 3 i 4 i Electromagnet Electromagnet unit No.3 No.4 No.5 No.1 No. Steel plate (8 mm 6 mm.7 mm Fig. 1 Electromagnet control sstem θ A A' Front view Side view (A-A' section Fig. Schematic illustration of eperimental apparatus the electromagnets positions. his stud is intended to suppress the elastic 1st mode that is the most dominant in the viration generated. We applied the continuous model that can e considered integrating the state acquired at all of the electromagnets positions. In this paper, appling the optimal control theor to the continuous model, ending levitation eperiments are carried out. We eamined the levitation stailit and levitation performance using a thin steel plate with a thickness of.7 mm.. Modeling of Steel Plate 5 In eperimental apparatus, we used the same sstem as that used Marumori 8. Figure 1 shows an outline of the electromagnet control sstem. Figure shows a schematic illustration of eperimental apparatus. In the past stud, the steel plate was divided into 5 hpothetical masses and each part was modeled as a lumped constant sstem 6. he 1 degree of freedom model (1-DOF model that has een used in past studies of the authors was not ale to consider specific virations that occurred from eing a fleile steel plate. his stud is intended to suppress the elastic 1st mode that is the most dominant in the viration generated. We applied the continuous model that can e considered integrating the state acquired at all of the electromagnets positions. In a continuous model, integrated control is carried out calculating 15 values: displacement, velocit of steel plate and all the current of the electromagnet which detected at each position of the five electromagnets. In this model, the motion of the steel plate is calculated from the equations of its elastic viration. Supporting the plate the static attracting force of each magnet creates an equilirium levitation state, where the steel plate maintains a certain distance from the electromagnets. he equation of small vertical motion around the equilirium state of the steel plate sujected to magnetic forces is epressed as follows: 3 Ch 4 4 h D t 1 t 5 f cn ( t{ ( a1 n ( a1n n1 ( an ( an } ( ( 4 4 Where C: internal damping coefficient [Ns/m ], D = Eh 3 /1(1-v [Nm], v: Poisson s ratio, f cn (t: dnamic magnetic force at the n-th coupled magnets [N], t: time [s], (, : vertical displacement [m],,, : coordinate aes indicated in Fig. 1 [m], a1n, an, a1n, an : location of the n-th coupled magnets (n = 1-5 [m], δ( : Dirac delta function [l/m]. he characteristic equations of the electromagnets can e derived as follows: Fn F f n cn sn, sn in Zn In Leff In R 1 in sn, sn in v L L Z n L Leff L Llea Zn (3 n (4 (5 Where F n : magnetic force of the coupled magnets in the equilirium state [N], I n : current of the coupled magnets in the equilirium state [A], sn, sn : position of the n-th sensor [m], v n : dnamic voltage of the n-th coupled magnets [V], i n : dnamic current of the n-th coupled magnets [A], Z n : gap etween the steel plate and electromagnet in equilirium state [m], L : inductance of one magnet coil in equilirium state [H], R : resistance of the coupled magnet coils [Ω], and L lea : leakage inductance of the one magnet coil [H]. 78 Proceedings of the School of Engineering, okai Universit, Series E
3 Bending Magnetic Levitation Control Appling the Continuous Model of Fleile Steel Plate Bending Magnetic Levitation Control Appling the Continuous Model of Fleile Steel Plate 1st mode 4th mode ( φ 1 = X 1 Y 1 ( φ 4 = X Y nd mode ( φ = X Y 1 3rd mode ( φ 3 = X 1 Y 5th mode (elastic 1st mode ( φ 5 = X 1 Y 3 Fig. 3 Mode shapes of the levitated steel plate State variales of the sstem are normal coordinates of vertical displacement of the plate W i (t (i = 1-5, their differential values Ẇ i (t (i = 1-5, and dnamic currents of the coupled magnet coils i n (t (n = 1-5. he control input of the sstem is the dnamic voltages of the magnets v n (t (n = l - 5. Output variales of the sstem are vertical displacements n ( sn, sn, t (n = 1-5. Using the state, control and output vectors, the forgoing eqs. (3-(6 are written as following state and output equations: W AW Bv (15 n CW (16 W 1 W5 W1 W W 5 i1 i5 (17 v v1 v 5 (18 n i1 i5 (19 3. State Equation and Controller he vertical displacement of the plate can e epanded to an infinite series of a space-dependent eigenfunctionφ i (, as shown in Fig. 3 multiplied the time-dependent normal coordinate. he eigenfunctions of the plate are assumed to e products of the elastic eam eigenfunctions of the - and -coordinates. he function of -coordinate Y nn ( (nn = l,, satisfies the free-free oundar condition, and the function of the -coordinate is epressed in rigid modes (parallel and rotational motions X 1 (, X ( onl. In addition, since the numer of sensors used in this eperiment are 5, we selected M = 5 for the