CHAPTER 3. FUZZY LOGIC DIRECT TORQUE CONTROL.

Transcription

1 CHAPTER 3. FUZZY LOGIC DIRECT TORQUE CONTROL Introduction. In DTC induction otor drive there are torque and fux rippe becaue none of the VSI tate i abe to generate the exact votage vaue required to ake zero both the torque eectroagnetic error and the tator fux error. The uggeted technique i baed on appying to the inverter the eected active tate jut enough tie to achieve the torque and fux reference vaue. A nu tate i eected for the reaining witching period, which won't aot change both the torque and the fux. Therefore, a duty ratio (δ) ha to be deterined each witching tie. By ean of varying the duty ratio between it extree vaue ( up to ), it i poibe to appy any votage to the 3.

2 otor. Therefore, thi technique i baed on a two-tate oduation. Thee two tate are the active one and a nu one. The optiu duty ratio per aping period i a non-inear function of the eectroagnetic torque error, the tator fux poition and the working point, which i deterined by the otor peed and the eectroagnetic torque. It i obviou that it i extreey difficut to ode uch an expreion ince it i a different non-inear function per working point. Thu, it i beieved that by uing a Fuzzy Logic baed DTC yte it i poibe to perfor a Fuzzy Logic baed duty-ratio controer, where the optiu duty ratio i deterined every witching period [BIR ] [VAS 3]. The uggeted Fuzzy Logic yte i divided into two different Fuzzy Logic controer. The firt one wi act each tie that the eected active VSI tate ha changed, being different to the previou one. The econd controer wi act in the oppoite ituation, which i when the active VSI eected tate i the ae a the previou one. Thee Fuzzy Logic controer and it functionaity are expained deeper in ection 3.. Both fuzzy ogic controer ue the Centroid defuzzification ethod. The reation between different condition in the ae rue i done by ean of "and" operator. On the other hand, the reationhip between different rue i done by ean of "or" operator. 3.

3 3. - Fuzzy Logic Direct Torque Contro. Fuzzy Logic Direct Torque Contro Fuzzy Logic controer Objective. Fro the ection entited "firt approach" (.3..) wa ead the idea of a and arge torque increae or decreae (ee figure.5). Thi idea wi be taken into account by ean of the tator fux poition a input of the Fuzzy Logic yte. Fro the ection entited "econd approach" (.3..) wa born the idea of the working point. It doe ee obviou that if the working point increae, then the duty cyce ut tend to one and in the oppoite cae the duty cyce ut tend to zero. Thi idea i conidered by ean of the working point eberhip input and it conequent ditribution in the working pane. Finay fro the ection entited "third approach" (.3..3) were born two ain idea. The firt one i that the higher the working point i, the ore torque i decreaed by the nu tate (intead of keeping it contant). The econd idea i that the torque decreae tate decreae the torque too uch. A a oution, once a a decreae in torque i required, it wi be generated by ean of oduating a torque increae tate and a nu one, being the reut after the entire period a a reduction in torque. The torque aintaining tate wi be generated by ean of a torque increae tate, (which aot do not increae the torque under thee condition), intead of a nu one. In thi Fuzzy Logic controer thee idea fro the third approach wi be ipeented by ean of the working point and torque error input Input and output eberhip function. In uch a Fuzzy Logic yte, there are three input, tator fux poition, eectroagnetic torque error and the otor working point i.e. peed and torque. The output i the duty ratio. Stator fux poition torque error f(w,t) Fuzzy ogic controer duty ratio Figure 3.. Fuzzy Logic duty ratio etiator 3.3

4 The fuzzy yte coprie four group of rue. Two of the are ued when the tator fux i aer than it reference vaue (Fux increae) and the other two in the oppoite cae (Fux decreae). The working point i firty divided into two different cae. Thee two cae are peed w pc higher than torque T pc (both in percent) and the oppoite cae. In any cae jut one fuzzy yte i ued per iteration, and it depend on the working point. Stator fux poition FI Fuzzy controer wpc<tpc torque error FI wpc>tpc duty ratio f(w,t) FD wpc<tpc FD wpc>tpc Figure 3.. Fuzzy ogic duty ratio etiator. It can be een it four different group of rue. Jut one group of rue i ued per iteration. Stator fux poition eberhip function i decopoed in three fuzzy et a it i hown in figure 3.3. º 3º º Stator fux poition Figure 3.3. Stator fux poition eberhip input. The torque error eberhip function i decopoed in ix fuzzy et. The "tei" vaue are a foow: te=5%tn, te=%tn, te3=%tn, where Tn i the noina torque vaue. The aboute vaue wi depend on the noina vaue of each eectrica achine. n- n- n- torque error -te3 -te -te te te te3 Figure 3.. Torque error eberhip input. The otor working point eberhip function i decopoed in jut three fuzzy et. However they are different depending on the working point poition. The "wti" vaue are a foow: wt=, wt=, wt3=75, wt=, wt5=, wt=7. The different zone in the working pane T,w can be een in figure

