Fuzzy Adaptive Neural-Network Model-Following Speed Control for PMSM Drives

Transcription

1 Fuzzy Adaptive Neual-Netwok Model-Following Speed Contol fo PMSM Dives FAYEZ F. M. EL-SOUSY MAGED N. F. NASHED Powe Electonics & Enegy Convesion Depatment Electonics Reseach Institute (ERI) Al-Tahi Steet, Dokki, Caio, Egypt EGYPT Abstact:- In this pape, a fuzzy adaptive neual-netwok model-following speed contolle fo pemanentmagnet synchonous moto (PMSM) dives is poposed. The fuzzy neual-netwok model-following contolle (FNNMFC) consist of a popotional plus integal (PI) like-fuzzy contolle in addition to an on-line tained neual-netwok model-following contolle (NNMFC). This contolle, FNNMFC, combines the meits of the fuzzy logic contol (FLC) and the neual-netwok model-following contol (NNMFC) fo PMSM dive. The weights of the NNMFC ae tained on-line to ealize high dynamic pefomance in distubance ejection and tacking chaacteistics. Accoding to the model-following eo between the outputs of the efeence model and the PMSM dive system, the NNMFC geneates an adaptive contol signal which is added to the fuzzy speed contolle output to attain obust model-following chaacteistics unde diffeent opeating conditions egadless of paamete vaiations and load distubances. A compute simulation is developed to demonstate the effectiveness of the poposed FNNMF speed contolle. The esults confim that the poposed FNNMF speed contolle poduces apid, obust pefomance and accuate esponse to the efeence model egadless of load distubances o PMSM paamete vaiations. Key-Wods: PMSM, Vecto Contol, Fuzzy Logic, Neual Netwok (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, high-toque/inetia atio, high toque capability, high efficiency and fee maintenance. Utilizing the vecto contol technique and by keeping 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 netwok and/o the hybid of fuzzy logic and neual netwok [5-7]. In the pevious wok [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. The aim of this pape is to design a poposed fuzzy adaptive neual-netwok model-following speed contolle fo PMSM dive system. The FNNMFC consists of PI-like fuzzy contolle in addition to an on-line tained neual-netwok modelfollowing contolle (NNMFC) to impove the dynamic pefomance of the dive system. The output of the NNMFC is added to the fuzzy contolle output to compensate the eo between the efeence model and the PMSM dive system output unde paamete vaiations and load distubances. The dynamic pefomance of the PMSM sevo 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 deived as follows [1-2]. The stato voltage equations in the d -q synchonously otating oto efeence fame can be caied out as follows:

2 d ' Vqs = Rsiqs + Lss iqs + ω Lssids + ωλm dt (1) d Vds = Rsids + Lss ids ω Lssiqs dt The electomagnetic toque can be expessed as: 3 P Te =.. λmiqs (2) d 2 T e = J m ω + β m ω + TL (3) P dt 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. ω, 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 linkage 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 kg.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 and a PI fuzzy contolle and a neual-netwok model-following contolle. A efeence model is deived fom the closed loop tansfe function of the PMSM dive system. Although the desied tacking and egulation speed contol can be obtained using the PI fuzzy speed contolle with the nominal PMSM paametes, the pefomance of the dive system still sensitive to paamete vaiations. To solve this poblem, a hybid speed contolle combining the PI fuzzy speed contolle and the neual-netwok 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 PI fuzzy speed contolle and δ is the adaptive contol signal geneated by the poposed NNMFC to automatically compensate the pefomance degadation. The inputs to the poposed NNMFC ae the eo signal, e ω, and the deivative of the oto speed, ω, that ae used to tain the weights of neual-netwok contolle on-line. eω = ( ω ω ) (5) & ω = k dω / dt ω whee ω is the output of the efeence model while ω is the oto speed of the PMSM. ω ω PMSM θ Fig. 1 The block schematic diagam of a field oiented PMSM dive system 4 Poposed Fuzzy Neual-Netwok Model-Following Speed Contolle 4.1 PI-Fuzzy Speed Contolle The actual inputs to the fuzzy contolle ae the speed eo, e ω (k), and the ate of the of cuent eo, e ω (k), linguistic vaiables ae consideed the inputs to the contolle and the output is the change of the q- axis stato cuent, ( k ). i qs uω = i = i = f ( eω, eω ) (6) qs s s i ds i ds qs i as i bs i cs a-b-c / d s -q s d s -q s /d -q G c -ω Refeence Model θ G c -d i ds = 0 ω 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 G c -q ( d / dt ω whee, eω = ω ω is the speed eo and eω = eω eω ( k 1) is the change of speed eo. The scaling factos ae selected and can be vaied to tune the output of the fuzzy contolle fo the k i dc V dc V as s V qs V qs c ω ) ω δiqs NNMFC-ω Contol Law

