Speed-feedbak Diret-drive Control of a Low-speed Transverse Flux-type Motor with Large Number of Poles for Ship Propulsion Y. Yamamoto, T. Nakamura 2, Y. Takada, T. Koseki, Y. Aoyama 3, and Y. Iwaji 3 The University of Tokyo, Japan 2 West Japan Railway Company, Japan 3 Hitahi Reseah Laboratory, Hitahi, Ltd., Japan Abstrat In speed-feedbak ontrol at low-speed region, it is diffiult to obtain enough speed information from enoder due to its low resolution. Thus, the stability of the system tends to get remarkably worse. For that reason, dual sampling rate observer (DSO) is applied to the drive system to resolve suh problem and avoid inreasing ost by installing high-resolution enoder simultaneously. The observer gains are deided by onverting appropriate poles in s plane based on Kessler method into z plane. We onfirm that the overshoot, rise time and setting time with DSO are about 84%, 9% and 27% lower than those without DSO by the experiments. The drive system is appliable to real operations suh as departure, stop and revolution alled for low-speed ontrol.. INTRODUCTION Eletri propulsion (EP) in marine industry has been developed due to savings in energy and maintenane requirements. Conventional EP systems omposed of motors with gearboxes have ompliated mehanism and improvement in effiieny and reliability were restritive. Thus, the diret-drive (DD) motors have been given attention. In order to ahieve high torque at low speed, prototype models with large number of poles taking advantage of TFMs, whih have ontrollable pole pith and are suitable for suh appliation, have been proposed and reated. Basially, ontrol of the motor is onsisted of speed feed-bak loop using enoder pulse information. In low-speed region, however, the stability of drive system is lost due to insuffiient resolution of the enoder. As a solution for this ritial problem, we demonstrate the validity of DSO based on simulations and experiments. 2. DETERMINATION OF MOTOR PARAMETERS FOR CONTROL SYSTEM DESIGN Identifiation of parameters used in ontrol of the motor is onduted in following steps by finite element analysis (FEA) and experiments. As for FEA, linkage flux in the armature winding with/without urrent flow is estimated from 3-D numerial study. Then, indued voltage, torque oeffiient and indutane are estimated by no-load flux waveform, absolute value and phase differene of flux between no load and load []. On the other hand, determination of parameters based on experiments as shown in Figure is onduted based on basi theory of synhronous mahine. Armature resistane, indutane and oeffiient of indued voltage/torque are obtained from DC voltage-drop method, sigle-phase AC stati test and no-load test using another motor respetively. Comparison of parameters alulated by FEA and experiments is shown in Table. The experimetal values are relatively high ompared to FEA values due to dispersion of materials and building fators, but it is pratial solution to design ontrol system and estimate harateristi before reating prototype model. In the following setions, parameters based on experiments are used for design of ontrol systems.
Table : Comparison of parameters identified by FEA and experiments in the prototype model. Symbol Desription FEA Experiments R a Armature resistane 7.58 Ω 8.6 Ω L d, L q d-axis/q-axis indutane 42 mh 2 mh K e Bak EMF oeffiient.28 Vs/rad.9 Vs/rad Torque oeffiient 5.2 Nm/A 4.76 Nm/A 2p Pole numbers 5 poles J r Rotor Inertia.326 kgm 2 Figure : Experimental setup in motor-drive system. 3. DESIGN AND TESTS OF CONTROL SYSTEM BY COEFFICIENT DIAGRAM METHOD (CDM) The design of ontrol system is onduted based on rotational d-q oordinates. The system is omposed of asade ontrol based on urrent and speed feed-bak ontrol systems on the assumption that eah feed-bak information is obtained from urrent sensor or enoder. Current ontrol system is d-axis urrent zero and speed ontrol system is onfigured by regarding the urrent ontrol system as first-order lag system by using CDM. 3.. DETERMINATION OF CONTROLLER GAINS IN THE FEED-BACK CONTROL SYSTEM [2] Current ontroller is omposed of P-I ontrol so that d-axis and q-axis urrents an follow ommands for eah urrent. Interferene in eah axis urrent is disregarded due to deoupling by feed-forward ompensation of referene signals. Speed ontroller is onsisted of I-P ontrol with two feed-bak loop by regarding urrent ontroller as first-order lag system to realize redution of overshoot, simultaneously ahieve quik response and desribe as simple system without zero point. The blok diagram of the system is shown in Figure 2. Transfer funtions G m (s) and G s (s) in the urrent/speed ontroller are giving in as Equation (). K pm s G m (s) = i m i = * m R K a pm s L m s 2, G s (s) = ω ω * = K ps s J r s 2 J τ r s 3 () K pd ˆωL î q q K i d* id s ωl q i q R a sl d i d K pq ˆωL î d ωl d d i d K i q* iq s R a sl q i q ω * s Current ontroller i * q i q τ s K e ˆω K e ω K ps T J r s ω ps (a) d-axis urrent ontrol (b) q-axis urrent ontrol () speed ontrol Figure 2: Blok diagram in eah ontrol system.
