An Adaptive Neural-Network Model-Following Speed Control of PMSM Drives for Electric Vehicle Applications

Transcription

1 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) An Adaptive Neual-Netwo Model-Following Speed Contol of PMSM Dives fo Electic Vehicle Applications FAYEZ F. M. EL-SOUSY Powe Electonics & Enegy Convesion Depatment Electonics Reseach Institute (ERI) Al-Tahi Steet, Doi, Caio, Egypt EGYPT Abstact:- A obust speed contol technique fo pemanent-magnet synchonous moto (PMSM) dives is poposed in this pape fo electic vehicle applications. The obust contolle consists of a neual-netwo contolle (NNC) in the speed feed-bac loop in addition to an on-line tained neual-netwo model-following contolle (NNMFC) in the feedfowad loop. The adaptive neual-netwo model-following contolle (ANNMFC) combines the meits of the feed-bac NNC and the feed-fowad NNMFC fo PMSM dive. The weights of the NNMFC ae tained on-line accoding to the model-following eo between the outputs of the efeence model and the PMSM dive system to ealize high dynamic pefomance in distubance eection and tacing chaacteistics. The NNMFC geneates an adaptive contol signal which is added to the feed-bac neual-netwo speed contolle output to attain obust model-following chaacteistics unde diffeent opeating conditions egadless of paamete uncetainties and load distubances. A compute simulation is developed to demonstate the effectiveness of the poposed obust ANNMFC. The esults confim that the poposed obust speed contolle gants obust pefomance and pecise tacing esponse to the efeence model egadless of load distubances and PMSM paamete uncetainties using the adaptive neual-netwo model-following contol. Key-Wods: PMSM, Vecto Contol, Neual Netwo (NN), Model Following Contolle (MFC). 1 Intoduction In ecent yeas, advancements in magnetic mateials, semiconducto powe devices and contol theoies have made the pemanent magnet synchonous moto (PMSM) dives play a vitally impotant ole in motion-contol applications. PMSMs ae widely used in high-pefomance applications such as industial obots and machine tools because of its compact size, high-powe density, high ai-gap flux density, hightoque/inetia atio, high toque capability, high efficiency and fee maintenance. Utilizing the vecto contol technique and by eeping d-axis cuent, i ds = 0, the PMSM toque may vay linealy with the q-axis cuent component,, and the maximum toque pe ampee is achieved which is simila to the contol of sepaately excited DC moto [1-3]. Seveal contol techniques in many eseaches have been developed to impove the pefomance of the PMSM dives and to deal with the nonlineaities and uncetainties of the dynamic model of the PMSM using fuzzy logic, neual netwo and/o the hybid of fuzzy logic and neual netwo [4-6]. In the pevious wo [3], the vecto contol tansfe functions of the PMSM and the d-q axes synchonous PI cuent contolles has been designed to achieve the time domain specifications of the cuent contol loops. In this pape, a obust speed contol stategy of a PMSM dive using an adaptive neual-netwo model-following speed contolle (ANNMFC) is poposed. The obust speed contolle consists of a feed-bac neual-netwo contolle (NNC) in addition to an on-line tained neual-netwo modelfollowing contolle (NNMFC) to impove the dynamic pefomance of the dive system. The output of the NNMFC is added to the neual-netwo speed contolle output to compensate the eo between the efeence model and the PMSM dive system output unde load distubances and paamete uncetainties. The dynamic pefomance of the PMSM dive system has been studied unde load changes and paamete vaiations. The simulation esults ae given to demonstate the effectiveness of the poposed contolles. 2 Mathematical Model of the PMSM The mathematical modeling of the PMSM in the synchonously otating oto efeence fames can be

