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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 64...
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Fuzzy control of a vertical shaft single axis controlled repulsive type

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Fuzzy control of a vertical shaft single axis controlled repulsive type

  1. 1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 200 FUZZY CONTROL OF A VERTICAL SHAFT SINGLE AXIS CONTROLLED REPULSIVE-TYPE MAGNETIC BEARING TAPAN SANTRA1 , Dr. D. ROY2 , A.B. CHOUDHURY3 1 Department of Electrical Engineering, Kalyani Government Engineering College, Kalyani, Nadia, Pin.-741235, W.B, India 2 Department of Electrical Engineering, Bengal Engineering & Science University, Shibpur, Howrah-711103, W.B, India 3 Department of Electrical Engineering, Bengal Engineering & Science University, Shibpur, Howrah-711103, W.B, India ABSTRACT In present century green technology is getting importance. This technology offers low loss, low noise, low pollution and low hazards. Magnetic bearing is one of the best examples of this technology. Among different type of magnetic bearings single axis controlled repulsive type magnetic bearing (SACRMB) is best fitted regarding performance and cost. This paper introduces a vertical shaft SACRMB, consists of permanent magnets for radial stability and electromagnets for levitation & axial stability. SACRMB has tremendous opportunities to become a common choice for house hold to industrial applications. A device becomes popular due to its simple construction, reliability & simple control system which do not depend upon system parameters. A person knows nothing about control system, when becomes able for understanding & maintenance of the control of SACRMB then only the mass production is possible. Here is the importance of fuzzy controller which is nonparametric and very simple in nature. In this paper the design & performance of fuzzy controller has been introduced for the axial control of the SACRMB. The radial control is done by passive permanent magnet. It is found that the radial & axial vibrations are under tolerable limit and SACRMB works extremely well. Keywords: SACRMB, fuzzy control, magnetic forces, stability, vibration. INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN ENGINEERING AND TECHNOLOGY (IJARET) ISSN 0976 - 6480 (Print) ISSN 0976 - 6499 (Online) Volume 4, Issue 4, May – June 2013, pp. 200-207 © IAEME: www.iaeme.com/ijaret.asp Journal Impact Factor (2013): 5.8376 (Calculated by GISI) www.jifactor.com IJARET © I A E M E
  2. 2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 201 I. INTRODUCTION The existing mechanical bearing has some disadvantages like high noise, requirement of lubrication, maintenance, high energy loss & frequent occurrence of hazards. So there is always a demand for a bearing which will be free from these disadvantages, will be simple, economic, standalone & reliable. To achieve all these requirements, magnetic bearing is one of the best solutions [1]. Most of the commercially available magnetic bearing is active or passive [2, 3, 4, 5 & 7] in nature. For pure passive magnetic bearing (MB) stability is one problem and for active MB, reliability and cost is another problem, due to its complex control system, high number of electromagnets requirement and associated circuit. In this background scenario, people has embarked on developing of single axis controlled repulsive type magnetic bearing [6] which provides the advantages like simple construction, high reliability and low cost. In this configuration the radial stability is achieved by repulsive force between stator permanent magnet (connected with fixed frame) and rotor permanent magnet (connected with shaft) as shown in Fig.1. Axial stability is achieved by the attraction force between a flywheel (connected with shaft) and electromagnets. Among different types of configuration, the vertical shaft configuration of SACRMB has been represented in our research. In this paper the constructional design has been done by ANSYS software and control design has been carried out by MATLAB. Fig. 1 Construction of SACRMB Fig. 2 Different forces acting on SACRMB Till date the people concentrate on PID controller for the tuning of SACRMB, which is not easy to tune and logically cumbersome to implement. This is a great hurdle for mass production of SACRMB. So for mass production of SACRMB, the primary requirement is a very simple control system so that anybody can maintain or develop the control mechanism, who knows very little bit of control theory. So we are embarked on designing a fuzzy logic
