## Bilgisayar yardımı ile step motorun hareket kontrolu 1997
Taştan, Latif
##### Yayınevi
Fen Bilimleri Enstitüsü
##### Özet
Step motorlar, girişi dijital sinyal olan ve çıkışı, her dijital sinyale karşılık artımsal dönme olan motorlardır. Günümüzde, sanayinin bir çok kesiminde; step motorlar konum ve hız kontrolü için kullanılmaktadır. Örneğin; floppy disk sürücülerinde, X-Y ploter'larda, nümerik kontrollü işleme tezgahlarında, robot sanayinde, motor kontrolü...vs alanlarda step motorlar kullanılmaktadır. Step motorları moment üretimi prensibine göre üç ayrı sınıfta toplayabiliriz. Bunlar,değişken reluktanslı motorlar (VR), daimi mıknatıslı motorlar (PM) ve hibrid step motorlar olarak isimlendirilirler. Step motorlar; iki, üç veya dört fazlı olabilirler. Faz sayısı motorun konstrüksiyonuna göre değişir. Step motorlar, uyan akımı altında stabil pozisyonda iken, tutabilecekleri maximum momenti taşırlar. Bu moment tutma moment (holding torque) olarak bilinir. Step motorlar, bilgisayar kontrol ünitesinin girişine uygulanan her puis (sinyal) için, motor yapısına bağlı olarak, step açısı kadar dönerler. Motorun bir devrine karşılık gelen step sayısına da step sayısı ismi verilir. Step sayısı, step motorlarda 2 ile 1000 arasında değişebilir. Bu tez çalışmasında kullanılan step motorun step açısı 1.8° olup, bir devirdeki toplam step sayısı da 200 step/devir ' dir. Motordaki frekans birimi, saniyedeki puis sayısı olarak verilir. Yani saniyedeki dönme sayısı yerine, step motorlarda saniyedeki puis sayısı ifadesi kullanılır. Step motorlarda önemli olan bir diğer problem de, motorun minimum zamanda istenilen referans hıza erişmesidir. Bunun için bu çalışmada iki yöntem kullanılmıştır. Bunlardan bir tanesi lineer ivmelenme, diğeri ise sinusoidal ivmelenmedir. Motorun ideal hız profili şekil 4.1'deki gibi lineer veya şekil 4.2' deki gibi sinusoidal olabilir. Bu hız profillerine göre diyagram üç bölgeye ayrılmıştır. İvmelenme bölgesi, sabit hızda çalışma bölgesi ve frenleme bölgesidir. İvmelenme ve frenleme zaman dilimleri birbirlerine eşit alınmışlardır. tn zaman diliminde gerçekleşen bu profile, çevrim ismi verilir. Bir çevrim boyunca motorun toplam dönme miktarından da, o çevrim için kaç adet puis gerektiği denklem (4.4) veya denklem (4.14) vasıtasıyla hesaplanır.
The step motor, also called the stepper motor or stepping motor, converts digital signals into fixed mechanical increments of motion. It is a synchronous motor such that the rotor rotates a spesific number of degrees (such as 0.9°, 1.8°, 3.6°, 7.5°, 15°, 30°, 45°, or 90°, among many other possible angles) for each pulse input given to the step-motor system. Thus, the step motor is used primarly for getting incremental motions. Because step motors are digital device, they can be easily incorporated into digital systems. An advantage is that by use of the step motor an accurate open- loop control of position or velocity is possible. That is, with a step motor, the closed loop control scheme is not required to make the output follow the input command. (An open loop control scheme is always simpler than closed loop control scheme.) Obviously, this is a convenient feature if the closed loop control of position (or velocity) using a dc motor is difficult or expensive, such as in the case involving the feedback of position (or velocity) signal in three-dimensional space. Also, in the step motor system, frequent start, stop, and reversal of motion are possible. Figure 1 shows a schematic diagram of a step motor system. The step motor must always be driven by an electronic driving unit, which includes an external drive logic circuit and power switch. External driving units are sometimes called translators. That is, the translator is an electronic control device that receives a command input in the form of a pulse and converts that pulse into appropriate switching of the drive module power translators to move the motor shaft one step angle. A microprocessor- based programmable motion controller that contains the translator, digital pulse generator, and the appropriate logic to control speed and distance, and to perform other programmable functions is known as an indexer. In figure 1, the command signal (a pulse train) is given to the input of the electronic diriving unit. The driving unit delivers appropriate currents to the stator windings of the step motor so as to make the axis of the air gap field switch arround as the input pulses are given to the input terminal. If the pulse rate (number of pulse per second) and load inertia are within designated limits, then the rotor rotates due to the reluctance torque or the permanent magnet torque, depending on the construction of the step motor. A dc voltage source is required to supply necessary power to the electronic driving unit. XI When no pulse is applied to the input, the rotor of