2 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) deived as follows [1,3]. The stato voltage equations in the d -q synchonously otating oto efeence fame can be caied out as follows: d ' Vqs = Rsiqs + Lss iqs + Lssids + λm (1) d Vds = Rsids + Lss ids Lssiqs The electomagnetic toque can be expessed as: 3 P Te =.. λmiqs (2) d 2 T e = J m + β m + TL (3) P P whee V qs, V ds, and i ds ae the stato voltages and cuents espectively. R s and L ss ae the esistance and self inductance of the stato., J m, β m and P ae the oto position, electical oto speed, effective inetia, fiction coefficient and the numbe of poles. T e, T L, and λ m ae the electomagnetic toque, the load toque and the flux linage of the moto espectively. The PMSM paametes ae: thee-phase, 1 hp, 4 poles, 208 V, 60 Hz, 1800 pm, voltage constant: v.s/ad, R s =1.5 Ω, L ss =0.05 H, J m =0.003 g.m 2, and β m = N.m/ad/sec. 3 Poblem Fomulations The system configuation of the poposed speed contol fo a FOC PMSM dive system is illustated in Fig. 1. It basically consists of a PI cuent contolles in d-q-axes, a feed-bac neual-netwo contolle and a neual-netwo model-following contolle. A efeence model is deived fom the closed loop tansfe function of the PMSM dive system [3]. Although the desied tacing and egulation speed contol can be obtained using the feed-bac neual-netwo contolle with the nominal PMSM paametes, the pefomance of the dive system still sensitive to paamete vaiations. To solve this poblem, a obust adaptive speed contolle combining the neual-netwo speed contolle (NNC) and the on-line tained neualnetwo model-following contolle (NNMFC) is poposed. The contol law is designed as: c qs i qs + δiqs = i (4) whee the q-axis cuent command geneated fom the poposed neual-netwo speed contolle and δ is the adaptive contol signal geneated by the poposed NNMFC to automatically compensate the pefomance degadation. The inputs to feedbac neual-netwo contolle ae the eo signal, e, and the deivative of the oto speed,. Similaly, the inputs to the NNMFC ae the modelfollowing eo signal, e, and the deivative of the oto speed that ae used to tain the weights of neual-netwo contolle on-line. e = ( ) (5) & = d / (6) e = ( ) (7) & = d / (8) whee e is the eo speed between the efeence and feed-bac speed while is the output of the efeence model while is the oto speed of the PMSM. PMSM θ s s i ds i ds i as i bs i cs a-b-c / d s -q s d s -q s /d -q ( d / ) Contol Law Refeence Model θ G c -d i ds = 0 CRPWM Voltage Souce Invete V cs s V ds V bs d s -q s / a-b-c d -q /d s -q s V ds FOC NNC- G c -q ( d / ) Fig. 1 The bloc schematic diagam of a field oiented PMSM dive system 4 Poposed Speed Contol Stategy The poposed obust speed contolle consists of a feed-bac neual-netwo contolle (NNC) in addition to an on-line tained neual-netwo modelfollowing contolle (NNMFC) to impove the i dc V dc V as s V qs V qs c δiqs NNMFC- Contol Law

3 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) dynamic pefomance of the dive system as shown in Fig. 1. The feed-bac neual-netwo contolle is designed fo load egulation o distubance eection while the NNMFC to attain the desied tacing speed esponse. 4.1 Neual-Netwos Signal Popagation The neual-netwos fo both feed-bac and modelfollowing speed contolles compise a thee layes neual-netwo as shown in Fig. 2. The input laye (i th ), the hidden laye ( th ) and the output laye ( th ). The signal popagation and activation functions fo both contolles ae intoduced as follows. A. Input Laye Fo evey node i in the input laye, the neualnetwo input and output ae expessed as: nn i = x i (9) yi = fi ( nni ) i = 1,2 (10) d x1 = e ( t), x2 = (11) x e ( t), x d (12) 1 = 2 = B. Hidden Laye The input and output of the hidden laye to a node ae intoduced, espectively, as follows. nn = ( W y ) + φ (13) i i i y = f ( nn ) = 1,... m (14) 1 f ( nn ) = nn 1+ e (15) C. Output Laye The input of the output laye to a node is given by: nn = ( W y ) + φ (16) and the coesponding output is 1 y = f ( nn ) = (17) nn 1+ e y = i, y = δi (18) qs e On-Line Leaning Algoithm d / NNC qs x i y i W i bias y W y c 4.2 On-Line Taining Algoithm The bac popagation taining algoithm is an iteative gadient algoithm designed to minimize the mean squae eo between the actual output of a feed-fowad net and the desied output. This technique uses a ecusive algoithm stating at the output units and woing bac to the hidden laye to adust the neual weights accoding to the following equations. Thus the enegy eo functions fo both NNC and NNMFC ae defined as follows: E = [ ( N) ( N)] = e 2 ( N) (19) E = [ ( N) ( N)] = e 2 ( N) (20) whee (N) and (N) ae the outputs of the efeence model and PMSM dive system at the N th iteation. Within each inteval fom N-1 to N, the bac popagation algoithm [3] is used to update the weights of the hidden and output layes in the NNMFC accoding to the following equations: W i ( N + 1) = W i ( N) + γ W i ( N 1) W i ( N), ε (21) W ( N + 1) = Wi ( N) + γ W ( N 1) W ( N) }, W i ( N 1) = W i ( N) W i ( N 1) }, W ( N 1) = W ( N) W ( N 1), ε (22) (23) (24) The equied gadients of E and E in (19-20) between the output and hidden layes is detemined in [4]. To inceases the on-line leaning ate of the weights, a contol laws ae poposed as follows. y y y δ = e = e W bias y + + & To PMSM Dive W i & y i x i NNMFC On-Line Leaning Algoithm d / e (25) (26) Fig. 2 The poposed obust speed contolle (ANNMFC)