3 desied speed esponse. The output gain, can also be tuned fo the same pupose. Fig. 2 illustates the membeship functions e ω (k), e ω (k) and δ which ae used fo the input and output fuzzy sets. The membeship functions coesponding to each element in the linguistic set can be defined using the fuzzy linguistic contol ules. The linguistic ules base fo PI-fuzzy speed contolle ae shown in Table 1. e ω HN MN LN ZE LP MP HP e ω HN HN HN MN MN LP ZE ZE LN HN MN MN LN LP LP ZE ZE MN MN LN LN ZE MP LP LP MN LN LN ZE LP MP MP HP LN ZE ZE LP LP HP MP LP ZE ZE LP LP MP MP HP HP ZE ZE LP MP MP HP HP Table 1 The linguistic ules base popagation taining algoithm uses a ecusive algoithm stating at the output units and woking back to the hidden laye to adjust the neual weights. The desied speed ω is obtained fom the efeence model, thus the enegy eo function is defined as follows: E = [ ( N) ( N)] = e 2 ω ω ω ω ( N) (7) 2 N 2 N whee ω (N) and ω (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 back popagation algoithm is used to update the weights of the hidden and output layes in NNMFC accoding to the following equations: Eω W ji ( N + 1) = W ji ( N) ε + γ W ji ( N 1) (8) W ji ( N) Eω Wkj ( N + 1) = Wkj ( N) ε + γ Wkj ( N 1) (9) Wkj ( N) To inceases the on-line leaning ate of the weights, a contol law is poposed as follows. Eω = eω kω ( d / dt) ω (10) y k NNMFC ω On-Line Leaning Algoithm e ω ω y k δ x i k d / dt ω Fig. 2 Membe ship function of PI-fuzzy speed contolle bias Fig. 3 The poposed NNMF speed contolle 4.2 Neual-Netwok Model-Following Speed Contolle The inputs to the NNMFC ae the eo e ω and kω ( d / dt) ω while the output is the obseved compensation signal δ. The eo between the efeence model and the output speed of PMSM is used to tain the weights and biases of the neualcontolle to povide a good model-following esponse. The weights and biases ae adjusted online to poduce the equied compensation signal. Utilizing this adaptive contol signal will make the dive system to follow the efeence model. The NNMFC compises a thee layes neual-netwok as shown in Fig. 3. The input laye (i th ), the hidden laye (j th ) and the output laye (k th ). The back 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 step speed command of 377 ad/sec unde no-load and load of 3.6 N.m is pedicted as illustated in Figs The distubance ejection capabilities have been checked when a load of 3.6 N.m is applied to the shaft at t = 1 s and emoved afte a peiod of 2 s. The simulation esults of the poposed PI fuzzy and FNNMF speed contolles ae shown in Fig. 4 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 tacking and load egulation

