英文資料圓鋼送料機(jī)械手,上下料機(jī)械手大學(xué)設(shè)計(jì)

1、英文資料The con tral tech niq ues drives and con trals han dbookChapter A4Torque, speed and positi on con trolA4.1 Gen eral prin ciplesA4.1.1 The ideal con trol systemMany applicati ons exist where somethi ng has to be con trolled to follow a referenee quantity. For example, the speed of a large motor m

2、ay be set from a low-power control signal. This can be achieved using a variable-speed drive as described in the followi ng.矚慫潤(rùn)厲釤瘞睞櫪廡賴(lài)。Ideally, the relati on ship betwee n the refere nce and the motor speed should be linear, and the speed should change instantly with changes in the reference. Any co

3、n trol system can be represe ntedas in Figure A4.1b, with an in put refere nce signal, a transfer function F and an output. For the system to be ideal, the transfer fun cti on F would be a simple con sta nt, so that the output would be proporti onal to the refere nce with no delay聞創(chuàng)溝燴鐺險(xiǎn)愛(ài)氌譴凈。Figure A

4、4.1 Variable-speed drive and motorA4.1.2 Open-loop controlUnfortunately, the transfer function of many practical systems is not a con sta nt, and so without any form of feedback from the output to correct for the non-ideal n ature of the tran sfer fun cti on, the output does not follow the dema nd a

5、s required. Using an in ducti on motor supplied bya simple ope n-loop variable-speed drive as an example, the followi ng illustrates some unwan ted effects that can occur in practical systems殘騖樓諍錈瀨濟(jì)溆塹籟。Speed regulation. The output of a simple open-loop drive is a fixed frequency that is proporti ona

6、l to the speed refere nce, and so the freque ncy applied to the motor remains constant for a constant speed reference. The speed of the motor drops as load is applied because of the slip characteristic of the motor, and so the speed does not rema in at the required level 釅錒極額閉鎮(zhèn)檜豬訣錐。In stability. It

7、is possible un der certa in load con diti ons and at certa in frequencies for the motor speed to oscillate around the required speed, even though the applied freque ncy is con sta nt. Ano ther major source of in stability in rotat ing mecha ni cal systems is low-loss elastic coupli ngs and shafts彈貿(mào)攝

8、爾霽斃攬磚 鹵廡。Non-Iinearity. There are many possible sources of non-linearity. If, for example, the motor is connected to a gearbox, the speed at the output of the gearbox could be affected by backlash betwee n the gear謀養(yǎng)摶篋飆鐸懟類(lèi)蔣薔。Variations with temperature. Some aspects of the system transfer function m

9、ay vary with temperature. For example, the slip of an in ducti on motor in creases as the motor heats up, and so for a give n load the motor speed may reduce from the starti ng speed whe n the motor was cold 廈礴懇蹣駢時(shí)盡繼價(jià)騷。Delay. With a simple ope n-loop in verter and in ducti on motor there can be a de

10、lay before the motor speed reaches the dema nded level after a cha nge in the speed referenee. In very simple applications such as controlling the speed of a conv eyor belt, this type of delay may not be a problem .In more complex systems, such as on a mach ine tool axis, delays have a sig nifica nt

11、 effect on the quality of the system.煢楨廣鰳鯡選塊網(wǎng)羈淚。These are just some of the unwan ted effects that can be produced if an ope n-loop con trol system is used. One method that improves the quality of the con troller is to use a measure of the output qua ntity to apply some feedback to give closed-loop c

12、on trol.鵝婭盡損鶴慘歷蘢鴛賴(lài)。A4.1.3 Closed-loop controlThe simple ope n-loop drive of Sectio n A4.1.2 can be replaced with a con trol system as in Figure A4.2. This con trol system not on ly provides a mea ns to correct for any error in the output variable, but also en able a stable resp onse characteristic 籟

13、叢媽羥為贍債蟶練淨(jìng)。A4.2 Con trollers in a driveA4.2.1 Ge neralAlthough a moder n variable-speed drive in cludes many features, the basic function of the drive is to control torque (or force), speed or position. Before proceeding to the specific details of how different types of variable-speed drive fun cti o

14、n, the theory of con trol for each of these qua ntities is discussed. A positi on con trol system is show n in Figure A4.5. This in cludes an inner speed con troller, and with in the speed con troller there is an inner torque con troller. It is possible to create a system where the position controll

15、er determines the mechanical torque that is applied to the load directly without the inner speed and torque loops. However, the position controller would need to be able to control the complex combined transfer function of the motor windings, the mechanical load and the conv ersi on from speed to po

16、sition預(yù) 頌圣鉉儐歲齦訝驊糴。Therefore it is more usual to use the format shown in Figure A4.5. The other advantage of this approach is that limits can be applied to the range or rate of change of speed and torque between each of the controllers. When a system is required to control speed only, the position co