In Equation (), index m, i m, i m *, K pm,, L m, ω, ω *, τ, K ps and represent d-axis or q-axis physial amount, real urrent, ommand of the urrent, proportional and integral gains of urrent ontroller, indutane, eletrial angular veloity, ommand of the angular veloity, equivalent time onstant in the urrent ontrol, proportional and integral gains of speed ontroller respetively. Kessler method, one of CDMs, is applied to denominator polynomial of the transfer funtion. Eah ontroller gain is determined as shown in Equation (2). K pm = 2L m τ R a, = 2L m τ, K = J r, K 2 ps 2 τ is = J r 8 τ 2 (2) where, equivalent time onstant in the speed ontrol is four times of that in the urrent ontrol. Eah gain is determined as shown in Table 2 by above proedure. In ideal differential of deviation, however, ontrol system is easy to beome unstable due to exessive amplifiation of high frequeny omponent and insuffiient energy in pulse output when the deviation auses hange like step input. Therefore, lagged derivative is applied to the system. Furthermore, the system is omposed of digital ontrol, so transformation from ontinuous system to disrete system is onduted by first approximation of Taylor s expansion of Z-transform. 3.2. INSPECTION OF CONTROL SYSTEM BASED ON CDM THROUGH EXPERIMENTS Figure 3 shows system response when the speed signal is alulated by lagged derivative. The speed signal follows the ommand, however steady-state harateristis inluding setting time and overshoot are poor. As shown in Table, the number of poles is fifty so that the motor requires high torque at low speed. On the other hand, resolution of enorder is limited due to its number of pulse per revolution. As a result, reliability of ontrol using speed alulated from finite differene of enorder pulse might derease due to its insuffiient information in low speed region. In the ontrol using only feed-bak loop, speed signal flutuates vigorously as shown in Figure 4 for a long period of time. Thus, feed-forward ompensation ontributes to redution of osillation in steady state to a ertain extent as shown in Figure 3. In order to improve low-speed drive ontrol, however, it is essential to apply additional solution. 3. 2.. Referene 3. 2.. Referene.5..5 2. 2.5 3. Figure 3: Response with feed-forward (FF) ompensation..5..5 2. 2.5 3. Figure 4: Response without FF ompensation Table 2: Controller gains in asade ontrol system deteted by Kessler method. Parameters Current Controller Speed Controller Proportional gain K p = 8.6 K ps =.246 Integral gain K i = 6 =.443 Equivalent time onstant τ = 3.9 mse. τ s = 55.6 mse. Control period T s =. mse.