5 It houd be noted fro figure 3.5 that the working pane behaviour can not be decribed by ean of three ine in hi entire pane. Therefore, the working pane i divided into two zone and the fuzzyfication of thee two zone i a we different. W pc<tpc W pc>tpc Tpc +wpc Tpc +wpc wt wt wt3 wt wt5 wt Tpc wp c=tpc Tpc wp c=tpc % % Tpc +wp c=wt3 T p c +w p c =wt Tpc +w pc =wt Tpc +w pc =wt T pc+wp c=wt5 T pc+wp c=wt % wpc % wpc Figure 3.5. Working point eberhip input and the three different zone in the T,w pane. Left w pc <T pc. Right w pc >T pc. Duty ratio eberhip function i decopoed in five fuzzy et. Notice that it eberhip vaue are inge tone to ipify the cacuation. The "dci" vaue are a foow: dc=.5, dc=.5, dc3=.75. z v duty ratio dcdc dc3 Figure 3.. Duty ratio eberhip Rue: The fuzzy yte coprie four group of rue, each of which contain rue. Two of the are ued when the tator fux i aer than it reference vaue (Fux increae) and the other two in the oppoite cae (Fux decreae). In any cae jut one fuzzy yte i ued per iteration, and it depend on the working point. A four group of rue are ited in ection A

6 3.. - Fuzzy Logic controer Objective. The objective i to create an adaptive yte. A ong a the eected tate i not changed, then taking into account the at evoution i poibe to predict next duty ratio increent to reduce the torque error. Two exape are hown in figure 3.7. n- n- n- n- n- Te* n- Te* Figure 3.7. It can be een the evoution of the torque during one Tz. Left: if the torque increent i negative ediu, and the error in the previou iteration wa negative arge, the duty ratio increent ha to be a. Thi cae correpond to the econd rue (ee ection A..). Right: if the torque increent i zero, and the error in the previou tate wa a, the increent in duty ratio ha to be zero. Thi cae correpond to the eventeenth rue (ee ection A..). Fro figure 3.7 can be een the adaptive characteritic of the Fuzzy Logic controer. On the eft of figure 3.7, it i obviou that next iteration houd not decreae the duty ratio becaue the torque vaue woud take a vaue under the reference torque vaue. Therefore, the action ut be to increae a bit the duty cyce in order to pace next torque vaue a bit above than the torque reference vaue. However, on the right of figure 3.7, it i obviou that the torque repone ha been exceent; therefore, it ut continue with the ae duty cyce vaue Input and output eberhip function. In uch a Fuzzy Logic yte, there are two input, torque increent and eectroagnetic torque error in the previou iteration. The output i the increent in duty ratio. 3.

7 torque torque error (i-) Fuzzy ogic controer δ Figure 3.. Fuzzy ogic controer increent_duty ratio etiator. The torque increent eberhip function i decopoed in even fuzzy et, and the torque error in the previou iteration eberhip function i decopoed in ix a hown in figure 3.9. n- n- n- z n- n- n- -te3 -te -te te te te3 torque -te3 -te -te te te te3 Figure 3.9. Torque increent and torque error in the previou iteration eberhip input. torque error(i-) The "tei" vaue in both cae are a foow: te=%tn, te=5%tn, te3=%tn, where Tn i the torque noina vaue. The aboute vaue wi depend on the noina vaue of each achine. The increent duty ratio eberhip function i decopoed in nine fuzzy et. Notice that it eberhip vaue are again inge tone to ipify the cacuation. The " δi" vaue are a foow: δ=., δ=.5, δ3=.35 and δ=.5. n-v n- n- n- z v δ δ δ3 δ δ δ δ δ3 δ Figure 3.. Increent duty ratio eberhip Rue: The fuzzy yte contain 37 rue. The rue nuber two and eventeen are expained in figure 3.7. A 37 rue are ited in ection A