  3. 3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 202 based controller which do not depends on the bearing parameters. The fuzzy rule based controller has been designed and simulated. The vibration characteristics along three different axes have been simulated which looks extremely well and under tolerable limit. II. CONSTRUCTION OF SACRMB A single-axis controlled repulsive-type magnetic bearing is a device which supports the rotor system by magnetic levitation and allows it to rotate freely with less vibration and low loss. Here two things are important; number one the rotor system should be levitated and number two the vibration of the rotor system should be less as much as possible at steady running condition as well as in different transient conditions like sudden change in load, on & off of the machine etc. In this paper vertical shaft configuration of SACRMB has been discussed. The levitation force can be achieved by the attractive force between electromagnet & flywheel and the radial stability can be achieved due to repulsive force between stator & rotor permanent magnet [Fig.1].To reduce the effect of radial disturbance, higher radial stiffness is desired which can be achieved by proper configuration of stator & rotor permanent magnet and by selecting proper magnet material. In this work NdFeB permanent magnet has been selected as magnetic material. The axial X-axis vibration can be controlled by the attraction force between electro magnet and flywheel. A controller will sense the X- axis vibration or displacement by a gap sensor (capacitive or eddy current type) and control the current through the coil of electro magnet [Fig. 2]. III. MODELLING OF SACRMB The rotor is assumed to be rigid body. The origin G of the stator fixed frame of reference and O is the mass center of the rotor. (xe, ye, ze) is the location of O with respect to the fixed frame of reference. The forces acting on the rotor are shown in the Fig. 2. The force and moment balance around ܺ௥ ܻ௥ & ܼ௥ and force of electromagnets are given by following equations. Force balance equations ‫ܨ‬௫ ൌ ݉‫ݔ‬ሷ௘=݂ଵ ൅ ݂ଶ ൅ ݂ଷ ൅ ݂ସ ൅ ݂௟௫ ൅ ݂௨௫ െ ݉݃….Equation.1 ‫ܨ‬௬ ൌ ݉‫ݕ‬ሷ௘=݂௟௬ ൅ ݂௨௬ ……Equation. 2 ‫ܨ‬௭ ൌ ݉‫ݖ‬ሷ௘=݂௟௭ ൅ ݂௨௭ …..Equation. 3 Moment balance equation ‫ܯ‬ ൌ ‫ܬ‬௬ߠሷ ൅ ‫ܬ݌‬௫߰ሶ ൌ ݂௟௭‫ܮ‬଴ଵ െ ݂௨௭‫ܮ‬଴ଶ െ ݂ଵ݈ ൅ ݂ଶ݈ ……Equation. 4 ܰ ൌ ‫ܬ‬௫߰ሷ െ ‫ܬ݌‬௫ߠሶ ൌ ݂௟௬‫ܮ‬଴ଵ െ ݂௨௬‫ܮ‬଴ଶ െ ݂ଶ݈ ൅ ݂ସ݈ ……Equation. 5 Equations for electromagnet ݂௝ ′ ൌ 2‫ܨ‬௝ሺ ௜ೕ ′ ூೕ െ ௚ೕ ௐ ሻ ……Equation. 6 dij/dt = (R/L) ij+ (1/L) v………Equation.7 where ݆ ൌ 1, … … 4
  4. 4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May Here m is the mass of rotor. to 4, i.e four number of electromagnet between stator & rotor permanent magnet along axial direction (X magnetic bearing respectively.f permanent magnet along radial direction (Y respectively. flz & fuz are the repulsive force between stator & rotor permanent magnet along radial direction (Z-axis) at lower & upper magnetic bearing respectiv inertia of rotor around X & Y axis respectively. shaft centre. L01 & L02 are the distance of lower & upper permanent magnetic bearing from mass centre o. R & L are the resistance & inductanc V is the supplied voltage to the electromagnet. rotor along X-axis, Y-axis, Z-axis ,angular rotation around Y & Z axis Fig. 3 Axial force Vs axial displacement (Y-axis) Fig. 5 Radial force Vs radial displacement (Z-axis) International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 203 Here m is the mass of rotor. fi are forces between electro magnets & flywheel, for i=1 to 4, i.e four number of electromagnets have been used. flx & fux are the repulsive force between stator & rotor permanent magnet along axial direction (X-axis) at lower & upper fly & fuy are the repulsive force between stato permanent magnet along radial direction (Y-axis) at lower & upper magnetic bearing are the repulsive force between stator & rotor permanent magnet along axis) at lower & upper magnetic bearing respectively. Jx inertia of rotor around X & Y axis respectively. l is the distance of each electromagnet from are the distance of lower & upper permanent magnetic bearing from mass centre o. R & L are the resistance & inductance of the electromagnet coil respectively. V is the supplied voltage to the electromagnet. xe, ye, ze, θ & ψ are the displacement of the axis ,angular rotation around Y & Z axis respectively. Vs axial Fig. 4 Radial force Vs axis) displacement (X-axis) radial Fig. 6 Dimension of permanent magnet in SACRMB International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN June (2013), © IAEME are forces between electro magnets & flywheel, for i=1 are the repulsive force axis) at lower & upper are the repulsive force between stator & rotor axis) at lower & upper magnetic bearing are the repulsive force between stator & rotor permanent magnet along & Jy are the is the distance of each electromagnet from are the distance of lower & upper permanent magnetic bearing from e of the electromagnet coil respectively. are the displacement of the respectively. radial axis) Dimension of permanent magnet