control in which consideration is given to the 5th mode (elastic 1st mode. M i i (6 i1,, W t i, X Y (mm, nn = 1,, (7 1 mm nn X 1 (8 3 X a (9 a 1 Y (1 1 3 Y (11 Ynn λnn λnn cos cosh sinλnn sinhλnn λ nn nn sin sinh cos nn cosh nn (1 cosh λ nn cos λnn 1 (13 1 λnn D f nn h (14 Here, details of matrices A, B and C are omitted due to space limitations 5. In this stud, a control sstem is constructed using a discrete time sstem; therefore, the evaluation function of a continuous sstem is digitied, and the optimal control law is otained ased on the optimal control theor of the discrete time sstem. he following discrete time sstem is here considered. d i Φ i Γv i 1 ( d d Φ ep A s (1 Γ s ep A d B ( Here, the evaluation function of the discrete time sstem is epressed as follows: J d d i Qd d i vd i rd vd i (3 i Qd1 Qd Qd Q d3 (4 Q d1 diag( q1q5 (5 Q d diag( qs1qs5 (6 Q d3 diag( qi1qi5 (7 r d r diag (8 M Φ MΦ Q d 1 r Γ MΓ Γ MΦ Φ MΓ d (9 v d F d d (3 1 r d Γ MΓ Γ MΦ F d (31 Vol., 15 79
4 Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO ale 1 Smols and values Smol Value Smol Value m kg E 6 GPa Z n m ν.3 R Z 1. Ω L H ρ kg/m 3 L lea H d.43 m L eff H C Ns/m s1 155 mm s 645 mm s3 155 mm s4 645 mm s5 4 mm s1 85 mm s 85 mm s3 515 mm s4 515 mm s5 3 mm s s Steel plate Electromagnet 15 mm 8 mm 5 5 mm mm mm 15 mm (a θ = ( θ = 5 9mm (c θ = 7 (d θ = 1 Fig. 4 Relationship etween tilt angle of electromagnets and shape of steel plate 1 Where Q d and r d are weighting coefficients, M is the solution of the algeraic matri Riccati equation, and s is a sampling interval. MALAB command lqrd was used to solve eq. (9 and the digital controller was designed using SIMULINK in the DSP. 4. Eperiment of Bended Levitation 4.1 Condition of eperiment ale 1 shows the specifications of the sstem. Optimal control theor (OP is applied for levitation control of the thin steel plate to compare the results under different electromagnet tilt angles. Figure 4 shows the relationship etween the tilt angle of electromagnets and shape of steel plate. In the ending levitation eperiment, the electromagnet tilt angle θ is increased at intervals of 5 from. In this stud, the standard deviation of displacement is measured. he standard deviation of displacement is measured 1 times at the electromagnet unit No. 1 for each electromagnet tilt angle, and the mean is used as the eperimental result. It is confirmed that the same tendenc is oserved in other electromagnetic units. o avoid the effect of the transient state of the thin steel plate, the measurement is started approimatel 1 s after the start of levitation. he weighting coefficients of OP (eq. (3 are set as follows: q 1 -q 5 = 1. 1 m - (3 q s1 -q s5 = (m/s - (33 q i1 -q i5 = 1 A - (34 r = V - (35 From eq. (14, natural frequenc (calculated value of elastic 1st mode = 4.3 H. 4. Levitation eperiment Figures 5 and 6 show the eperimental results otained when tilt angles of the electromagnets θ = and 15 under continuous model. In these figures, (a shows the displacement of the steel plate over time, ( shows its amplitude spectrum. Figures 7 and 8 show the eperimental results under 1-DOF model for comparison. In 1-DOF model levitation eperiments, we used the same method as that used Narita 6. When 1-DOF model is applied (Figures 7 and 8, elastic virations are ostensile on the steel plate. his is ecause the elastic viration is caused the elastic force that is applied to the steel plate as a restoring force. A peak of the amplitude spectrum is oserved at 4.3 H, which is the frequenc of the elastic 1st mode of the steel plate used on this eperiment. his is due to e a model that does not consider the virations ecited in the steel plate. herefore, it is confirmed that the viration occurs in various frequencies in Fig. 7. However, the case of ent levitation steel plate in 1-DOF model (Fig. 8, onl the viration of the elastic 1st mode is mainl generated. B ending the steel plate at θ = 7, the viration of steel plate is suppressed compared to θ =. Also, applied to continuous model, viration suppression ailit appears against the elastic 1st mode (4.3 H. Figure 9 shows the relationship etween the tilt angle of electromagnets θ and standard deviation of displacement. Standard deviation of displacement decreases with increasing electromagnet tilt angles. At a tilt angle of 7, the standard deviation of displacement is the smallest. he reason ehind the standard deviation of displacement of an increase at a tilt angle of 1 is that a tilt angle of 1 eceeds the natural deflection angle (8.5 of the steel plate with a thickness of.7 mm, leading to difficult in levitation. As a result, appling the continuous model considering the elastic viration, it is possile to suppress the elastic 1st mode of the steel plate. Moreover, ending the steel plate 8 Proceedings of the School of Engineering, okai Universit, Series E