4 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) 5 Simulation Results The simulations esults of the PMSM dive systems ae pesented to veify the feasibility of the poposed contol scheme unde vaious opeating conditions. The dynamic pefomance of the dive system due to speed command of 377 ad/sec unde load of 3.6 N.m is pedicted as illustated in Fig. 3. The distubance eection capabilities have been checed when a load of 3.6 N.m is applied to the shaft at t = 1.25 s and emoved afte a peiod of 1.5 s. The simulation esults of the poposed NNC and ANNMFC speed contolles ae shown in Fig. 3 that includes the command and actual esponses fo speed, d-q axes stato cuents in the otating and stationay efeence fames fo both speed contolles. These Figues clealy illustate good dynamic pefomances in command tacing and load egulation pefomance ae ealized fo both contolles. Impovement of the contol pefomance by addition the poposed ANNMFC speed contolle can be obseved fom the obtained esults in command tacing and load egulation chaacteistics. The obustness of the poposed ANNMFC appoach against lage vaiations of PMSM paametes and extenal load distubances has been simulated fo demonstation. The speed esponse and the load egulation pefomance of the dive system with the NNC and ANNMFC speed contolles ae shown in Figs. 4-6 unde the thee cases of PMSM paamete vaiations. The contol pefomance by addition the poposed ANNMFC speed contolle is obust in command tacing and load egulation chaacteistics as illustated in Fig Also, the poposed ANNMFC speed contolle attains a apid and accuate esponse fo the efeence model and quicly etuns the speed to the efeence unde full load with a maximum dip of 7 ad/sec and 0.25 s unde paamete vaiations while the NNC povides a maximum dip of 11 ad/sec and 0.25 s. The esults shown in Figs. 4-5 clealy indicate that as the vaiations of the PMSM paametes occued, the esponses deviate significantly fom that nominal case with NNC speed contolle but the ANNMFC speed contolle confims the coect opeation and slightly influenced by paamete vaiations. It is evident that fom Fig. 6 an obvious model-following eo (MFE) due to the NNC speed contolle eaches to ±1.5 ad/sec while the MFE due to ANNMFC speed contolle is about ±0.5 ad/sec. Also, good model-following tacing esponses at all cases of paametes vaiations ae obseved fom these esults, and the esulting egulation pefomances ae also much bette, in both speed dip and ecovey time, than those obtained by the NNC speed contolle. 6 Conclusions This pape poposes a obust speed contolle fo PMSM dive system unde FOC which guaantees the obustness in the pesence of paamete vaiations. The poposed obust speed contolle (ANNMFC) consists of a feed-bac neual-netwo contolle (NNC) in addition to an on-line tained neual-netwo model-following speed contolle (NNMFC). The design pocedues fo both speed contolles have been successfully designed accoding to the given command tacing and distubance eection specifications of the dive system. The NNMFC povides an adaptive feedbac contol signal based on the eo between the efeence model and the output speed of PMSM. This eo was used to tain the weights and biases of the NNMFC to povide a good model-following esponse. So, the oto speed tacing esponse can be contolled to closely follow the esponse of the efeence model unde a wide ange of opeating conditions. Simulation esults have shown that the poposed ANNMFC gant obust model-following tacing esponse and good egulation chaacteistics in the pesence of PMSM paamete uncetainties and extenal load distubance. Refeences [1] Ned Mohan, Advanced Electic Dives: Analysis, contol, and Modeling using Simulin, MNPERE Pess, USA, [2] Faa-Jeng and Chih-Hong Lin, A Pemanent- Magnet Synchonous Moto Sevo Dive Using Self-Constucting Fuzzy Neual Netwo Contolle, IEEE Tans., Enegy Convesion, EC-19, No. 1, 2004, pp [3] Fayez F. M. El-Sousy and Maged N.F. Nashed, Fuzzy Adaptive Neual-Netwo Model- Following Speed Contol fo PMSM Dives, WSEAS Tansactions on Systems, Issue 4, Vol. 4, Apil, 2005, pp [4] Fayez F. M. El-Sousy, Intelligent Model- Following Position Contol fo PMSM Sevo Dives, 6 th WSEAS Intenational Confeence on Neual Netwos, Lisbon, Potugal, June 16-18, 2005, pp [5] K. S. Naenda and K. Pathasaathy, Identification and contol of dynamical systems using neual netwos, IEEE Tans., Neual Netwo, NN-1, 1990, pp [6] T. Fuuda and T. Shibata, Theoy and applications of neual netwos fo industial contol systems, IEEE Tans., Ind. Elect., IE-39, 1992, pp

5 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) (a) Using NNC speed contolle (b) Using ANNMFC speed contolle Fig. 3 Speed esponse fo a efeence speed of 377 ad/sec and subsequent loading of 3.6 N.m

6 Poceedings of the 9th WSEAS Intenational Confeence on Applied Mathematics, Istanbul, Tuey, May 27-29, 2006 (pp ) (a) The tacing speed and cuent esponses with NNC (b) The tacing speed and cuent esponses with ANNMFC Fig. 4. The speed model following esponse of the dive system unde paamete vaiations using NNC and ANNMFC speed contolles (a) The load egulation pefomance with NNC (b) The load egulation pefomance with ANNMFC Fig.5. The load egulation pefomance of the dive system unde paamete vaiations using NNC and ANNMFC speed contolles (a) MFE using NNC (b) MFE using ANNMFC Fig. 6. The model-following eos (MFE) of speed esponse using NNC and ANNMFC speed contolles unde paamete vaiations