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1、a closed loop feedback method for a manual barstraightenerrobert j. miklosovic, zhiqiang gaodepartment of electrical and computer engineeringcleveland state universitycleveland, ohio, usaabstractautomation of a unique manually controlled industrial bar straightener is proposed. a continuous-time clo

2、sed loop model is constructed in simulink for an event-driven process through the use of asynchronous timers. the system is simulated with linear and nonlinear pd controllers. a nonlinear filter,called the tracking differentiator, is introduced as an alternative to a linear approximate means of prov

3、iding accurate derivative feedback in the presence of noise. in both cases, the nonlinear techniques outperformed their linear counterparts while retaining tuning simplicity.i. backgroundprecision straightening of a cylindrical metal bar is largely based on the ability to precisely measure its geome

4、try. a few fundamental measurements and how each influences the tolerance specification on straightness should first be understood. methods for measuring roundness and straightness are covered to lay the groundwork for the problem formulation. the basic operation of the machine is outlined in sectio

5、n ii, and its fundamental limitations and need for automation are discussed. section iii addresses the task of closing the loop through block diagrams and the role of new hardware in the process. section iv contains descriptions of all of the blocks that are modeled in simulink. the linear and nonli

6、near controller designs are discussed in section v, the system is simulated in section vi, and concluding remarks are made in section vii.a. measuring roundnessroundness is a quantity derived from comparing the shape of a cross-sectional area at one distinct point along a cylinders length against a

7、circle. a round metal bar that is arbitrarily long with respect to its diameter has to be checked for roundness in many locations lengthwise and averaged to insure overall consistency. roundness is approximated by rotating the work piece one revolution in a vee block while measuring the surface with

8、 an indicator. taking the difference between the minimum and maximum indicator readings in this case is referred to as the total indicator reading (tir) 1.b. measuring straightnessstraightness is a quantity derived from comparing the axial centerline of a specific section of a cylinders length again

9、st a straight line. a simple method for approximating straightness is by rotating the bar one revolution between two vee blocks that are a fixed distance (d) apart, while measuring in the center with an indicator. the distance that the axial centerline of the part deviates from a theoretically strai

10、ght centerline directly below the indicator equals the extent to which the part is bowed, or warped, over length d. the maximum and minimum indicator readings (ix and in) are physically represented in fig.1. from this, tir is derived as:tir= ix in = (r + |bow|)-(r |bow|) =2*|bow| (1)deviations in ro

11、undness, outside diameter (od) size, and finish can adversely affect the measurement.figure 1. max. and min. indicator readings of a bowed partc. straighteningthe straightening process, which can be broken into steps, simply involves correcting any error while checking for straightness. first, the p

12、art is measured for straightness. then, it is rotated so that the bow is oriented 180 degrees away from the vee blocks with the maximum indicator reading facing upwards. finally, a counter-bending force replaces the indicator and straightens the work piece against the vee blocks.ii. machine operatio

13、nthe straightener to be automated uses a non-contact ultrasonic sensor in place of the indicator and rollers in place of the vee blocks in an effort to minimize contact wear. the part slowly spirals through the machine. the indicator reading becomes a continuous sinusoid at the sensors output, havin

14、g a peak-to-peak value equal to the tir each revolution. tir is sampled from the sensor output and calculated each revolution, making the sample period of one revolution the minimum time between consecutive bends (ysp). tir is the plant output (y) to be controlled. when the part is straightened, the

15、 machine stops rotation with the bow facing upwards, but the part continues to feed lengthwise while an air cylinder counterbends the part over a period of time. this bend time (bt) is the control variable (u). fig. 2 illustrates this operation.figure 2. the straightener to be automateda. process li

16、mitationsthere are aspects of the process that can limit the controllers performance and slow it down by extending ysp. each is observed and taken into consideration when producingan accurate simulation model:1. the ultrasonic sensor introduces rfi noise into its. the use of a feedback filter is ess