5 Bending Magnetic Levitation Control Appling the Continuous Model of Fleile Steel Plate Bending Magnetic Levitation Control Appling the Continuous Model of Fleile Steel Plate Displacement [mm] ime [s] (a ime histor of displacement Frequenc [H] ( Amplitude spectrum of displacement Fig. 5 Viration of a levitation steel plate for continuous model (θ = Displacement [mm] ime [s] (a ime histor of displacement Frequenc [H] ( Amplitude spectrum of displacement Fig. 6 Viration of a levitation steel plate for continuous model (θ = Frequenc [H] Fig. 7 Viration of a levitation steel plate for 1-DOF model (θ = Frequenc [H] Fig. 8 Viration of a levitation steel plate for 1-DOF model (θ = 7 Standard deviation 1 [mm].6.4. Elastic 1st mode ilt angle of electromagnets θ [ ] Fig. 9 Relationships etween tilt angle of electromagnets θ and standard deviation of displacement at sensor No. 1 at the optimal tilt angle of the steel plate, viration suppression performance was superior to 1-DOF model. From the aove, the advantage of appling the continuous model is shown without ending the steel plate. Moreover, usefulness of ending levitation can e confirmed from eperimental result with the continuous model. he model with considering elastic viration is effective to levitate thin steel plates which easil occur the viration. 5. Conclusion In this paper, appling the optimal control theor to Vol., 15 81
6 Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO Hikaru YONEZAWA, Hiroki MARUMORI, akaoshi NARIA and Hideaki KAO the continuous model, ending levitation eperiments were carried out. As a result, it was effective for a thin steel plate with thickness of.7 mm to e ent to an etent that did not eceed natural deflection angle and we were ale to suppress the viration as compared with the case of appling to the 1-DOF model. herefore, we confirmed the utilit of continuous model which takes account of elastic viration of steel plate. References 1 S. Matsumoto, Y. Arai,. Nakagawa: Noncontact Levitation and Conveance Characteristics of a Ver hin Steel Plate Magneticall Levitated a LIM-Driven Cart, IEEE ransactions on Magnetics, 5 No. 11, (14.. Namerikawa, D. Miutani, S. Kuroki: Roust H DIA Control of Levitated Steel Plates, IEEJ ransactions on Industr Applications, 16, No. 1 (6, Jung Soo Choi, Yoon Su Baek: Magneticall-Levitated Steel-Plate Conveance Sstem Using Electromagnets and a Linear Induction Motor, IEEE RANSACIONS ON MAGNEICS, 44, No. 11 (8, H. akamine, S. orii,. Yanagida, S. Iwashita, S. odoroki: Stud of Electromagnetic Suspension Sstem Using Acceleration Signal of Electromagnet Supported with Spring, IEEJ ransactions on Industr, 133, No. 5 (8, Y. Oshinoa,. Oata: Noncontact Viration Control of a Magnetic Levitated Rectangular hin Steel Plate, JSME International Journal, Series C, 45, No. 1, ( Narita, H. Marumori, S.Hasegawa, Y. Oshinoa: Basic Eperimental Considerations on Bending Levitation Control Electromagnetic Force for Fleile Steel Plate, Proseedings of the School of Engineering of okai Universit, Series E, 38 (13, H. Yoneawa, H. Marumori,. Narita, S. Hasegawa, Y. Oshinoa: Bending Magnetic Levitation Contril for hin Steel Plate (Eperimental Consideration UsingSliding Mode Control, International Power Electronics Conference, (14, H. Marumori, H. Yoneawa,. Narita, H. Kato, S. Hasegawa, Y. Oshinoa: Effective Plate hickness Range in Bending echnique for Levitation Control of Fleile Steel Plate, Proseedings of the School of Engineering of okai Universit, Series E, 39 (14, Proceedings of the School of Engineering, okai Universit, Series E
(Received on Mar. 30, 2013 and accepted on Jul. 11, 2013)
Proc. Schl. Eng. Tokai Tokai Univ., Univ., Ser. ESer. E 38 (3) (3) - 53-58 Effect of a Magnetic Field from the Horiontal Direction on a Magnetically Levitated Steel Plate (Fundamental Considerations on
More information(Received on Mar. 30, 2013 and accepted on Jul. 11, 2013)
Proc. Schl. Eng. Tokai Tokai Univ., Univ., Ser. ESer. E 38 (23) (23) - 59-66 Optimal Placement of Permanent Magnets in a Hybrid Magnetic evitation System for Thin Steel Plate by Takayoshi NARITA *, Shinya
More information6 Degrees of Freedom Control through Three Electromagnets and Three Linear Induction Motors
6 Degrees of Freedom ontrol through Three s and Three Linear Induction Motors Yusuke MKINO, Lilit KOVUDHIKULRUNGSRI and Takafumi KOSEKI Department of Electrical Engineering, School of Engineering The Universit
More informationExact Free Vibration of Webs Moving Axially at High Speed
Eact Free Viration of Wes Moving Aially at High Speed S. HATAMI *, M. AZHARI, MM. SAADATPOUR, P. MEMARZADEH *Department of Engineering, Yasouj University, Yasouj Department of Civil Engineering, Isfahan
More informationSection 8.5. z(t) = be ix(t). (8.5.1) Figure A pendulum. ż = ibẋe ix (8.5.2) (8.5.3) = ( bẋ 2 cos(x) bẍ sin(x)) + i( bẋ 2 sin(x) + bẍ cos(x)).