4. DESIGN AND VERIFICATION OF CONTROL SYSTEM USING DSO THROUGH THE TESTS In SECTION 3, it is impossible to estimate speed by differene method in every ontrol period in low speed region, resulting in lost of stability of ontrol system due to insuffiient enorder pulse. Consequently, we use DSO whih has the potential to realize low-speed drive without hanging any hardware. Its objetive is to give ontroller position and speed in suh low speed region by both state estimation with model of ontrolled objet and orreting error of the estimation in obtaing pulse information. 4.. DETERMINATION OF OBSERVER GAIN IN CURRENT-TYPE DSO [3,4] Position θ, angular veloity ω from enorder and disturbane torque T d are hosen as state variables and a state equation is desribed. After that, it is neessary to onvert to disrete system in order to ondut online alulation by a omputer [5]. Current-type DSO, one of derivation of the urrent-type observer, is onsisted of enoder pulse yle T, ontrol period T 2 and an iteger N defined as ratio of T to T 2 as shown in Figure 5. When T < T 2, DSO operates as the usual urrent-type observer with disrete yle T 2. Otherwise, DSO is operated at following two manners. In only any one time per N samples, state estimation is orreted by real output value. In another ase (N- samples), state estimation is onduted by using one earlier estimated values and input values. Consequently, DSO is expeted to make determination of observer gains easier as well as to orret urrent state estimate by error alulated in urrent sample. The observer gains of DSO are determined based on period of enorder pulse T, but it is diffiult to predit appropriate pole assignment in disrete Z plane. In this paper, appropriate obserber gains in Z plane are obtained by onverting poles s i (i =~3) as fixed with CDM in SECTION 3. The observer gain matrix L is designed so as to fulfill harateristi equation under absolute value of all poles in Z plane of less than in Equation (3) and (4). u x x = Ax Bu y = Cx Physial plant system A/D: T 2 A/D: T Computer u n ˆx y n n x n y n B d z z C d n = mn ˆx n m Z A L d Feedbak Figure 5: Configuration of Current-type DSO. y 6. 4. 2. Referene 2. 4. 6. 8. Figure 7: Variable speed ontrol with DSO. 3. 2.. Referene 3. 2.. Referene 3. 2.. Referene.5..5 2. 2.5 3..5..5 2. 2.5 3..5..5 2. 2.5 3. (a) τ ob = 4. mse. (b) τ ob = 8. mse. () τ ob = 2. mse. Figure 6: Response with DSO
det zi { A d L C d A d } =, z < (3) L = l l 2 l 3 = e 4T τ ( ) e 2T τ { } 3 e 4T τ ( ) 2 e 3T τ 2T e T τ ( )os 3T τ J r e 2T τ ( ) e 2T τ 2e T τ os 3T τ T 2 { ( )} (4) 4.2. OBSERVATIONS ON APPLICABILITY OF DSO THROUGH THE EXPERIMENTS It is important to hoose equivalent time onstant of DSO. In short time onstant, effet of orretion on position signal inreases and estimation works well for disturbane due to its large gains. On the other hand, in long time onstant, the gains are small and the effet of orretion is poor. Moreover, it is sensitive to noise, error, disturbane and variation of parameters, so we deide the gains through the experiments. Time onstant of observer τ ob is hosen as 8. mse, whih gives low flutuation and relatively good response in the tests as shown in Figure 6. The validity of DSO for variable speed ontrol is verified at low speed as well as high speed as shown in Figure 7. DSO is one of the effetive solutions for motor alled for low-speed drive by only hanging software without adding speial hardware. 5. CONCLUSION A systemati method to determine ontroller gains in asade ontrol based on CDM and observer gains in DSO has been desribed. The observer gains of DSO an be obtained easily by onverting appropriate poles in s plane. The appliation of the proposed DSO has solved the problem of instability aused by oarse enoder pulsed in low speed drive, whih often ours in low speed diret drive motors with large number of poles. ACKNOWLEDGEMENT We would like to thank the members of Hitahi Researh Laboratory for their tehnial advie and supprt of this researh and those of MT Drive, ACM and Shin-Etsu Chemial for manufaturing the experimental mahine. REFERENCES. Morimoto, S., Y. Takeda, and T. Hirasa, Parameter Measurement of PM Motor in dq Equivalent Ciruit, IEEJ Trans. Industry Appliations, Vol.3, No., pp.33-33, 993. 2. Manabe, S., Appliation of oeffiient diagram method to dual-ontrol-surfae missile, 5th IFAC Symposium on Automati Control in Aerospae, pp.499-54, 2. 3. Yusuke, K., and Y. Hori, Instantaneous Speed Observer with Improved Disturbane Rejetion Performane based on Higher Order Dynamis, IEEJ Trans. Industry Appliations, Vol.2, No.6, pp.539-544, 992. 4. Lilit, K., and T. Koseki, Preise Speed Estimation From a Low-Resolution Enoder by Dual-Sampling-Rate Observer, IEEE/ASME Trans. Mehatronis, Vol., No.6, pp.66-67, 26 5. Farzad, N., and M. Gene, Digital ontrol using digital signal proessing, Prentie Hall, In. PTR, 999 6. Nakamura, T., T. Koseki, and Y. Aoyama, A low-speed high-torque permanent magnet synhronous motor Reduing ogging torque and eddy urrent loss, Journal JSAEM, Vol.2, No.2, pp.4 45, 22.