17、ential.2. a rough part surface finish adds distortion to the sensor output.3. an out-of-round part superimposes harmonics on the sensor output sinusoid, placing a bound on the minimum steady state error that is achievable.4. inconsistent material density produces false measurements. the measured foc

18、al length of atransducer is dependent on the density of the material that is being measured 2. the unit cannot measure accurately in the presence of a time-variant material density (i.e. hard spots). although unavoidable, it can be detected, since tir changes monotonically.5. an inconsistent od caus

19、es vertical shifts in the sensor output. a differential tir measurement cancels these affects.6. a twisted part condition is detected when the angular position of the maximum indicator reading slowly moves with each revolution. this condition is created when the part is not straightened at the preci

20、se angular location and occurs because of the quantization affect of the digital readout used by the operator. the new controller will use a continuous signal and the part can be straightened 30 to 45 degrees ahead of the twist when encountered.b. the need for automationreplacement of the operator w

21、ith electronic hardware is beneficial in several ways. the cost of the electronics is much less than the ongoing hourly wage and schedule of an operator. the limitations associated with the digital readout are eliminated, which helps the machine to straighten faster with more precision. the process

22、can be drastically sped up to produce more. though the minimum sample time is one revolution, it does not need to be slow enough for human comprehension. a programmable logic controller (plc) can make several calculations and test the result against a set of rules many times faster than a human bein

23、g.c. research methodologythe focus is split between modeling and control design, since this is a new control problem. the process is manually controlled rather than being strictly manual in operation, meaning the machine needs only a new controller. there is no need for a complete mechanical overhau

24、l, so the best method of straightening is not researched. typical of a small company, time and money are limited. gao and huang 3 presented a new error-based control design framework including such innovations as a nonlinear tracking differentiator and a nonlinear proportional-integral-derivative (n

25、pid) control method. these methods prove to be powerful and simple to tune, which make them ideal for use in an industrial environment.iii. a closed loop solutionthe task of automation can begin once the process is well defined. a straightforward system block diagram is developed, and each block is

26、modeled in simulink. aspects of the hardware configuration are carefully considered.a. from open loop to closed loopthe open loop multi-input-multi-output (mimo) block diagram, in fig. 3, represents the manually controlled process. the operator calculates tir and monitors the angular position (h

27、8576; p) of the bow with each revolution. when y approaches a specified limit, the operator sets bt proportional to y and itsrate, and then pushes a button (bp) to straighten the part. the bend timer creates a pulse triggered by bp that counter-bends the part for bt minutes. this event forces the pa

28、rt to have a specific rate for a period of time. after the event, the part takes on a new rate and the process perpetuates. therefore, y is apiece-wise continuous function of time. the operators involvement in the process is represented as a block in fig. 4.figure 3. open loop block diagramfigure 4.

29、 operator blockrearranging the blocks and breaking each function down into smaller more-manageable blocks reduces the representation to a usable closed loop, single-input-singleoutput (siso) form. fig. 5 shows how a siso plant is obtained by combining the process with the task of sampling the tir, s

30、ince it can be consistently computed.figure 5. siso plant blockthe plant has a variable-width pulse as the input (u) and the sampled tir (y) as the output to be controlled. the incoming changing position of the work piece is modeled as an unknown rate disturbance (d). the closed loop siso block diag

31、ram is shown in fig. 6.figure 6. closed loop block diagramb. hardware configurationdepicted in fig. 7, an encoder and a plc are the only hardware needed for automation. the encoder feeds the angular position of the part back to the controller, and the plc handles all of closed loop functions outside

32、 of the process.figure 7. hardware configurationfig. 8 depicts the hardware layout for plant data acquisition during manual operation. the plc is also used to calibrate a strip chart recorder, shown in fig. 9, which simplifies calibration for the operator and removes room for error during data acqui

33、sition. using the plc for both data acquisition andcontrol keeps costs lower.figure 8. open loop data acquisition configurationfigure 9. chart recorder settings for a .006” tir signaliv. modelingsimulation modeling involves the construction of simulink blocks for each of the blocks in the siso diagr