17、ntroller is omitted, and when a system is required to con trol torque only, the positi on and speed con trollers are omitted.滲釤嗆儼勻諤鱉調(diào)硯錦。A positi on sen sor is show n provid ing feedback for the system, but this may be replaced by a speed sen sor or it may be omitted altogether as follows誅 臥瀉噦圣 騁貺頂廡。

18、Position information is required by the torque controller to function in an a.c. motor drive (see the dotted line). If position feedback is provided the speed feed-back is derived as the cha nge of speed over a fixed sample period. Sen sorless schemes are possible for speed and torque con trol of a.

19、c. motors, i n which case the sen sor is not required.擁締鳳襪備訊顎輪爛薔。Positi on feedback is not n ecessaryfor the torque con troller in a d.c. motor drive, so a speed feedback device such as a tacho-ge nerator can be used to provide the feed-back for the speed controller. Again, sensorlessschemes are pos

20、sible where a speed feedback device is not requirec贓 熱俁閫歲匱閶鄴鎵騷。A4.2.2 Torque controlA torque con troller for a rotary motor, or a force con troller for a lin ear motor, is the basic inner loop of most variable-speed drives. Only torque control is discussed here, but the principles also apply to forc

21、e control for a linear applicati on. In order to expla in the prin ciples of torque con trol, the simple d.c. motor system in Figure A4.6 is used as an example. The an alysis of torque con trol in an a.c. motor can be done in exactly the same way, provided suitable transformations are carried out in

22、 the drive. These transformations will be discussed late壇搏鄉(xiāng)囂懺蔞鍥鈴氈淚。The torque dema nd or refere nee (Te*) is conv erted by the torque con troller into a curre nt in the motor armature, and the motor itself converts the curre nt intotorque蠟變黲癟報(bào)倀鉉錨鈰贅。Figure A4.6Torque and curre nt con trollers in a d.

23、c. motor drive: (a) torquecon trol;買(mǎi)鯛鴯譖曇膚遙閆擷凄。(b) curre nt con trol to drive the mecha ni cal load. Figure A4.6b shows the system required to convert the torque refere nee into motor curre nt. The torque refere nee (Te*) is first transformed into a current referenee (ia*) by including the scaling ef

24、fect of the motor flux. The motor flux, con trolled by the motor field curre nt (if ), is no rmally reduced from its rated level at higher speeds whe n the termi nal voltage would exceed the maximum possible output voltage of the power circuit without this adjustme nt. Curre nt limits are the n appl

25、ied to the curre nt refere nee so that the required current does not exceed the capa-bilities of the drive. The current refere nee (limited to a maximum level) becomes the in put for the PI con troller. The electrical equivale nt circuit of the motor eon sists of a resista nee (Ra), an in ducta nee

26、(La) and a back emf that is proporti onal to flux and spee綾 鏑鯛駕櫬鶘蹤韋 轔糴。(Kevc/crated).The PI eon troller alone could successfully eon trol the curre nt in this circuit becauseas the speed i ncreases,the voltage required to overcome the back emf would be pro-vided by the integral term. The integral eo

27、ntrol is likely to be relatively slow, so to improve the performa nee duri ng tran sie nt speed cha nges a voltage feed-forward term equivale nt to Kevc/crated is in eluded. The comb ined output of the PI eon troller and the voltage feed-forward term form the voltage refere nee (va*), and in resp on

28、se to this the power circuit applies a voltage (va) to the motor ' s electrical circuit to give a current (ia). The current is measured by a sen sor and used as feedback for the curre nt eon troll驅(qū)躓髏彥浹綏譎飴憂錦。As well as the lin ear comp onents show n in Figure A4.6, the curre nt eon trol loop in a

29、 digital drive in eludes sample delays as well as delays caused by the power circuit. In practice, the response of the eontroller is dominated by the proporti onal gain. In particular, if a voltage feed-forward term is used, the in tegral term has very little effect on the tran sie nt resp on s貓蠆驢繪燈

30、鮒誅髏貺廡。Sett ing of the eon trol loop gains is clearly very importa nt in optimis ing the per-formanee of the eontrol loop. One of the simplest methods to determine a suitable proporti onal gai n is to use the followi ng equati on 揪籟饗逕瑣筆襖鷗婭薔。where La is the motor in ducta nee and Ts the curre nt con t

31、roller sample time. K is a con-sta nt that is related to the curre nt and voltage scali ng, and the delays prese nt in the con trol system and power circuit. Most moder n variable-speed drives in clude auto-t uning algorithms based on measureme nt of the electrical parameters of the motor take n by