Difference Equations to Differential Equations Section 8.5 Applications: Pendulums Mass-Spring Systems In this section we will investigate two applications of our work in Section 8.4. First, we will consider
More informationJournal of Mechanical Systems for Transportation and Logistics
Comparison of Methods to Reduce Vibrations in Superconducting Maglev Vehicles b Primar Suspension Control* Erimitsu SUZUKI **, Jun SHIRASAKI ***, Ken WATANABE **, Hironori HOSHINO **, and Masao NAGAI ***
More informationASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR
ASEISMIC DESIGN OF TALL STRUCTURES USING VARIABLE FREQUENCY PENDULUM OSCILLATOR M PRANESH And Ravi SINHA SUMMARY Tuned Mass Dampers (TMD) provide an effective technique for viration control of flexile
More informationSIMILARITY METHODS IN ELASTO-PLASTIC BEAM BENDING
Similarity methods in elasto-plastic eam ending XIII International Conference on Computational Plasticity Fundamentals and Applications COMPLAS XIII E Oñate, DRJ Owen, D Peric and M Chiumenti (Eds) SIMILARIT
More informationPARAMETER IDENTIFICATION, MODELING, AND SIMULATION OF A CART AND PENDULUM
PARAMETER IDENTIFICATION, MODELING, AND SIMULATION OF A CART AND PENDULUM Erin Bender Mechanical Engineering Erin.N.Bender@Rose-Hulman.edu ABSTRACT In this paper a freely rotating pendulum suspended from
More informationINELASTIC RESPONSE SPECTRA FOR BIDIRECTIONAL GROUND MOTIONS
October 1-17, 008, Beijing, China INELASTIC RESPONSE SPECTRA FOR BIDIRECTIONAL GROUND MOTIONS WANG Dong-sheng 1 LI Hong-nan WANG Guo-in 3 Fan Ying-Fang 4 1 Professor,Iinstitute of Road and Bridge Eng.,
More informationExact Shape Functions for Timoshenko Beam Element
IOSR Journal of Computer Engineering (IOSR-JCE) e-iss: 78-66,p-ISS: 78-877, Volume 9, Issue, Ver. IV (May - June 7), PP - www.iosrjournals.org Exact Shape Functions for Timoshenko Beam Element Sri Tudjono,
More informationModeling of Rebound Phenomenon of a Rigid Ball with Friction and Elastic Effects
American Control Conference Marriott Waterfront, Baltimore, MD, USA June -Jul, WeB8. Modeling of Reound Phenomenon of a Rigid Ball with Friction and Elastic Effects Akira Nakashima, Yuki Ogawa, Yosuke
More informationSolution: (a) (b) (N) F X =0: A X =0 (N) F Y =0: A Y + B Y (54)(9.81) 36(9.81)=0
Prolem 5.6 The masses of the person and the diving oard are 54 kg and 36 kg, respectivel. ssume that the are in equilirium. (a) Draw the free-od diagram of the diving oard. () Determine the reactions at
More informationThe Theory of a Scroll Profile
Purdue Universit Purdue e-pus International Compressor Engineering Conference School of Mechanical Engineering 006 The Theor of a Scroll Profile Huert Bukac Little Dnamics Follow this and additional works
More informationVibrational Power Flow Considerations Arising From Multi-Dimensional Isolators. Abstract
Vibrational Power Flow Considerations Arising From Multi-Dimensional Isolators Rajendra Singh and Seungbo Kim The Ohio State Universit Columbus, OH 4321-117, USA Abstract Much of the vibration isolation
More informationragsdale (zdr82) HW7 ditmire (58335) 1 The magnetic force is
ragsdale (zdr8) HW7 ditmire (585) This print-out should have 8 questions. Multiple-choice questions ma continue on the net column or page find all choices efore answering. 00 0.0 points A wire carring
More informationSimulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes
Simulation of Nonlinear Behavior of Wall-Frame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced
More informationStructure analysis of levitation chassis of medium-to-low speed maglev vehicles based on left-right decoupling
Journal of Modern Transportation Volume 0, Numer, June 01, Page 8-87 Journal homepage: jmt.swjtu.edu.cn DOI: 10.1007/BF033578 Structure analysis of levitation chassis of medium-to-low speed maglev vehicles
More information908. Dynamic responses of an elastic beam moving over a simple beam using modal superposition method
98. Dynamic responses of an elastic eam moving over a simple eam using modal superposition method Y. J. Wang, J. Shi, Y. Xia 3, School of Civil Engineering, Beijing Jiaotong University, Beijing 44, China,
More information2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media,
2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in an current or future media, including reprinting/republishing this material for advertising
More informationab is shifted horizontally by h units. ab is shifted vertically by k units.
Algera II Notes Unit Eight: Eponential and Logarithmic Functions Sllaus Ojective: 8. The student will graph logarithmic and eponential functions including ase e. Eponential Function: a, 0, Graph of an
More informationPARAMETER IDENTIFICATION OF A FORK-LIFT TRUCK DYNAMIC MODEL
11 th National Congress on Theoretical and Applied Mechanics, -5 Sept. 9, Borovets, Bulgaria PARAMETER IDENTIFICATION OF A FORK-IFT TRUCK DYNAMIC MODE E. S. CHANKOV Strength of Materials Dep., Technical
More informationVibration of Plate on Foundation with Four Edges Free by Finite Cosine Integral Transform Method
854 Vibration of Plate on Foundation with Four Edges Free b Finite Cosine Integral Transform Method Abstract The analtical solutions for the natural frequencies and mode shapes of the rectangular plate
More informationManeuvering Target Tracking Method based on Unknown but Bounded Uncertainties
Preprints of the 8th IFAC World Congress Milano (Ital) ust 8 - Septemer, Maneuvering arget racing Method ased on Unnown ut Bounded Uncertainties Hodjat Rahmati*, Hamid Khaloozadeh**, Moosa Aati*** * Facult
More informationInvestigation of a Ball Screw Feed Drive System Based on Dynamic Modeling for Motion Control
Investigation of a Ball Screw Feed Drive System Based on Dynamic Modeling for Motion Control Yi-Cheng Huang *, Xiang-Yuan Chen Department of Mechatronics Engineering, National Changhua University of Education,
More informationThree-dimensional free vibration analysis of functionally graded rectangular plates using the B-spline Ritz method
The 01 World Congress on Advances in Civil, Environmental, and Materials Research (ACEM 1) Seoul, Korea, August 6-30, 01 Three-dimensional free viration analsis of functionall graded rectangular plates
More informationDesign Parameter Sensitivity Analysis of High-Speed Motorized Spindle Systems Considering High-Speed Effects
Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation August 5-8, 2007, Harin, China Design Parameter Sensitivity Analysis of High-Speed Motorized Spindle Systems Considering
More informationME 323 Examination #2
ME 33 Eamination # SOUTION Novemer 14, 17 ROEM NO. 1 3 points ma. The cantilever eam D of the ending stiffness is sujected to a concentrated moment M at C. The eam is also supported y a roller at. Using
More informationStructural Analysis of an Exhaust System for Heavy Trucks
Structural Analsis of an Ehaust Sstem for Heav Trucks Mr N. Vasconcellos, Mr F. dos Anjos and Mr M. Argentino, debis humaitá IT Services Latin America, Brail ABSTRACT The present work describes the use
More informationDavid A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan
Session: ENG 03-091 Deflection Solutions for Edge Stiffened Plates David A. Pape Department of Engineering and Technology Central Michigan University Mt Pleasant, Michigan david.pape@cmich.edu Angela J.