34、am. three modular blocks are first designed to accommodate the presenceof an event-driven plant in a continuous-time environment where the control variable is an asynchronous pulse width. they are all based on creating asynchronous timers in simulinkby integrating a constant until it reaches a prese

35、t value, then shutting it off by feeding the input with a zero. equation (2) will reach a value of one in the time interval equal to the average of u(t) over it. the accuracy increases if the interval is very small or u(t) is a constant function. a suitable differenceequation is given in (3).a. trig

36、gered sample-and-hold (tsh) blockthe output and rate of the plant immediately after the part has been straightened are dependent on bt, and the previous y and y, all of which occur over different time intervals. the function of the tsh block is to sample a value at one point in time so that it can b

37、e used at another time. shown in fig. 10, the block basically samples the input for a small period of time on the rising edge of an enabling pulse, and then holds that value constant at the output until the block is re-enabled. in simulink, a constant value can be maintained for an arbitrary period

38、of time by building the output of an integrator to a desired value. a t-second timer is created by integrating 1/t until it equals one. it is used to control the small time interval in (4) which takes a time average of the input.figure 10. tsh simulink blockb. pulse blockthe bend timer must be able

39、to convert bt from a value into the timed pulse, u. the pulse block, illustrated in fig. 11, was designed for this purpose. by incorporating (2), it creates a pulse that has a magnitude equal to the sign of the input and a pulse width equal to the inputs absolute value.figure 11. pulse simulink bloc

40、kthe heart of the pulse block is the pulse subsystem block, shown in fig. 12. the reciprocal block generates a divide-byzero error whenever its input is zero. consequently, the reciprocal block needs to be isolated in a subsystem that is only enabled when supplied with a value that is larger than a

41、userdefined constant.v. control designthere are currently many different control structures available, the simplest of which is the pid controller design. for this reason, a pd controller is first applied to the closed loop model to verify its response and stability. it is used as a benchmark for ot

42、her controllers. next, a nonlinear pd (npd) control scheme is introduced. it retains the tuning ease of the pd controller while improving performance. last, a nonlinear filter, called the tracking differentiator (td), is introduced asan alternate means of providing an accurate derivative feedback to

43、 the controller in the presence of noise, thus improving performance.a. linear pid controlfor many reasons, pid control is still used in 90% of industrial applications 3. there are only three tuning parameters, each having direct physical significance to the error signal, not the model. this makes f

44、or easy tuning, without having to spend considerable resources on the construction of a linear model. linear models are often inaccurate and require re-tuning when the real-world plantsthey represent are nonlinear and time varying. a control structure that is error-based, and not model-based, is mor

45、e resilient to model uncertainties 3. the pid control law in (6) represents the direct physical meanings of the three parameters, where e is the error signal, kp is the proportional gain, ki is the integral gain, and kd is the derivative gain. k e k edt k= p + i _ + d (6)vi. simulationthe pd control

46、ler and the npd controller are simulated in simulink on the closed loop model. the significance of practical initial conditions and disturbances are considered. simulation results from the two cases are presented and discussed. next, the steady state error is compared under various noise and disturb

47、ance conditions. finally, a second order approximation and a td are implemented in the feedback loop and simulated with heavy feedback noise for both controllers.a. transient performancesimulating the system and individually adjusting plant parameters to emulate various real world conditions verifie

48、d the design. fig. 19 graphs the output and rate response for the pd controller. notice the control action occurs when the rate is at ±r2 (i.e. ±.001 in this case). the performance measures are defined as follows:1. the settling time (ts) is the time it takes for y to be within ±.001,

49、 since this is the general object ofstraightening.2. overshoot (os) is the maximum |y| after it has reached zero.3. steady state error (ess) is the maximum |y| in the steady state region.the linear and nonlinear pd controllers were tuned to achieve the same ts. the results of the transient responses

50、 of the two controllers for two widely different initial positions are tabulated in table i, to compare os and ess. all units are in thousandths except for settling time.4. the process can be modeled in discrete time and/or with different software. writing the entire plant and bend timer in c may si