8 Fuzzy Logic DTC chea. Finay the cheatic of the DTC baed on fuzzy controer i a hown in figure 3.. Fux ref T ref Tabe δ VSI induction otor w T + w T+w FLC δ ' δ DT z FLC δ + + z - z - ode Figure 3.. Scheatic of the Fuzzy Logic DTC. In dahed ine i eparated the nove fuzzy controer part. It houd be cear that depite the fact that there are two Fuzzy Logic controer, jut one fuzzy controer i ued per iteration. Therefore, the coputation capabiity of the rea yte won't be neceariy that uch. It houd be noted a we, that the cheatic in figure 3. i pretty iiar to the caica DTC one in figure., incuding the otor ode, which wi cacuate the torque, tator fux oduu vaue and it poition. However, the torque error i jut given in two eve intead of three. It ean that fro the caica DTC tabe II.II jut four row are ued, being dicharged the nu tate. However, nu tate are introduced by ean of the duty cyce. Obviouy, there i a nove part that correpond to the nove Fuzzy Logic controer aready decribed. Finay thi new controer wi give a duty ratio vaue, which can be obtained by ean of two different way. The firt way i through the FLC (Fuzzy Logic controer ). Thi way wi be the eat ued. The econd way correpond to the adaptive controer thought to track the reference vaue. Thi other way give an increent of the duty ratio, which wi be added to the previou duty ratio vaue. The fu yte wi work firt a the caica DTC obtaining the active tate through the caica tabe. Then the fuzzy controer wi give the duty ratio. 3.

9 3.. - Stator Fux Reference Optiu Controer. A it ha been expained in the previou ection, the rippe in the eectroagnetic torque and tator fux are extreey reduced by uing controer baed on Fuzzy Logic yte or predictive ethod. However, in order to obtain even a better reduction, tator fux reference vaue ha to be adapted to an optiu vaue, which houd be jut arge enough to produce the deired torque. The reaon i that with thi optiu vaue both the increae in the active tate i jut arge enough and the ight reduction in the nu tate i ower. Moreover, it i achieved a reduction in the reactive power conuption taken fro the ain uppy. The optiu expreion, which give the jut arge enough tator fux for the deired torque i given in equation.3 fro ection.3.5. In figure 3. can be een the fina Fuzzy Logic DTC chea with the tator fux reference optiu controer. Notice how the optiu tator fux vaue i cacuated fro the torque et point vaue. optiu fux T ref Tabe δ VSI induction otor w T + w T+w FLC δ ' δ DT z FLC δ + + z - z - ode Figure 3.. Fux reference optiied controer in a Fuzzy Logic DTC. 3.9

10 3.3 - Siuated reut. It i hown the iuation reut per different working point, coparing the caica DTC and the Fuzzy Logic DTC (FLDTC). More iuation than the one hown have been done, and the obtained reut have been uaried in tabe III.I and tabe III.II. In a iuation preented, it can be oberved a uch better behaviour of the FLDTC perforance, achieving one of the ain objective of the preent work, which wa to reduce the torque rippe and conequenty iprove the otor perforance. A good adaptation of the FLC to any otor i proved ince the iuation reut are done for two different otor, achieving in both cae a good repone. Thee otor are the "otor_kw" and "otor_.5kw". (A otor' detai can be found in chapter ). An index error ha been ued to quantify the error in both the tator fux and torque repone. Thi index i the integra of the quare error (IE), which i coputed by ean of the quare error intead of jut the error; therefore, the ore error i produced the ore ephai it i given in the index. A iuation have been reaied with an idea induction otor drive with no deay and the aping tie (Tz) ha been fixed to µ. 3.

11 peed/ (rd/) torque (N) fux x 5 (Wb) ψ ψ IE T =.3 IE ψ =.9e-3 peed/ (rd/) torque (N) fux x 5 (Wb) ψ ψ IE T =.73 IE ψ =.57e Figure 3.3 A. Stator fux, torque and peed otor_.5kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. peed/ (rd/) torque (N) fux x (Wb) ψ ψ IE T =.5 IE ψ =.55e peed/ (rd/) torque (N) fux x (Wb) ψ ψ IE T =.97 IE ψ =.e Figure 3.3 B. Stator fux, torque and peed otor_kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. 3.

12 peed (rd/) torque (N) fux x (Wb) ψ IE T =. IE ψ =.e ψ Figure 3. A. Stator fux, torque and peed otor_.5kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. peed (rd/) torque (N) fux x (Wb) - ψ IE T =. ψ IE ψ =.e-3 peed/ (rd/) torque (N) fux x (Wb) IE T =.35e-3 ψ IE ψ =.e ψ Figure 3. B. Stator fux, torque and peed otor_kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. peed/ (rd/) torque (N) fux x (Wb) IE T =.37 ψ ψ IE ψ =7.e-3 3.