More informationSTATIONARY AND TRANSIENT VIBRATIONS OF DAVI VIBROINSULATION SYSTEM.
STTIONRY ND TRNSIENT VIBRTIONS OF DVI VIBROINSULTION SYSTEM. Jerzy Michalczyk, ul.zagorze c, 3 398 Cracow, Poland Piotr Czuak, ul. Szujskiego /4, 3-3 Cracow, Poland address for correspondence Grzegorz
More informationAnalysis of Effects of Rebounds and Aerodynamics for Trajectory of Table Tennis Ball
SICE Annual Conference 21 August 18-21, 21, The Grand Hotel, Taipei, Taiwan Analsis of Effects of Reounds and Aerodnamics for Trajector of Tale Tennis Junko Nonomura Mechanical Science and Engineering,
More informationPHY451, Spring /5
PHY451, Spring 2011 Notes on Optical Pumping Procedure & Theory Procedure 1. Turn on the electronics and wait for the cell to warm up: ~ ½ hour. The oven should already e set to 50 C don t change this
More informationThe exact region of stability for MacCormack scheme. Hoon Hong. Research Institute for Symbolic Computation. Johannes Kepler University
The eact region of stailit for MacCormack scheme Hoon Hong Research Institute for Smolic Computation Johannes Kepler Universit A- Linz, Austria e-mail: hhong@risc.uni-linz.ac.at Astract Let the two dimensional
More informationSimultaneous Orthogonal Rotations Angle
ELEKTROTEHNIŠKI VESTNIK 8(1-2): -11, 2011 ENGLISH EDITION Simultaneous Orthogonal Rotations Angle Sašo Tomažič 1, Sara Stančin 2 Facult of Electrical Engineering, Universit of Ljubljana 1 E-mail: saso.tomaic@fe.uni-lj.si
More informationTHE KINETICS OF PHASE TRANSITIONS: I. THE ROLE OF HETEROGENEITY. F. Paladi* and V. Gamurari
THE KINETICS OF PHASE TRANSITIONS: I. THE ROLE OF HETEROGENEITY F. Paladi* and V. Gamurari Department of Theoretical Phsics Moldova State Universit 60 A. Mateevici str. MD-009 Chisinau Repulic of Moldova
More informationProblem 3 Solution Page 1. 1A. Assuming as outlined in the text that the orbit is circular, and relating the radial acceleration
Prolem 3 Solution Page Solution A. Assug as outlined in the text that the orit is circular, and relating the radial acceleration V GM S to the graitational field (where MS is the solar mass we otain Jupiter's
More informationMechanics Departmental Exam Last updated November 2013
Mechanics Departmental Eam Last updated November 213 1. Two satellites are moving about each other in circular orbits under the influence of their mutual gravitational attractions. The satellites have
More informationMODELLING OF ACOUSTIC POWER RADIATION FROM MOBILE SCREW COMPRESSORS
11 th International Conference on Viration Prolems Z. Dimitrovová et.al. (eds.) Lison, Portugal, 9 12 Septemer 213 MODELLING OF ACOUSTIC POWER RADIATION FROM MOBILE SCREW COMPRESSORS Jan Dupal* 1, Jan
More informationARTICLE IN PRESS. Thin-Walled Structures
RTICLE I PRESS Thin-Walled Structures 47 () 4 4 Contents lists availale at ScienceDirect Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws Buckling analsis of plates using the two variale
More informationMath 216 Second Midterm 28 March, 2013
Math 26 Second Midterm 28 March, 23 This sample exam is provided to serve as one component of your studying for this exam in this course. Please note that it is not guaranteed to cover the material that
More informationSurvey of Wave Types and Characteristics
Seminar: Vibrations and Structure-Borne Sound in Civil Engineering Theor and Applications Surve of Wave Tpes and Characteristics Xiuu Gao April 1 st, 2006 Abstract Mechanical waves are waves which propagate
More informationTHE DIRIHLET PROBLEM FOR THE FRACTIONAL POISSON S EQUATION WITH CAPUTO DERIVATIVES A Finite Difference Approximation and a Numerical Solution
Beialaev, V. B., et al: The Dirihlet Prolem for the Fractional Poisson's Equation... THERMAL SIENE: Year, Vol. 6, No., pp. 385-394 385 THE DIRIHLET PROBLEM FOR THE FRATIONAL POISSON S EQUATION WITH APUTO
More information589. Investigation of motion control of piezoelectric unimorph for laser shutter systems
589. Investigation of motion control of piezoelectric unimorph for laser shutter systems A. Buulis 1, V. Jurenas 2, S. Navickaite, V. Rugaityte 4 Kaunas University of Technology, Kaunas, Lithuania e-mail:
More informationUniversity of California at Berkeley Structural Engineering Mechanics & Materials Department of Civil & Environmental Engineering Spring 2012 Student name : Doctoral Preliminary Examination in Dynamics
More informationGREEN FUNCTION MATRICES FOR ELASTICALLY RESTRAINED HETEROGENEOUS CURVED BEAMS
The th International Conference on Mechanics of Solids, Acoustics and Virations & The 6 th International Conference on "Advanced Composite Materials Engineering" ICMSAV6& COMAT6 Brasov, ROMANIA, -5 Novemer
More informationUNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 20, 2011 Professor A. Dolovich
UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 20, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT
More informationModeling of Resonators
. 23 Modeling of Resonators 23 1 Chapter 23: MODELING OF RESONATORS 23 2 23.1 A GENERIC RESONATOR A second example where simplified discrete modeling has been found valuable is in the assessment of the
More informationf 0 ab a b: base f
Precalculus Notes: Unit Eponential and Logarithmic Functions Sllaus Ojective: 9. The student will sketch the graph of a eponential, logistic, or logarithmic function. 9. The student will evaluate eponential
More informationIntroduction to structural dynamics
Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static
More informationMeasurement of Structural Intensity Using an Angular Rate Sensor
Measurement of Structural Intensity Using an Angular Rate Sensor Nobuaki OMATA 1 ; Hiroki NAKAMURA ; Yoshiyuki WAKI 3 ; Atsushi KITAHARA 4 and Toru YAMAZAKI 5 1,, 5 Kanagawa University, Japan 3, 4 BRIDGESTONE,
More informationspring magnet Fig. 7.1 One end of the magnet hangs inside a coil of wire. The coil is connected in series with a resistor R.