51、mplify the simulation model. from this, a class of problems can be clearly studied.5. the process can be investigated and modeled as a finite state machine.調(diào)直機(jī)的反饋方法羅伯特·j·miklosovic,高志強(qiáng)電氣工程和計(jì)算機(jī)系克利夫蘭州立大學(xué)美國俄亥俄州克利夫蘭手動控制獨(dú)特自動化的建議。一個連續(xù)時(shí)間的閉環(huán)模型在simulink中構(gòu)建事件驅(qū)動的過程中,通過使用異步定時(shí)器。該系統(tǒng)是模擬線性和非線性pd控制器。非線性濾波器

52、,稱為跟蹤微分,介紹了作為一個替代的存在噪音,提供準(zhǔn)確的微分反饋線性近似手段。在這兩種情況下,非線性技術(shù)優(yōu)于線性,同時(shí)保留調(diào)整簡單。一,背景主要是基于能夠精確地測量其幾何精度的圓柱形金屬條調(diào)直。應(yīng)先了解一些基本的測量和如何每個影響的直線度公差規(guī)范。圓度和直線度測量方法覆蓋問題制定奠定了基礎(chǔ)。本機(jī)的基本操作是在第二節(jié),概述,并討論了其基本的限制和對自動化的需要。第三節(jié)討論通過框圖的循環(huán)過程中的作用和新的硬件關(guān)閉任務(wù)。第四節(jié)包含所有的塊,在simulink建模描述。在第五節(jié)討論的線性和非線性控制器的設(shè)計(jì),該系統(tǒng)是模擬在第六節(jié),第七節(jié)總結(jié)。答:測量圓度圓度是從一個不同點(diǎn),以及對一個圓圈一個圓柱體的長

53、度比較的橫截面積形狀的數(shù)量。一個圓形的金屬條,其直徑是任意長有縱向許多地方要檢查圓,平均以確保整體一致性。圓度近似v型塊在旋轉(zhuǎn)工件革命的一個指標(biāo),同時(shí)測量表面。在這種情況下的最低和最高指示讀數(shù)之間的差異被稱為總讀數(shù)(tir)1。b.測量直線度直線是比較一個圓柱體的長度對直線的一個特定部分的軸向中心線派生的數(shù)量。一個簡單的方法是近似直線旋轉(zhuǎn)酒吧之間,是一個固定的距離(四)除v型塊革命,而在測量指標(biāo)的中心。的一部分的軸向中心線偏離的指標(biāo)低于直接從理論上直中心線的距離等于其中部分是鞠躬,或扭曲的程度,超過長度d。身體的最高和最低的指標(biāo)讀數(shù)(九中)代表圖。外徑(od值)的大小,圓度偏差,并完成產(chǎn)生不利

54、影響測量結(jié)果。一個弓形部分的指標(biāo)讀數(shù)在整頓過程中,它可以分解成步驟,只涉及糾正任何錯誤,同時(shí)檢查直線。首先,部分的直線度測量。然后,它是旋轉(zhuǎn),以便弓是面向180度的v型塊朝上最大的指標(biāo)讀數(shù)。最后,反彎曲力的替代指標(biāo),并拉直對v型塊的工件。二、機(jī)器操作矯直機(jī)是自動化,在地方指標(biāo)和地方努力的v型塊輥使用一種非接觸式超聲波傳感器,以盡量減少接觸磨損。部分慢慢地通過機(jī)器螺旋。該指標(biāo)讀數(shù)在傳感器的輸出連續(xù)正弦波,有等于每個革命的tir的峰 - 峰值。公路運(yùn)輸從傳感器輸出進(jìn)行采樣,并計(jì)算出每個革命,做一個革命的樣本期間連續(xù)彎(ysp)之間的最短時(shí)間。公路運(yùn)輸是廠輸出(y)進(jìn)行控制。部分拉直,當(dāng)機(jī)器停止與弓