4 pefomance ae ealized fo both contolles. Impovement of the contol pefomance by addition the poposed FNNMF speed contolle can be obseved fom the obtained esults in command tacking and load egulation chaacteistics as illustated in Fig. 6-b. It is clea fom this Figue that the poposed FNNMF speed contolle povides a apid and accuate esponse fo the efeence model within 0.3 s. Also, the poposed contolle quickly etuns the speed to the efeence unde full load with a maximum dip of 12 ad/sec. The obustness of the poposed F NNMF 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 PI fuzzy and FNNMF speed contolles ae shown in Figs. 5-7 unde the thee cases of PMSM paamete vaiations. The contol pefomance by addition the poposed FNNMF speed contolle is obust in command tacking and load egulation chaacteistics as illustated in Fig. 8. Also, the poposed FNNMF speed contolle attains a apid and accuate esponse fo the efeence model within 0.3 s and quickly etuns the speed to the efeence unde full load with a maximum dip of 12 ad/sec unde paamete vaiations. The esults shown in Figs. 5-6 clealy indicate that as the vaiations of the PMSM paametes occued, the esponses deviate significantly fom that nominal case with PI fuzzy speed contolle but the FNNMF speed contolle confims the coect opeation and slightly influenced by paamete vaiations. It is evident that fom Fig. 7 an obvious model-following eo (MFE) due to the PI fuzzy speed contolle eaches to 125 ad/sec while the MFE due to FNNMF speed contolle is about ±5 ad/sec. Also, good model-following tacking 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 PI fuzzy speed contolle. 6 Conclusions This pape poposes a obust hybid FNNMF speed contolle fo PMSM dive system unde FOC which guaantees the obustness in the pesence of paamete vaiations. The design pocedues fo the PI fuzzy and FNNMF speed contolles have been successfully designed accoding to the given command tacking and distubance ejection specifications of the dive system. The pefomance of the dive system is still sensitive to paamete vaiations using the PI fuzzy speed contolle. To solve this poblem, a FNNMFC with on-line leaning was designed and added to the PI fuzzy speed contolle to peseve the good model-following chaacteistics unde the conditions of paamete vaiations and extenal distubances. The NNMFC povides an adaptive feed-back 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 tacking 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 FNNMF speed contolle gant accuate tacking and egulation chaacteistics in the pesence of PMSM paamete vaiations and extenal load distubance. Also, a obust model-following tacking esponse is obtained utilizing the FNNMF speed contolle. Refeences [1] Ned Mohan, Advanced Electic Dives: Analysis, contol, and Modeling using Simulink, MNPERE Pess, USA, [2] Fayez F. M. El-Sousy and M. M. Salem, High Pefomance Simple Position Neuo-Contolle fo Field-Oiented Induction Moto Sevo Dives, WSEAS Tansactions on Systems, Issue 2, Vol. 3, Apil 2004, pp [3] Fayez F. M. El-Sousy, A Vecto-Contolled PMSM Dive with a Continually On-Line Leaning Hybid Neual-Netwok Model- Following Speed Contolle, The Koean Institute of Powe Electonics (KIPE), Jounal of Powe Electonics (JPE), Vol. 5, No. 2, Apil, 2005, pp [4] Fayez F. M. El-Sousy and Maged N. F. Nashed, PID-Fuzzy Logic Position Tacking Contolle fo Detuned Field-Oiented Induction Moto Sevo Dive, WSEAS Tansactions on Systems, Issue 2, Vol. 3, Apil 2004, pp [5] Leonid Reznik, Fuzzy Contolles, Biddles Ltd, Guildfod and King's Lynn, England, [6] Cheng F. and Yeh S., Application of fuzzy logic in the speed contol of ac sevo systems and an intelligent invete, IEEE Tans. Enegy Convesion, Vol-8, June 1993, pp [7] Faa-Jeng and Chih-Hong Lin, A Pemanent- Magnet Synchonous Moto Sevo Dive Using Self-Constucting Fuzzy Neual Netwok Contolle, IEEE Tans., Enegy Convesion, EC-19, No. 1, 2004, pp

5 (a) Using PI fuzzy speed contolle (b) Using FNNMF speed contolle Fig. 4 Step speed esponse fo a efeence speed of 377 ad/sec and loading of 3.6 N.m

6 (a) The tacking speed and cuent esponses with FLC (b) The tacking speed and cuent esponses with FNNMFC Fig. 5. The speed model following esponse of the dive system unde paamete vaiations using PI fuzzy and FNNMF speed contolles (a) The load egulation pefomance with FLC (b) The load egulation pefomance with FNNMFC Fig.6. The load egulation pefomance of the dive system unde paamete vaiations using PI fuzzy and FNNMF speed contolles (a) Using PI fuzzy speed contolle (b) Using FNNMF speed contolle Fig. 7. The model-following eos (MFE) of speed esponse using PI fuzzy and FNNMF speed contolles unde paamete vaiations