1 A magnet is suspended vertically from a fixed point by means of a spring, as shown in Fig. 7.1. spring magnet coil R Fig. 7.1 One end of the magnet hangs inside a coil of wire. The coil is connected
More informationExperimental Evaluation on H DIA Control of Magnetic Bearings with Rotor Unbalance
Experimental Evaluation on H DIA Control of Magnetic Bearings with Rotor Unbalance Hiroki Seto and Toru Namerikawa Division of Electrical Engineering and Computer Science Kanazawa University Kakuma-cho,
More informationSHADOW AND BACKGROUND ORIENTED SCHLIEREN INVESTIGATION OF SHOCK WAVES IN GAS-DISCHARGE MEDIUM
SHADOW AND BACKGROUND ORIENTED SCHLIEREN INVESTIGATION OF SHOCK WAVES IN GAS-DISCHARGE MEDIUM J. JIN 1, I.V. MURSENKOVA 1,c, N. N. SYSOEV 1 and I.A. ZNAMENSKAYA 1 1 Department of Phsics, Lomonosov Moscow
More informationDIGITAL CORRELATION OF FIRST ORDER SPACE TIME IN A FLUCTUATING MEDIUM
DIGITAL CORRELATION OF FIRST ORDER SPACE TIME IN A FLUCTUATING MEDIUM Budi Santoso Center For Partnership in Nuclear Technolog, National Nuclear Energ Agenc (BATAN) Puspiptek, Serpong ABSTRACT DIGITAL
More informationSolving Homogeneous Trees of Sturm-Liouville Equations using an Infinite Order Determinant Method
Paper Civil-Comp Press, Proceedings of the Eleventh International Conference on Computational Structures Technology,.H.V. Topping, Editor), Civil-Comp Press, Stirlingshire, Scotland Solving Homogeneous
More informationChapter 2 Surface Acoustic Wave Motor Modeling and Motion Control
Chapter 2 Surface Acoustic Wave Motor Modeling and Motion Control 1 Abstract For miniaturization of ultrasonic transducers, a surface acoustic wave device has an advantage in rigid mounting and high-power-density
More informationON THE CHARACTERISTICS OF SOFT SOIL INELASTIC DESIGN RESPONSE SPECTRAS FOR THE CITY OF GUAYAQUIL, ECUADOR
ON THE CHAACTEISTICS OF SOFT SOIL INELASTIC DESIGN ESPONSE SPECTAS FO THE CITY OF GUAYAQUIL, ECUADO 837 Otton LAA 1 And moncao MACELO SUMMAY Five accelerograph records obtained in the cit of Guaaquil,
More informationa b a b ab b b b Math 154B Elementary Algebra Spring 2012
Math 154B Elementar Algera Spring 01 Stud Guide for Eam 4 Eam 4 is scheduled for Thursda, Ma rd. You ma use a " 5" note card (oth sides) and a scientific calculator. You are epected to know (or have written
More informationGraphs and polynomials
1 1A The inomial theorem 1B Polnomials 1C Division of polnomials 1D Linear graphs 1E Quadratic graphs 1F Cuic graphs 1G Quartic graphs Graphs and polnomials AreAS of STud Graphs of polnomial functions
More information2.18: Control of Beam Loss and Improving Efficiency in High-Repetition-Rate High- Power Klystrons
.18 Accelerator Phsics.18: Control of Beam Loss and Improving Efficienc in High-Repetition-Rate High- Power Klstrons (Progress Report) Accelerator Phsics Contact person Chiping Chen chenc@psfc.mit.edu
More information3 Mathematical modeling of the torsional dynamics of a drill string
3 Mathematical modeling of the torsional dynamics of a drill string 3.1 Introduction Many works about torsional vibrations on drilling systems [1, 12, 18, 24, 41] have been published using different numerical
More informationHomogenization Approaches for Laminated Magnetic Cores using the Example of Transient 3D Transformer Modeling
Homogeniation Approaches for Laminated Magnetic Cores using the Eample of Transient 3D Transformer Modeling H.Neuert *1, J. Ziske 1, T. Heimpold 1,and R. Disselnkötter 2 1 Technische Universität Dresden,
More informationCharacterisation Programme Polymer Multi-scale Properties Industrial Advisory Group 22 nd April 2008
Characterisation Programme 6-9 Polymer Multi-scale Properties Industrial Advisory Group nd April 8 SE: Improved Design and Manufacture of Polymeric Coatings Through the Provision of Dynamic Nano-indentation
More informationDEVELOPMENT OF A REAL-TIME HYBRID EXPERIMENTAL SYSTEM USING A SHAKING TABLE
DEVELOPMENT OF A REAL-TIME HYBRID EXPERIMENTAL SYSTEM USING A SHAKING TABLE Toshihiko HORIUCHI, Masahiko INOUE And Takao KONNO 3 SUMMARY A hybrid experimental method, in which an actuator-excited vibration
More informationKINEMATIC RELATIONS IN DEFORMATION OF SOLIDS
Chapter 8 KINEMATIC RELATIONS IN DEFORMATION OF SOLIDS Figure 8.1: 195 196 CHAPTER 8. KINEMATIC RELATIONS IN DEFORMATION OF SOLIDS 8.1 Motivation In Chapter 3, the conservation of linear momentum for a
More informationSteady State Modeling of Doubly Fed Induction Generator
Steady State Modeling of Douly Fed Induction Generator Bhola Jha 1, Dr. K. R. M Rao 2 1 Dept. of Electrical Engg., G. B. Pant Engg. College, Pauri-Garhwal, India 2 Dept. of Electrical Engg., M. J. College
More information10 Lorentz Group and Special Relativity
Physics 129 Lecture 16 Caltech, 02/27/18 Reference: Jones, Groups, Representations, and Physics, Chapter 10. 10 Lorentz Group and Special Relativity Special relativity says, physics laws should look the
