6 Degrees of Freedom Control through Three Electromagnets and Three Linear Induction Motors

Transcription

1 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 of Toko unko-ku, Hongo , Toko, JPN Phone , FX takafumikoseki@ieee.org URL: Kewords ic suspension, linear induction drive, magnetic levitation, motion control, and twodimensional drive bstract onfiguration that the mover has three electromagnets and three linear induction motor (LIM) has been proposed for contactless flexible conveance sstem. Hbrid electromagnet that uses permanent magnet can let power consumption converge to ero in stead state, and its stator becomes simple because the combination of three LIM s is used for two-dimensional drive. The normal attractive force of LIM can increase the carring capacit of the mover, although it can be also disturbance force for the stabiliation of the magnetic levitation sstem. uthors have experimentall confirmed that the proposed configuration can realie six-degrees of freedom control of the mover. Position sensing for the closed loop control of two-dimensional linear drive is difficult: one possible approach based on visual sensing combined with dual sample-rate digital observer is proposed and discussed. 1 Introduction The combination of electromagnetic suspension technolog (EMS) and linear motor is useful in the conveance sstems, but its movement is usuall limited to single dimension. For more flexible conveance sstem, we have proposed the coordination of a four-pole shaped hbrid electromagnet and two-dimensional linear snchronous motor[1]. It had, however, some disadvantages, such as its lack of damping in the awing direction and complexit of its stator.we have proposed a mover that has 3 U-shaped electromagnets and three linear induction motors (LIMs)[2] in order to overcome these disadvantages. In this configuration, which is shown in figure 1, six-degrees of freedom of the mover can be controlled and the stator is simpl composed of iron and conductor plate. 2 ontrol method of magnetic suspension Three hbrid electromagnets that have permanent magnets on the surface and coils are used to suspend the mover and control its posture in this stud. The hbrid electromagnets can let power consumption converge to ero in the stead state. The relationship between the coil current I f, effective gap length g e (air gap + thickness of secondar conductor d) of electromagnet and attractive force f m has been calculated based on a simple magnetic circuit analsis. k is an attractive force coefficient, L m is thickness of the permanent magnet and I m is magnetmotive force of the permanent magnet. The equation is described as follows : 953

2 LIM F 2 LIM E LIM D Figure 1 onfiguration of the proposed mover. γ x I f + I m f = m k ge + L (1). m s methods to control the posture of the mover, both of decentralied and centralied controls have been proposed. In the decentralied control, each of the three electromagnets controls its gap length suspending one-third of total mass. In the centralied control, total posture (,, ) is cont-rolled using coordinates transformations, which include the location of electromagnets. The location of electro-magnets and LIMs is shown in figure 2. The l e is the distance between the center of the mover and its electromagnet, l l is the one between the center of the mover and its LIM s. F tf LIM F F F te F nf le F ne F LIM D l l F nd F td LIM E F γ x Figure 2 Location of s and 2.1 Decentralied Motion ontrol We call the conventional control method as the decentralied control, in which the gap of each magnet is controlled and stabilied separatel b its own controller. The block diagram of decentralied control is shown in figure 3. In this stud, the three hbrid electromagnets have same characteristics, so one can use the same controller in each gap length of, and. 2.2 entralied Motion ontrol The centralied control uses coordinates transformation to change gap length and currents of electromagnets to posture (,, ) and virtual currents (i,i,i ). These coordinates transformations are described as follows. 1/3 = 2/3l 0 i i i 1 = 1 0 e 1 1/ 2 3 / 2 1/3 1/3l e 1/ 3l e 1/3 g 1/3l e g 1/ 3l e g g = T g g 1 i i 1/ 2 i = H i 3 / 2 i i using these virtual variables, dnamic equations of motions are described. For example, linearied dnamic equation of direction is described as follows : Ms 2 = K i + 3K (4). The controllers of, and directions are designed depending on the linearied dnamic equations and assuming these equations are realied independentl. The controller s gains are determined as is the case with decentralied control. The block diagram of the centralied control is illustrated in figure 4. (2) (3) 954