  5. 5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 204 F, I, & W are the electromagnetic force, coil current & gap between electromagnet & flywheel at steady operating condition respectively. g, i are the instantaneous gap between flywheel and electromagnet & coil current respectively. Now the forces flx & fux, fly & fuy, flz & fuz are to be formulated as a function of displacement along X- axis, Y-axis & Z-axis respectively (equation...8). For that purpose the rotor has been shifted along three different axis and the corresponding forces has been derived by ANSYS software. The result has been displayed in Fig. 3, Fig. 4 & Fig. 5 respectively. . flx or fux =Sx(x-A)+FA, fly & fuy=-Sy(y-B)+FB, & flz fuz =-Sz(z-C)+FC….Equation.8 Where (A, B, C) is the steady operating point of the rotor. Sx, Sy & Sz are the measured slope of the force Vs displacement characteristics from Fig. 3, Fig. 4 & Fig. 5 respectively. FA, FB & FC are the steady force at operating point or force offset. The 14 number variables xe, ye, ze, dxe/dt, dye/dt, dze/dt, , θ , dθ/dt , ψ, dψ/dt,i1,i2,i3&i4 are taken as state variables. So from equation 1 to 7 the following state space model can be achieved. ୢ ୢ୲ ൣXሶ൧ ൌ AഥሾXሿ ൅ BഥሾUሿ Y ൌ CതሾXሿ………equation. 9 IV. PARAMETER OF SACRMB The proposed bearing system has two axially magnetized stator and rotor permanent magnets (Fig. 1) which passively supports along radial direction (Z & Y axis) due to the repulsive force between stator & rotor magnet. The tentative dimension of these magnets for a 2 kg rotor system is shown in Fig. 6. This device also consists of four number electromagnets which provide the levitation force as well as actively controls the rotor in the axial direction (X-axis) by the attractive force between electromagnet & flywheel. So here the detailed specification of stator & rotor permanent magnet, rotor system & electromagnet has been given. Permanent Magnet Specification: physical dimension: As shown in Fig. 6. Type: NdFe35 .Steady axial force (X axis) = 3.98 N, Steady radial force (Y & Z axis) = 0.747395N & - 0.51385 N Stiffness along three axis Sx= 77120 N/m, Sy=-72500N/m and Sz=-76900 N/m respectively. Rotor: Mass=2 Kg, Inertia with respect to X & Y Axis 0.0161 kg-m2 & 0.0383 kg-m2 respectively, length of shaft=0.210m, radius of flywheel= 0.060 m Electromagnet: Coil resistance=2.93 ohm, Coil inductance=0.0485 H, Steady Current=1.33 A & Steady Attractive Force=3.91 N Gap sensor: scaled output= 1V/mm V. FUZZY CONTROLLER DESIGN After modelling of the SACRMB as per equation. 9 , all the paratemeter values can be placed in A, B & C matrix. Then the model has been simulated for axial & radial vibration with a unit step input. Axial vibration is unbounded in nature [Fig. 7]. This means the open loop system is unstable along axial (X-axis) direction.
  6. 6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May Fig. 7 Axial vibration without controller From Fig. 8 & Fig. 9 it is observed that there is very negligible radial vibration because of the passive vibration control by stator & rotor permanent magnet. So the system is inherently radially stable but axial make the system axially(x-axis) stable. This control scheme is given in Fig. 10 . In this respect it is observed that PID controller may be used but the tuning of this controller is found to be cumbersome. So the its non parametric nature which is very much usefull for mass production of SACRMB. To design the fuzzy controller first the input & output membership functions has been developed. In SACRMB the errror ( set change in axial position position by gap sensor) & deviation of this error are taken as the input of the controller and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The range of allowable error is -3 mm to +3 mm & deviation in error is Accordingly the input MF has been developed such as nz (negative zero), sp (small positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium negative) & vn (very negative). The output of the controller is the control force, that is current through electromagnet coil & the corresponding membership functions are shown in Fig. 13 such as z (zero), increment), sd (small decrement), md (medium decrement) & ld (large decrement). The range of the control force is -4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is show in Table. 1 & corresponding Fig. 10 International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 205 Fig. 8 Z-axis radial vibration Fig. 9 Y controller vibration & Fig. 9 it is observed that there is very negligible radial vibration because of the passive vibration control by stator & rotor permanent magnet. So the system is inherently radially stable but axially unstable. So a controller is required to axis) stable. This control scheme is given in Fig. 10 . In this respect it is observed that PID controller may be used but the tuning of this controller is found to be cumbersome. So the idea of fuzzy logic controller has been introduced due to its non parametric nature which is very much usefull for mass production of SACRMB. To design the fuzzy controller first the input & output membership functions has been rror ( set change in axial position – sensed change in axial position by gap sensor) & deviation of this error are taken as the input of the controller and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The 3 mm to +3 mm & deviation in error is -6 mm to +6 mm. MF has been developed such as nz (negative zero), sp (small positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium tive). The output of the controller is the control force, that is current through electromagnet coil & the corresponding membership functions are shown in Fig. 13 such as z (zero), si(small increment), mi (medium increment), li (large decrement), md (medium decrement) & ld (large decrement). The 4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is show in Table. 