Electromagnetic Levitation Control of Contactless Linear Synchronous Drive for Flexible Vertical Transportation

Transcription

1 Electromagnetic Levitation Control of Contactless Linear Synchronous Drive for Flexible Vertical Transortation Toshiyuki NAKAI*, Daisuke TATEISHI**, Takafumi KOSEKI*, and Yasuaki AOYAMA*** (*)Deartment of Electrical Engineering of The niversity of Tokyo, 7-- Hongo, Bunkyo-Ku Tokyo Telehone: / Fax: , (**) Mitsubishi Electric Cor. (***) Shin-etsu Chemical Cor. Keywords electromagnetic levitation, elevator, Halbach magnet array, linear synchronous motor Abstract Roeless elevators have been studied for efficient transortation in high buildings. This system can achieve higher caacity and flexibility of transortation than conventional elevators can. To realize such a system, authors have roosed contactless transortation system which has coreless linear synchronous motor for driving, and four -shaed hybrid electromagnets for osture control. These electromagnets are also used as field magnets when the cage moves in horizontal direction. In this aer, authors exlain the outline of roosed system, results of levitation tests and future works for its vertical and horizontal drive control. Introduction Poulation density of urban cities in Asian countries like Tokyo, Shang-Hai etc., is extremely large and such cities have the roblem of insufficient sace. So, increase of high buildings is exected, and high erformance of vertical transortation system will be required. However, conventional elevator using wire can drive only one cage in one shaft, and elevators occuy large sace in buildings. It is rincial obstacle for efficient use of sace. For this reason, several Jaanese construction comanies and elevator manufactures researched about the ossibility of the vertical linear drive [] in early 99's. According to the results, the most feasible method is a long stator-tye linear synchronous motor, in which the moving cages have rare-earth strong ermanent magnets as a magnetic field of the synchronous motor. Authors have also reconsidered the concet, fundamental design and investigated oeration method of such a system [], and summarized as below:. For efficient sace use and realization of large transortability, we aim to construct new elevator system whose cage moves both vertically and horizontally.. From the asect of flexible movement of cage, we decided to construct elevator system without any mechanical contact.. According to the receding research about the oeration of roeless elevator [], required seed of cage for large transortability is relatively low. But in the case of horizontal movement, moving erformance equivalent to vertical one is demanded. Profile of roosed system Our system consists of three comonent arts as below.

2 . -shaed hybrid electromagnets for osture control. LSM for vertical movement. LSM for horizontal movement As a osture controlling system, four -shaed electromagnets are attached in four vertex of the cage and LED ga sensors are attached in the other four vertex. Herewith, we can realize three-degree-of-freedom osture control. And they are also used as field magnets of LSM for horizontal movement. Hoisting LSM is long stator tye, and it has no armature core for avoiding strong normal force. And Halbach magnet array is used in field magnets. So, LSM can generate sufficient hoisting ower without core, and also enables suression of the rile of hoisting force. Fig. shows the entire structure of our roosed system. Fig. Fundamental Structure of our roosed system Posture controlling system. Basic rincile of osture controlling As above mentioned, osture controlling of cage is conducted by four -shaed hybrid electromagnets. In the system shown in fig., hoisting LSM control the osture of z direction, and -shaed electromagnets oerate -degree-of-freedom osture control, in x direction, itching direction and rolling direction. Posture control needs coordinated control of -shaed electromagnets because they cannot generate reulsive force. In the roosed system, relation between the force generated by electromagnets and controlling force in resective direction is as below. F x T / L z T r / L y = F = = F () F, F, F, F : Force generated by -shaed electromagnet resectively. F x : Controlling ower in x direction T, T r : Controlling torque in itching or rolling direction L y, L z : Dislacement of electromagnets in x or y direction from center of gravity of cage

3 And, allocated attractive forces are reresented by equations below. F =.5F F =.5F F =.5F F =.5F x x x x / / / / + T / Lz Tr / L y T / Lz + Tr / Ly + T / Lz + Tr / L y T / L T / L z r y () F : Maximum attractive force of actuator Thus, -degree-of-freedom control is oerated. Additionally, by using electromagnet and ermanent magnet in combination, for generating attractive force.5f with zero controlling current, consumtion of electric ower can be reduced greatly and can enable control system easier. Fig. shows the structure of the -shaed hybrid electromagnet used for osture controlling. Iron Core Perm anent M agnet. Controlling method Fig. Structure of electromagnets and their layout Exeriment of osture controlling is oerated by two methods, I-PD controlling and state feedback control with observer, for the comarison of their erformance. First, attractive force of -shaed hybrid electromagnet is reresented as the equation below. ( i + ig ) ( i + ig ) F = k = k () g + G g ( ) a i G : Current equivalent value of magnetomotive force of ermanent magnet G : Airga equivalent value of ermanent magnet and iron core of electromagnet And conducting linearization of equation() around the nominal oint i =, g =g, we can reresent attractive force as below. F F A g + Bi () where, F = F i =, g = g, F A =, g i= F B =, g = g g i g = g Here, we must ay attention to the existence of ermanent magnet installed in -shaed hybrid electromagnet. ithout ermanent magnets, the value of B in equation() becomes zero because attractive force of electromagnet is roortional to the square value of coil current. But by installing ermanent magnets and moving nominal oint, we can avoid above-mentioned roblem and can design controller easily. Moreover, electrical energy consumtion decreases because the F/I sloe around