3 T -1 g g g controller controller controller i i Magnetic Levitation Sstem g g g T controller controller controller Figure 3 lock diagram of the decentralied control. i i i H -1 i i Magnetic Levitation Sstem g g g T Figure 4 lock diagrm of the centralied control. 3 Two-Dimensional Drive Scheme using Three Linear Induction Motors Three LIMs are used for controlling two-dimensional drive. When linear motor generates thrust, normal force is simultaneousl generated in the vertical direction. In a stead state, we use normal attractive force of LIMs to suspend 10% of the mover s mass. In terms of suspension and propulsion, we prefer small gap length to get large attractive force and thrust. ut the shorter the gap becomes, the smaller the range of motion becomes. In order to keep sufficient range of motion and obtain thrust large enough, we have determined the air gap length to 4.0[mm]. The speed of the mover is not high (lower than 0.05[m/s]) and slip frequenc ma be low in prospective experiments. We have, therefore, simpl adopted slip frequenc control as a control method of a LIM because thrust increases in proportion to its slip frequenc in the region of low slip frequenc. pproximated linearied thrust equation is described as follows : F t K sf (5). We have to measure the speed of each LIM s for the drive control. coordinates transformation is used to estimate the velocit from the mover s velocit. This is described in equation (6) and the coordinates transformation from each LIM s thrust to forces and torque toward x,, and γ direction described in equation (7). v 1 0 l D l vx vx v = = E 1/ 2 3 / 2 l l v P v v F 1/ 2 3 / 2 l ω γ ω l γ F x 1 1/ 2 1/ 2 F td FtD F = 0 3 / 2 3 / 2 F = te L F te T ll ll ll FtF F γ tf (6) (7) 4 ommand response ( direction, decentralied control).simulation and Experimental Results The two magnetic levitation control methods are compared experimentall. The experiments of linear drives interacting with magnetic suspension will be also reported. 955

4 4.1 ontrol Sstem and Experimental ench Levitation and drive are controlled b a DSP-sstem. The DSP sstem enables constant samplingand control- ccles. In this case, that ccle was 500[µs]. The configuration of control sstem is shown in figure 5. Three different gap-lengths of electromagnet are detected b LED sensor. Measured gap lengths are taken into the DSP through an /D board, command currents of three electromagnets are calculated and the currents are given to electromagnets b chopper. The position in the direction are detected b supersonic sensor for linear drive controls. ommand currents are calculated and given to LIM E and LIM F. oefficients of the test bench are shown in table 1 and a photograph of the experimental sstem is shown in figure 6 Table 1 oefficients of the facilit M 14.2[kg] k [Nm 2 / 2 ] G 5.70[mm] I m 15.0[] 0 L m 3.00[mm] d 2.00[mm] J [kgm 2 ] J [kgm 2 ] J γ [kgm 2 ] l e [m] l l 0.100[m] τ [s] P Program download Data upload DSP Inverter board D board Inverter Inverter Inverter urrent urrent urrent Position sensor Gap sensor urrent sensor Figure 5 Suspension control sstem. Figure 6 Photograph of the test bench. 4.2 Experiments of Magnetic Suspension ommand responses of the -direction in the decentralied and the centralied controls are shown in figures 7 and 8, respectivel. The command responses of the -direction in decentralied and centralied controls are shown in figures 10 and 11. ommand values in the - and directions are changed from 0[mm] to 0.5[mm] and from 0[rad] to 0.588[rad] at 1.5[s]. When we compare figures 9 and 10, the command responses in the direction are the same in decentralied and centralied controls. ut when we compare figures 9 and 10, the response in centralied control can converge to command value more quickl, since we can design the controller explicitl considering rotational dnamics. When one uses the centralied control, one can let the controller robust to rotational disturbance. We have, therefore, applied centralied control to suspend the mover in the following one-dimensional drive experiments. 956

5 Figure 7 ommand response (-direction, decentralied control). Figure 8 ommand response (-direction, centralied control). Figure 9 ommand response (-direction, decentralied control). Figure 10 ommand response (-direction, centralied control). Position[m] 0.18 YREF Time[s] Figure 11 Vibration in -direction with -direction drive Position[m] Position[m] YREF alpha Time[s] Figure 12 Vibration of -direction with -direction drive alpha Inclination[rad] 4.3 Experiment of Position Feedback ontrol in One-Dimensional Linear Drive We can control the position of the mover in the -direction using LIM E and LIM F. The position in the -direction converged to the command value smoothl, but the two LIM s cause vibration to -, and directions. The responses of - and directions are shown in figures 11 and 12, respectivel. ompared with static magnetic levitation, the vibration becomes larger since the normal forces of LIM s change in unstabiliing wa depending on their gap length. 957