More informationUnit 12 Study Notes 1 Systems of Equations
You should learn to: Unit Stud Notes Sstems of Equations. Solve sstems of equations b substitution.. Solve sstems of equations b graphing (calculator). 3. Solve sstems of equations b elimination. 4. Solve
More informationChapter #6 EEE State Space Analysis and Controller Design
hapter #6 EEE3-83 State Space nalsis and ontroller Design State feedack Linear Quadratic Regulator (LQR) Open and closed loop estimators Reduced Order Estimators (not assessed) racking Module Leader: Dr
More informationGIMC-based Switching Control of Magnetically Suspended Steel Plates
Proceedings of the 2006 IEEE International Conference on Control Applications Munich, German, October 4-6, 2006 WeB11.3 GIMC-based Switching Control of Magneticall Suspended Steel Plates Hideto Maruama
More informationComments on A Time Delay Controller for Systems with Uncertain Dynamics
Comments on A Time Delay Controller for Systems with Uncertain Dynamics Qing-Chang Zhong Dept. of Electrical & Electronic Engineering Imperial College of Science, Technology, and Medicine Exhiition Rd.,
More informationBuckling Behavior of Long Symmetrically Laminated Plates Subjected to Shear and Linearly Varying Axial Edge Loads
NASA Technical Paper 3659 Buckling Behavior of Long Symmetrically Laminated Plates Sujected to Shear and Linearly Varying Axial Edge Loads Michael P. Nemeth Langley Research Center Hampton, Virginia National
More informationThree-Dimensional Explicit Parallel Finite Element Analysis of Functionally Graded Solids under Impact Loading. Ganesh Anandakumar and Jeong-Ho Kim
Three-Dimensional Eplicit Parallel Finite Element Analsis of Functionall Graded Solids under Impact Loading Ganesh Anandaumar and Jeong-Ho Kim Department of Civil and Environmental Engineering, Universit
More informationModal analysis of waveguide using method of moment
HAIT Journal of Science and Engineering B, Volume x, Issue x, pp. xxx-xxx Copyright C 27 Holon Institute of Technology Modal analysis of waveguide using method of moment Arti Vaish and Harish Parthasarathy
More informationIntroduction to Vibration. Professor Mike Brennan
Introduction to Vibration Professor Mie Brennan Introduction to Vibration Nature of vibration of mechanical systems Free and forced vibrations Frequency response functions Fundamentals For free vibration
More informationChapter 6 2D Elements Plate Elements
Institute of Structural Engineering Page 1 Chapter 6 2D Elements Plate Elements Method of Finite Elements I Institute of Structural Engineering Page 2 Continuum Elements Plane Stress Plane Strain Toda
More informationThe Robust H Control for Inhibition of Load on Offshore Wind Turbines Variable Pitch Control Ping JIANG1,2, SHU-zhen GUO1
3rd International Conference on Machinery, Materials and Information echnology Applications (ICMMIA 25) he Roust H Control for Inhiition of Load on Offshore Wind urines Variale Pitch Control Ping JIANG,2,
More informationStructural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.
Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear
More informationDesign and Analysis of Silicon Resonant Accelerometer
Research Journal of Applied Sciences, Engineering and Technology 5(3): 970-974, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organization, 2013 Sumitted: June 22, 2012 Accepted: July 23,
More informationP = ρ{ g a } + µ 2 V II. FLUID STATICS
II. FLUID STATICS From a force analysis on a triangular fluid element at rest, the following three concepts are easily developed: For a continuous, hydrostatic, shear free fluid: 1. Pressure is constant
More informationIN-PLANE VIBRATIONS OF PINNED-FIXED HETEROGENEOUS CURVED BEAMS UNDER A CONCENTRATED FORCE
5th International Conference on "Advanced Composite Materials Engineering" COMAT 4 6-7 OCTOBER 4, Braşov, Romania IN-PLANE VIBRATIONS OF PINNED-FIXED HETEROGENEOUS CURVED BEAMS UNDER A CONCENTRATED FORCE
More informationResearch Article Trial Application of Pulse-Field Magnetization to Magnetically Levitated Conveyor System
Advances in Condensed Matter Physics Volume 2, Article ID 5657, pages doi:1.1155/2/5657 Research Article Trial Application of Pulse-Field Magnetization to Magnetically Levitated Conveyor System Yoshihito
More informationDEVELOPMENT OF SEISMIC ISOLATION TABLE COMPOSED OF AN X-Y TABLE AND WIRE ROPE ISOLATORS
DEVELOPMENT OF SEISMIC ISOLATION TABLE COMPOSED OF AN X-Y TABLE AND WIRE ROPE ISOLATORS 7 Hirokazu SHIMODA, Norio NAGAI, Haruo SHIMOSAKA And Kenichiro OHMATA 4 SUMMARY In this study, a new type of isolation
More informationJournal of System Design and Dynamics
Zero Power Non-Contact Suspension System with Permanent Magnet Motion Feedback* Feng SUN** and Koichi OKA** ** Kochi University of Technology 185 Miyanokuchi, Tosayamada, Kami city, Kochi 782-8502, Japan
More informationStrong echo eect and nonlinear transient growth in. shear ows U.S.A.