the step motor tends to stay at the stabil position. (This means that the step motor acts as a hold device.) In the presence of distrubances, the motor exhibits resistance to the rotation caused by external torques. I I I I I I J INPUT PULSES DC POWER SUPPLY ELEKTRONIC DRIVER CIRCUIT OUTPUT (ANGULAR INCREMENT) STEP MOTOR Figure 1. Schematic diagram of a step motor system Having a high torque-to-inertia ratio, the step motor has good start and stop characteristics. If a pulse train whose pulse rate increases within a certain specified range is applied to a step motor at rest, it will start to rotate and synchronize with the input pulse rate. If there is any change in the pulse rate, the electronic driving unit (translator) changes the motor speed to correspond to the changed pulse rate. Thus the speed of the step motor becomes proportional to the pulse rate. Hence a wide range of speed control is possible by varying the pulse rate. The chief characteristics of the step motor are that the time constants involved are small, it is mechanically rugged because it is a brushless dc motor and there is no friction except at the bearings, and it gives maintenance-free operation for a long time. The step motor is very dependable and very accurate. The applications of step motors are limited to situations where high power is not required. The power ratings of step motors range from microwatts to several kilowatts. The speed that ordinary step motors can follow is up to approximately 1200 pulse per second. Some step motors, howower, can follow much higher speeds. XH The angular positional error induced by the step motor is equal to its final angular positional accuracy. Normally, such accuracy is within a few percent of the last step taken. The error is npncumulative. That is, the final angular position is within a few percent of the final step position, regardless of how many steps are taken. Step motors may be classified according to the principle of generating torques as follows: a. Variable reluctance type (VR type) b. Permanent magnet type (PM type) c. Hybrid (hybrid of VR and PM types) Hybrid-type step motors are frequently included as members of the permanent-magnet type of step motors. The step motor used in this application is hybrid step motor. Figure 2. Schematic structure of a stepping motor X1U Specifications of the step motor used are given below. Another important problem of controlling stepping motor is that the step motor can accelerate in a minimum time without losing pulse. In this application, the minimum time to reach to reference angular speed of 5000 rpm is 0.3 second as experimental and is calculated for different speeds as linear. (For example, minimum acceleration time is 0.15 second for angular speed of 2500 rpm). «(t) rom tp-1 \ tP tk-1 tm-1 tm tn Figure 3. Angular speed-time diagram for linear acceleration As seen from the graph above, there are three regions in the speed profile. In the first region, the step motor is accelerated. In this situation, equation of angular speed is calculated as below. co(t) = CO m t fm " 9s t (1) XIV When a pulse is applied to the step motor input, the step motor rotates only one step angle. This means that the hatched region between tk and tk-1 is equal to one step angle. î tk-1 tk-1 la V ©m.m (3) To accelerate to the reference angular speed in ta (ta=tm) second is required m pulses. This is calculated as below. -^ (4, When tk is calculated step by step, we obtain time intervals for each pulses. t1 = " V ©m t2=V2-t., t3=V3-t1 2ta-9s (5) tm = VS-t1 = | m 2-m.ta-9s (6) In the second region of speed profile, angular speed is constant so that acceleration is equal to zero. Time intervals are constant and are calculated as below. tp-Vi = f~= constant (7) XV Acceleration and decelaration are same. For tn second, total pulses is co. mtot=-^L(ta+t0) (8) Total rotation of step motor is (9) As a second alternative, It can be used sinusoidal acceleration modelling instead of lineer acceleration modelling because we can get more smooth acceleration to reach reference angular speed. oîm - tp tl f tk tin / tp-1 tn tk-1 Figure 4. Angular speed-time diagram for sinusoidal acceleration As seen from the graph above, acceleration function is given as, m. sin(-. t) = a)m. sin(cok. t) (10) ®k = 2t« Like as in linear acceleration graph, the hathced area between tk and tk-1 is equal to one step angle. XVI J ct)(t). dt = J com. sin(cok. t). dt = - -. [cos(cok. tk ) - cos(cok. tk-1 )] = 6S (11) k-1 tk_i o:)k tk-1 tk-1 cos(cok -tk) = cos(cok -tk_i)-0s cos(cok tk)= C cok CO m (12) As finally, time intervals for sinusoidal acceleration are calculated as, 1. _ i Vl^
##### Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Sosyal Bilimler Enstitüsü, 1997
##### Anahtar kelimeler
Adım motoru, Bilgisayar destekli denetim, Step motors, Computer aided control