6 4.4 Difficult in Position Sensing in the Two-Dimensional Drive and its Strateg We have accomplished onl fundamental experiments of one-dimensional linear drive in the last section, since the position detection in the three-degrees-of-freedom x -, -and γ - directions in the proposed two-dimensional drive is substantiall difficult in practice. We can appl the technique of visual position sensing sstem as shwon in figure 13, although the sampling frame rate of ordinar video sstems is onl approximatel 30 fps, whose dnamic range in its frequenc response ma be too narrow as a sensor for motion controls. We have, therefore, developed an observer theor for solving such problems of speed controls in general motor drive sstems with a slow position sensor and a fast digital controller, based on digital signal processing theor with multiple sample rates. The application of the multiple sample rate observer [3] combined with visual servo-technolog will give an appropriate solution also to our two-dimensional three degrees-of-freedom linear drive control. p 2 ( x 2, 2, 2 ) ( x i, i, i ) x Left camera p 1 ( x 1, 1, 1 ) ( x ol, ol, ol ) ( x L, L, L ) ( x or, or, or ) ( x R, R, R ) Right camera Figure 13 Principle of visual popsition sensing. suppression. Damper & Spring Figure 14 pplication to oscillation 5 onclusions The structure of a mover that has three LIM s and three electromagnets to control six-degrees of freedom was proposed for a flexible contactless conveance sstem. The decentralied and the centralied controls were proposed as methods of its levitation control, and both were compared in the experiments. The centralied control gives better dnamic response, if one can assume sufficientl rigid iron plate on ground as well as the mover bodies, since the centralied controller directl stabilie the rotational motors based on their dnamic model described explicitl in advance. The centralied levitation control sstem is, therefore, a preferable for such a conveance sstem, which has a compact mover driven b linear induction motors, since their attractive normal force generated b the linear motors with their thrust control simultaneousl are often considerable disturbances for the magnetic levitation. The combination with the electromagnetic levitation with the static magnetomotive force b permanent magnets has also enabled the ero-power control [4] whose mechanical response seems like negative stiffness in its low frequenc region between and cut-off frequenc of the electromagnetic levitation controller in its frequenc domain. This fundamental feature would be also used for a novel active oscillation-suppressing sstem in multiple direction combined with an appropriate passive and positive mechanical suspension and the fundamental structure of the magnetic levitation sstem illustrated in figure 14, which enables the active stabiliation and motion control separatel in multiple directions [5]. 958

7 6 cknowledgments The authors are ver grateful to Mr. Ohashi and Mr. oama at Shin-Etsu hemical o., Ltd. for their substantial support in suppling good permanent magnets as well as their advises as experts of permanent magnets. References [1] J. Liu, and T. Koseki: 4 Poles 3 Degrees of Freedom Magnetic Levitation ontrol and its oordination with Two-Dimensional Linear Motor, The 17th International onference on Magneticall Levitated Sstems and Linear Drives, (Switerland), September 2nd-6th, 2002 [2] T. Koseki, Y. Makino, J. Liu, S. Inui, and Y.Ohira: Two-Dimensional Linear Drive ombined with ic Levitation for a Flexible Transportation Line, Proceedings of the 4th International Smposium on Linear Drives for Industr pplications, LDI2003 PL-04, pp , (United Kingdom), 8th-10th September 2003 [3] L. Kovudhikulrungsri, and T. Koseki: Performance Improvement of a Linear Encoder b Mltirate Sampling Observer, Proceedings of the 4th International Smposium on Linear Drives for Industr pplications, LDI2003 MI-07, pp , (United Kingdom), 8th-10th September 2003 [4] M. Morisita, T. ukiawa, S. Kanda, N. Tamura, and T. Yokoama: new Maglev Sstem for Magneticall Levitated arrier Sstem, IEEE Trans. Vehicular Technolog, Vol.38, No4, pp , 1989 [5] K. Erkan, and T. Koseki: 6 Degrees of Freedom ontrol of Vibration Isolation Stage b Emploing Novel Staggered E Tpe Hbrid, Technical Meeting on Linear Drives, IEE-Japan, (Japan), pp , September