Strong echo eect and nonlinear transient growth in shear ows J. Vanneste 1,P. J. Morrison and T. Warn 3 1 Dept. of Phsics, Universit oftoronto, Toronto, Canada. Dept. of Phsics and Institute for Fusion
More informationPHYSICS PART II SECTION- I. Straight objective Type
PHYSICS PAT II SECTION- I Straight objective Tpe This section contains 9 multiple choice questions numbered to 1. Each question has choices,, (C) and, out of which ONLY ONE is correct.. A parallel plate
More informationController strategy for a 6 DOF piezoelectric translation stage
UCR-ROC-93 Controller strateg for a 6 DOF pieoelectric translation stage E.. Buice, H. ang,. T. mith, R. J. Hocken, D.. Trumper, D. Otten, R. M. eugling March 4, 6 EUEN 6th International Conference Baden,
More informationExperimental study of delayed positive feedback control for a flexible beam
THEORETICAL & APPLIED MECHANICS LETTERS 1, 063003 (2011) Experimental study of delayed positive feedback control for a flexible beam Kun Liu, Longxiang Chen, and Guoping Cai a) Department of Engineering
More information(Refer Slide Time: 00:01:30 min)
Control Engineering Prof. M. Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 3 Introduction to Control Problem (Contd.) Well friends, I have been giving you various
More informationSimulation of a Single and Double-Span Guideway under Action of Moving MAGLEV Vehicles with Constant Force and Constant Gap
Simulation of a Single and Doule-Span Guideway under Action of Moving MAGLEV Veicles wit Constant Force and Constant Gap Reinold Meisinger Mecanical Engineering Department Nuremerg University of Applied
More information1 Fig. 3.1 shows the variation of the magnetic flux linkage with time t for a small generator. magnetic. flux linkage / Wb-turns 1.
1 Fig. 3.1 shows the variation of the magnetic flux linkage with time t for a small generator. 2 magnetic 1 flux linkage / 0 10 2 Wb-turns 1 2 5 10 15 t / 10 3 s Fig. 3.1 The generator has a flat coil
More information13 IRIS Active Vibration Absorber (AVA) for Vibration Reduction at Piping Systems in Chemical Plants
13 IRIS Active Vibration Absorber (AVA) for Vibration Reduction at Piping Sstems in Chemical Plants Chapter 13- Authors: Jürgen Engelhardt Herbert Friedmann Motivation Vibration reduction in piping sstems
More informationDynamic Fields, Maxwell s Equations (Chapter 6)
Dynamic Fields, Maxwell s Equations (Chapter 6) So far, we have studied static electric and magnetic fields. In the real world, however, nothing is static. Static fields are only approximations when the
More informationwe make slices perpendicular to the x-axis. If the slices are thin enough, they resemble x cylinders or discs. The formula for the x
Math Learning Centre Solids of Revolution When we rotate a curve around a defined ais, the -D shape created is called a solid of revolution. In the same wa that we can find the area under a curve calculating
More informationEffect of Optimal Placement of Permanent Magnets on the Electromagnetic Force in the Horizontal Direction
actuators Article Effect Optimal Placement Permanent Magnets on Electromagnetic Force in Horiontal Direction Yasuaki Ito 1, Yoshiho Oda 1, Takayoshi Narita, * ID and Hideaki Kato 1 Course Mechanical Engineering,
More informationSIMPLE PENDULUM AND PROPERTIES OF SIMPLE HARMONIC MOTION
SIMPE PENDUUM AND PROPERTIES OF SIMPE HARMONIC MOTION Purpose a. To investigate the dependence of time period of a simple pendulum on the length of the pendulum and the acceleration of gravity. b. To study
More information14.1 Systems of Linear Equations in Two Variables
86 Chapter 1 Sstems of Equations and Matrices 1.1 Sstems of Linear Equations in Two Variables Use the method of substitution to solve sstems of equations in two variables. Use the method of elimination
More informationDynamics of the synchronous machine
ELEC0047 - Power system dynamics, control and stability Dynamics of the synchronous machine Thierry Van Cutsem t.vancutsem@ulg.ac.be www.montefiore.ulg.ac.be/~vct October 2018 1 / 38 Time constants and
More informationCH. 1 FUNDAMENTAL PRINCIPLES OF MECHANICS
446.201 (Solid echanics) Professor Youn, eng Dong CH. 1 FUNDENTL PRINCIPLES OF ECHNICS Ch. 1 Fundamental Principles of echanics 1 / 14 446.201 (Solid echanics) Professor Youn, eng Dong 1.2 Generalied Procedure
More information