13 peed (rd/) torque (N) fux x 5 (Wb) ψ ψ IE T =.3 IE ψ =3.e-3 peed (rd/) torque (N) fux x 5 (Wb) ψ ψ IE T =. IE ψ =.e Figure 3.5 A. Stator fux, torque and peed otor_.5kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. peed/ (rd/) torque (N) fux x (Wb) ψ ψ IE T =.9 IE ψ =.7e peed/ (rd/) torque (N) fux x (Wb) ψ ψ IE T =.9 IE ψ =.53e Figure 3.5 B. Stator fux, torque and peed otor_kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=%T n. =%n. Notice the IE fux and torque error indexe vaue. 3.3

14 peed/ (rd/) torque (N) fux x (Wb) ψ IE T =. ψ IE ψ =.e-3 peed/ (rd/) torque (N) fux x (Wb) ψ ψ IE T =. IE ψ =3.e Figure 3. A. Stator fux, torque and peed otor_.5kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=5%T n. =5%n. Notice the IE fux and torque error indexe vaue. peed/ (rd/) torque (N) fux x (Wb) ψ..... ψ IE T =.33 IE ψ =.e-3 peed/ (rd/) torque (N) fux x (Wb) IE T =. IE ψ =.57e ψ ψ Figure 3. B. Stator fux, torque and peed otor_kw repone in Fuzzy Logic DTC (eft) and caica DTC (right). T=5%T n. =5%n. Notice the IE fux and torque error indexe vaue. 3.

15 3. - Interi concuion. After a the reearch done in ection.3, thi thei i focued on introducing a oduation in the DTC. A Fuzzy Logic controer contro thi oduation, between the eected active tate and a nu one. Therefore, it ha been uggeted and deepy decribed the Fuzzy Logic controer, which together with the DTC wi create the Fuzzy Logic DTC. The Fuzzy Logic controer deigned i adaptive, iproving even ore the whoe FLDTC. Siuation reut how the vaidity of the FLDTC ethod not ony achieving a coniderabe reduction in torque rippe, but ao reducing the reactive power conuption taken fro the ain uppy. Siuated reut corroborate a the preented work. Moreover, the iuation correpond to two different otor being proved the vaidity of the FLDTC for any otor. It ha been ued jut one witching period (µ) in a iuation, and no deay have been conidered. In tabe III.I i hown the error vaue index (IE) obtained in the iuation per different working point for the otor_.5kw. In tabe III.II i hown the error vaue index (IE) obtained in the iuation per different working point for the otor_kw. In both otor the reut are pretty iiar. Therefore, the firt concuion i that the Fuzzy Logic controer work propery in any otor, thu the FLDTC i a good contro ethod for any otor. Fro the tabe III.I and III.II, it can be concuded: IE in torque i away aer in FLDTC than in caica DTC. Therefore, the vaidity of FLDTC i corroborated. IE in fux i neary away aer in FLDTC than in caica DTC. The aer the torque et point i the aer fux FLDTC IE vaue i. However, there are jut a few exception when the torque et point i near to the noina one. Under thee circutance, both fux error indexe are pretty iiar. The reaon i that the tator fux rippe i reduced by ean of the tator fux reference optiu controer introduced in ection.3.5, that away work but when the torque et point i near to the noina vaue. 3.5

16 IE FLDTC c_dtc Tpc Wpc Fux Torque Fux Torque % % 3.e-3.3.e-3. 5% 5%.e e-3. % %.9e-3..e-3.93 % %.9e e % 5%.e-3.3.e % %.e-3.3.e % 75%.35e-3.7.e-3.33 Tabe III.I: Error index vaue (IE) obtained for the otor_.5kw iuation per different working point. A coparion between the caica DTC and the Fuzzy Logic DTC i done, not ony for the torque error vaue but ao for the tator fux one. IE FLDTC c_dtc Tpc Wpc Fux Torque Fux Torque % %.7e e-3.9 5% 5%.e e-3. % %.e e-3.37 % %.55e-3.5.e-3.97 Tabe III.II: Error index vaue (IE) obtained for the otor_kw iuation per different working point. A coparion between the caica DTC and the Fuzzy Logic DTC i done, not ony for the torque error vaue but ao for the tator fux one. 3.