4 nominal oint becomes large. Fig. shows the block diagram of controller of x-direction. Controlling of itching direction and rolling direction is the same way. X*(s) Controller V x R +sl I x B F dx m s X(s) A Fig. Linear Plant Model of Posture Controlling System (x-axis).. Designing of controller (I-PD) I/O gain of I-PD controller is reresented as below using the constants K P, K I, K D. X K B = I (5) * X mls + mrs (AL + K B) s (AR + BK ) s + K B D Comaring the denominator olynomial of equation(5) to Kessler standard form, we can decide three constants as below... Designing of controller (state feedback) Fig. can reresent like equation(6) using state equation. x & = Ax + Be x, y = Cx (6) R / L T where, A = A / m B / m, x = x&, B = ( / L), C = ( ) x ix Here, we add the integral of dislacement to state variable for removing the steady-state deviation. At this time, state equation is reresented as below, and block diagram is exressed as fig.. A / m A = x & = A x + B e x (7) B / m where, ( ) T R / L, x = x x&, = i B x xdt P L I

5 - + F x * + s + F x^. F + ^ I x + F V x R +sl R +sl B I x F ^ dx k(i x +i G ) (g x +G) observer + - F dx m s x Fig. Block Diagram of State Feedback Control And resective feedback gain can be calculated as follows. If we let the feedback gain F=(F, F, F, F ), characteristic olynomial can is as below. z I ( A + BF) = (8) Comaring the left art of equation(8) to Kessler standard form, we can calculate resective feedback gains as follows. F x AL 6mL AL ml 8L 6mL =, F =, F = R, F = Bτ x x τ x (9) Bτ B τ B Bτ And we adoted minimal order observer. Only ga length between iron core and electromagnet is measured, and other variables are calculated by observer. Observer is designed by Goinath s method.. Vertical transort system.. Armature windings In our roosed system, vertical driving is oerated by Linear Synchronous Motor (LSM). For avoiding strong normal force, we adoted coreless armature. Moreover, for obtaining strong thrust and for decreasing thrust rile, we adoted short itch windings. Generally, short itch windings is inferior to full itch windings in the asect of thrust, but fig.5 indicates that the sace of slot occuied by cuer is larger when we adoted short itch windings. So, also from the asect of the thrust value, it is valid to adot short itch windings. V V.. Field magnets V Full itch windings Fig.5 Difference of both windings V V Short itch windings In field magnets, we adoted Halbach magnet array. Magnetic field generated by Halbach magnet array is shown in fig.6. Halbach magnet array generates strong and sinusoidal magnetic field on only one side. This array enables the reduction of thrust rile and increase of thrust value. So, we can obtain

6 enough thrust value without armature core. Result of exeriment Fig.6 Magnetic field generated by Halbach magnet array e conducted the test of osture controlling using our rototye. Fig.7 shows the aearance of our rototye. In exeriment, cage is stringed for osture controlling. For comarison, we conducted osture controlling by two different method, I-PD controlling and state feedback controlling. Result of exeriment is shown in fig.8. hen t=[s], we change the commanded value from [mm] to.5[mm]. Fig.7 Aearance of our rototye Fig.8 Posture controlling exerimental results and the comarison of two different controllers. 5

7 5 Conclusion In this aer, we roosed contactless vertical transort system with coreless LSM for vertical drive and four -shaed electromagnets for osture controlling. And osture controlling in three directions, x-direction, itching direction, yawing direction, by using both I-PD controller and state feedback controller. From the exeriment result, vibration after reaching commanded osition is lower when we adoted state feedback controller. And our future works are to install the system for horizontal movement to rototye. References. Linear-Motor-Driven Vertical Transortation System", Elevator orld, (996). K. Yoshida, S. Moriyama, X. Zhang: Contactless Elevator Motion Control in Roeless Linear Elevator, National Convention Record, IEE Jaan, 5-8,. (). M. Miyatake, T. Koseki, S. Sone: Evaluation of Oerational Performance in Roeless Elevator Systems", Journal of The Jaan Society of Alied Electromagnetic and Mechanics, Vol. 5, No., (997) (in Jaanese) 6