1 & corresponding circuit is given in Fig. 14. Fig. 10 Control scheme for SACRMB International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN June (2013), © IAEME Y-axis radial vibration & Fig. 9 it is observed that there is very negligible radial vibration because of the passive vibration control by stator & rotor permanent magnet. So the ly unstable. So a controller is required to axis) stable. This control scheme is given in Fig. 10 . In this respect it is observed that PID controller may be used but the tuning of this controller is idea of fuzzy logic controller has been introduced due to its non parametric nature which is very much usefull for mass production of SACRMB. To design the fuzzy controller first the input & output membership functions has been sensed change in axial position by gap sensor) & deviation of this error are taken as the input of the controller and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The 6 mm to +6 mm. MF has been developed such as nz (negative zero), sp (small positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium tive). The output of the controller is the control force, that is current through electromagnet coil & the corresponding membership functions are shown si(small increment), mi (medium increment), li (large decrement), md (medium decrement) & ld (large decrement). The 4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is
  7. 7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May Fig. 11 input MF ‘Erroe Fig. 13 Fig. 14 Fuzzy logic controller International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 206 Erroe’ Fig. 12 Input MF ‘Deviation error Fig. 13 Output MF ’current’ Table 1. Rulle Base Fuzzy logic controller Fig. 15 Axial vibration with Fuzzy controller International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN June (2013), © IAEME Deviation error’ Axial vibration with Fuzzy controller
  8. 8. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME 207 Fig. 15 represents the axial vibration characteristic of SACRMB with a fuzzy controller. It is observed that at first some vibration is there but within 3 sec the vibration deceases to almost zero. The maximum peak of vibration is 0.45 mm which is acceptable. The fuzzy controller work exceptionally well. VI. CONCLUSION In this paper modelling & controller design of a vertical shaft single axis controlled repulsive type magnetic bearing has been represented. For its advantageous position over existing mechanical bearing, SACRMB will replace all the existing bearing within next few years. For this mass production is necessary, which is possible only when a simple, low cost construction & control system of SACRMB is adopted. For this purpose it is advantageous to use a nonparametric controller (fuzzy controller) which is simple and logically easy to implement. In this paper by using a fuzzy controller excellent axial stability of SACRMB has been achieved. REFERENCES [1] J. P. Yonnet, “Passive magnetic bearing with permanent magnets”, IEEE Trans. Magn .1978,14, (5), pp. 803-805 [2] Lembke. T, “Design for magnetic induction bearing”, in Chalmers Univesity of Technology, Göteborg, 1990 [3] Xu Feipeng, Li Tiecai, Liu Yajing,”A study on passive magnetic bearing with Halbach magnetized array", Electrical Machines and Systems, 2008. ICEMS 2008, pp. 417 - 420, Volume: Issue: 17-20 Oct. 2008 [4] Falkowski K., Henzel M.: “High Efficiency Radial Passive Magnetic Bearing”, SOLID STATE PHENOMENA, Vol. 164, pp. 360-365, 2010 [5] SAMANTA, P. HIRANI, H. “MAGNETIC BEARING CONFIGURATIONS: THEORETICAL AND EXPERIMENTAL STUDIES”, MAGNETICS, IEEE TRANSACTIONS ON, ON PAGE(S) 2038 - 2042 VOLUME: 44 ISSUE: 2, FEB. 2008 [6] S. C. mukhopadhyay, T. Ohji, M. Iwahara, S. Yamada and F. Matsumura, "influence of permanent magnet configuration on the stability of repulsive type magnetic bearing", proceeding of japanese national conference on linear drive, ld - 96 - 105, pp. 57-66, 1996 [7] Abdul Rashid Husain, Mohamad Noh Ahmad, and Abdul Halim Mohd. Yatim “asymptotic stabilization of an active magnetic bearing system using lmi-based sliding mode control”, world academy of science, engineering and technology, p. 37, 20 [8] Neeraj Tiwari, D. Bhagwan Das and Prabal Pratap Singh, “Design, Development and Hardware Realization of X-Beebased Single Axis Solar Tracking System”, International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 3, 2012, pp. 8 - 20, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [9] Amit Shrivastava and Dr. S. Wadhwani, “Application of Time-Domain Features with Neural Network for Bearing Fault Detection”, International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 2, 2012, pp. 151 - 155, ISSN Print : 0976-6545, ISSN Online: 0976-6553.

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