32、the drive itself, and so the user does not no rmally n eed to adjust the curre nt con troller gai ns構(gòu)氽頑黌碩飩薺齦話騖。It is useful to know the closed-loop tran sfer fun ctio n of the torque con troller (i.e. Te/Te*) so that the resp onse of a sta nd-al one torque con troller, or the effect of an inner torq

33、ue controller on outer loops such as a speed controller, can be predicted. As the resp onse is domin ated by the system delays it is appropriate to represe nt the closed-loop resp onse as simple gains and a un ity gain tran sport delay as show n in Figure A4.7輒嶧陽(yáng)檉籪癤網(wǎng)儂號(hào)澩。The torque refere nee could b

34、e in N m, but it is more conven tio nal to use a value that is a perce ntage of the rated motor torque. Figure A4.7a gives the tran sfer fun cti on whe n the torque con troller is used alone. Kt is the torque con sta nt of the motor in N m A21. If the torque con troller is used with an outer speed c

35、on troller a slightly different representation must be used, as in Figure A4.7b. The speed controller pro-duces a torque referenee where a value of unity corresponds to a curre nt level that is specified for the size or rati ng of the drive. From a con trol perspective it is uni mporta nt whether th

36、is is the maximum curre nt capability of the drive, the rated curre nt or some other level. The actual level 側(cè)閏繭絳闕絢勵(lì)蜆贅。used is defined as Kc (in amperes), and should be included in the transfer function as shown. These simple models allow the drive user to predict the performa nee of a sta nd-al one

37、 torque con troller or a torque con troller with an outer speed loop識(shí)饒鎂錕縊灩筧嚌儼淒。A4.2.3 Flux controlThe motor flux and hence the motorterminal voltage for a given speed are defi ned by the flux produc ing curre nt. I n the example of a simple d.c. motor drive used pre-viously, the motor flux level is

38、set by the field current, if. The flux controller (Figure A4.8) includes an inner current loop and an outer loop that maintains rated flux in the motor until the armature terminal voltage reachesits maximum limit. Whe n the motor speed in creases above rated speed it the n con trols the field curre

39、nt and hence the flux, so that the armature voltage remai nsat the maximum required level凍鈹鋨勞臘錯(cuò)癇婦脛糴。A4.2.4 Speed controlA4.2.4.1 Basic speed controlClosed-loop speed con trol can be achieved by appl ying a simple PI con troller around the torque con troller described previously. For the purposes of

40、this an alysis it is assumed that the load is an in ertia J, with a torque Td that is not related to speed (frictio n is n eglected). The result ing system is show n in Figure A4.1恥諤銪滅 縈歡煬鞏鶩錦。Figure A4.10Speed con trollerIf the PI controller is represented as Kp t Ki/s, the torque controller is assu

41、med to be ideal with no delays so that the unity transport delay can be n eglected, and the in ertia load is represe nted as 1/Js the n the forward loop gain in the s doma in is give n by鯊腎鑰詘漣鉀溈懼統(tǒng)庫(kù)。The closed-loop tran sfer fun ctio n in the s doma in v(s)/v*(s) is give n by G(s)/ 1 t G(s). Substitu

42、t ing for G(s) and rearra nging gives碩癘鄴頏謅攆檸攜驤蘞。If the n atural freque ncy of the system is defi ned as vn ? (KcKtKi=J ) and the damping factor is defined as j ? vnKp/(2Ki) then 閿擻輳嬪諫遷擇植秘騖。As with the torque con troller, it is useful to know the closed-loop resp onse so that the resp onse of a sta n

43、d-al one speed con troller, or the effect of an inner speed controller on an outer position loop, can be predicted. If a moderate response is required from the speed con troller it is not sig nifica ntly affected by system delays, and a linear transfer function such as equation (A4.4) can be used. A

44、ll the con sta nts in these equati ons and the delays associated with the curre nt con trollers are normally provided to users so that calculations and/or simulations can be carried out to predict the performa nee of the speed con trolie氬嚕躑竄貿(mào)懇彈濾頷澩。In additi on to providi ng the required closed-loop

45、step resp on se, it is importa nt for the system to be able to preve nt unwan ted moveme nt as the result of an applied torque tran sie nt. This could be because a load is sudde nly applied or because of an un eve n load. The ability to preve nt unwan ted moveme nt is referred to as stiff ness. The

46、com-plia nee an gle of the system is a measure o釷鵒資贏車(chē)贖孫滅獅贅。Figure A4.11Responses of an ideal speed controller: (a) closed-loop stepresp onse慫闡譜鯪逕導(dǎo)嘯畫(huà)長(zhǎng)涼。Figure A4.12Unwan ted delays in a practical digital drive 諺辭調(diào)擔(dān)鈧諂動(dòng)禪瀉類(lèi)。Dyn amics 115UMC 3 000 rpm servo motor (Kt ? 1.6 N m A21, J ? 0.00078 kg m2) wit