55、朝上旋轉(zhuǎn),但部分繼續(xù)養(yǎng)活縱向氣缸counterbends過了一段時(shí)間的一部分。這彎曲的時(shí)間(bt)是控制變量(美)。圖2說明了這種操作。a.工藝限制有方面的過程中,可以限制控制器的性能和擴(kuò)大永信藥品減緩下來。每個觀察和考慮生產(chǎn)精確的仿真模型:1、超聲波傳感器引入到其rfi噪聲。反饋濾波器的使用是必不可少的。2、一個粗糙的零件表面光潔度增加了傳感器輸出的失真。3、一個地地道道的圓形部分疊加在傳感器輸出正弦波的諧波,放置一個最低的穩(wěn)態(tài)誤差是可以實(shí)現(xiàn)的約束。4、材料的密度不一致產(chǎn)生虛假的測量。一個測得的焦距傳感器是依賴于正在測量2材料的密度。本機(jī)無法準(zhǔn)確測量中存在的時(shí)間變材料的密度(即硬點(diǎn))。雖然不

56、可避免的,它可以檢測到,因?yàn)檫\(yùn)輸單調(diào)變化。5、不一致的外徑導(dǎo)致傳感器輸出的垂直變化。一個差的tir測量抵消這些影響。6、一個扭曲的部分條件被檢測到時(shí)最大的指標(biāo)讀數(shù)的角位置慢慢移動每個革命。這種情況下被創(chuàng)建時(shí)的精確角位置拉直的部分不發(fā)生由運(yùn)營商所使用的數(shù)字讀數(shù),因?yàn)榱炕挠绊?。新的控制器將使用一個連續(xù)信號,并提前30至45度的扭轉(zhuǎn)時(shí)遇到的一部分可以被拉直。b.自動化的必要性更換運(yùn)營商與電子硬件在幾個方面是有利的。電子產(chǎn)品的成本是遠(yuǎn)遠(yuǎn)高于目前的每小時(shí)工資和操作員的時(shí)間表。數(shù)字讀數(shù)相關(guān)的限制被取消,這有助于機(jī)器更快更精確整頓。這個過程可以被大大加快生產(chǎn)更多。雖然最小的采樣時(shí)間是一個革命,它不需要是緩

57、慢的,對人類的理解不夠??删幊踢壿嬁刂破鳎╬lc),可以使一些計(jì)算和一套規(guī)則,對測試結(jié)果比人類快很多倍。c.研究方法論分裂之間的建模和控制設(shè)計(jì)的重點(diǎn),因?yàn)檫@是一個新的控制問題。手動控制的過程,而不是嚴(yán)格的操作手冊,這意味著機(jī),只需要一個新的控制器。有沒有必要為一個完整的機(jī)械檢修,所以最好的方法是不整頓研究。典型的一家小公司,有限的時(shí)間和金錢。高和黃3提出了一個新的基于錯誤控制設(shè)計(jì)框架,包括非線性跟蹤微分器和非線性比例 - 積分 - 微分(非線性pid)控制方法等創(chuàng)新。這些方法被證明是強(qiáng)大的和簡單的曲調(diào),使它們在工業(yè)環(huán)境中使用的理想選擇。第三。閉環(huán)解決方案一旦這個過程被很好地定義,自動化的任務(wù)就可以開始。開發(fā)一個簡單的系統(tǒng)框圖,每塊在simulink建模。硬件配置方面慎重考慮。答:從開環(huán)到閉環(huán)開環(huán)多輸入多輸出(mimo)的框圖,如圖。 3,代表手動控制的過程。操作計(jì)算的tir和監(jiān)控每個革命弓的角位置。當(dāng)y接近指定的限制,操作員設(shè)置bt的比例為y然后按下一個按鈕(bp)的整頓部分。彎曲定時(shí)器創(chuàng)建的bp觸發(fā)脈沖,這一事件迫使一部分有一段時(shí)間的具體稅率。活動結(jié)束后,部分需要一個新的速度和進(jìn)程延續(xù)。因此,y“是一個分段連續(xù)函數(shù)的時(shí)間。在這個過程中運(yùn)營商的參與,是塊圖作為代表。 圖3、開

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