47、h the speed controller gains set to Kp ? 0.0693j and Ki ? 14.32.嘰覲詿縲 鐋囁偽純鉿錈。As the damp ing factor is in creased, the closed-loop resp onse overshoot is reduced and the speed of resp onse improves. The closed-loop resp onse in cludes 10 per cent overshoot with a damping factor of unity becauseof the

48、 s term in its nu merator熒紿譏鉦鏌觶鷹緇機(jī)庫(kù)。As the damp ing factor is in creased, the overshoot of the resp onse to a torque tran-sie nt is reduced and the resp onse becomes slower. n this case there is no s term in the nu merator and the resp on sei ncludes no overshoot with a damp ing factor of unity.鶼漬螻偉

49、閱劍鯫腎邏蘞。It would appear from these results that the higher the proporti onal gain, and hence the higher the damp ing factor the better the resp on ses; however, the results so far assume an ideal torque con troller and no additi onal unwan ted delays. In a real digital drive system the delays give n

50、in Figure A4.12 are likely to be prese nt. A delay is in cluded to represe nt the sample period for speed measureme nt, but this is only releva nt if the speed feedback is derived from a positi on feedback device such as an en coder and is measured as a cha nge of positi on over a fixed sample perio

51、d.紂憂蔣氳頑薟驅(qū)藥憫騖。The effect of the unwan ted delays can be see n in the closed-loop step resp onse for a real system as show n in Figure A4.13. In each case the resp onse of the real system has more overshoot tha n the ideal system. If the damp ing factor is set to un ity the n the overshoot may be acce

52、ptable, but with a damp ing factor of 1.25 the resp onse is quite oscillatory and is likely to be un acceptable. The effect of the unwan ted delays is more pronoun ced the Ion ger the delay and also as the set ban dwidth of the speed con troller is in crease(穎芻莖峽餑億頓裊賠瀧。The effect of the additional d

53、elays can be seen in the Bode plot of the closed-loop resp onse of the speed con troller set up to give unity damp ing factor (Figure A4.14). The freque ncy at the 23 dB point of the gai n characteristic has increasedsignificantly from the ideal speed controller, whereas the frequency at the 608 poi

54、nt of the phase characteristic is almost un cha nged. If this is to be used as a stand-alone controller the gain characteristic could be used to predict the ban dwidth, although it should be no ted that the gain is greater tha n un ity at some freque ncies. Often the ban dwidth based on the gain cha

55、racteristic is the only ban dwidth that is quoted, because this makes the performa nee appear to be better, in this case 2 000 rad s21濫驂膽閉驟羥闈詔寢賻。Figure A4.13 Effect of delays on a closed-loop step respons銚銻縵嚌鰻鴻鋟謎諏涼。(a) damp ing factor ? 1; (b) damp ing factor ? 1.25 based on the phase delay (672 rad

56、 s21 for this example) must be used, as this affects the performa nee of the outer loop.擠貼綬電麥結(jié)鈺贖嘵類(lèi)。Unwan ted delays limit the performa nee of the speed con troller. The qua ntised n ature of speed feedback whe n it is derived from a positi on sen sor as the cha nge of positi on over a fixed sample p

57、eriod can also limit this. A high proporti onal gain in the speed con troller, and hence high ban dwidth, gen erate high-freque ncy torque ripple and acoustic no ise from the qua ntised speed feedback荊紳諮侖驟遼輩襪錈。 Figure A4.14 Bode plot of closed-loop resp onse of a speed con trolley 礙籟饈決穩(wěn)賽 釙冊(cè)庫(kù)。The cha

58、racteristic defi ned by equati on (4.11) is show n in Figure A4.15. The required damp ing factor must first be selected, and from this the ratio vbw/v n is take n from the graph. For example, if a damp ing factor of unity is required, the value of vbw/v n is 2.5.裊樣祕(mì)廬廂顫諺鍘羋藺。Figure A4.15 Effect of dam

59、pi ng factor o n ban dwidth 倉(cāng)嫗盤(pán)紲囑瓏詁鍬齊驚。The defi niti on of damp ing factor is j ? vn Kp/(2Ki). By rearra nging this and substitut-i ng for n atural freque ncy, a suitable value for the proporti onal gain can be derived綻萬(wàn)璉轆娛閬蟶鬮綰瀧。Select ion based on complia nee an gleFrom equati on (A4.9) the steady-state resp onse to a torque tran sie nt can be derived by setting s ? 0. The resulting change of output angle for a given steady-state torque Td is顧燁鶚巰瀆蕪領(lǐng)鱺賻