關(guān)于步進電機與單片機英語原文

1、LIYU CAO and HOWARD M. SCHWARTZDepartment of Systems and Computer Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada(Received: 18 February 1998; accepted: 1 December 1998) Abstract. novel approach i.o ar.filyzir.K instability in permanent-magnet stepper motors is pre

2、sented. It is shown that there are two kinds of unstable phenomena in this kind of motor: mid-frequency oscillation and high-frequency instability. Nonlinear bifurcation theory is used to illustrate the relationship between local instability and midfrequency oscillatory motion. novel analysis is pre

3、sented Lo analyze the loss of synchroni stti phenomenon, which is identified as high frequency instability. The concepts of separa rices and at rac tors i phase-space a re used o derive a quantity to evaluate the high-frequency instability. By using this quant i ty one can eas iy est i mate the stab

4、 i1i Ly for h i gh supply frequenc i es. Furthermore, a stabilization method is presented. generalized approach to analyze the stabi1izaLion problem based on feedback theory is given. It is shown that the mid-frequency stabilityand the high-frequency stability can be improved by state feedback. Keyw

5、ords: Stepper motors, instability, nonlinearity, state feedback. IntroductionStepper motors are electromagnetic incremental-motion devices which convert digital pulse inputs to analog angle outputs. Their inherent stepping ability allows for accurate position control without feedback. That is, they

6、can track any step position in open-loop mode, consequently nofeedback is needed to implement position control. Stepper motors deliver higher peak torque per unit weight than DC motors; in addition, they are brushless machines and therefore require less maintenance. All of those properties have made

7、 stepper motors a very attractive selection in many position and speed control systems, such as in computer hard disk drivers and printers, XY-tables, robot manipulators, etc.Although stepper motors have many salient properties, they suffer from an oscillation or unstable phenomenon. This phenomenon

8、 severely restricts their open-loop dynamic performance and applicable area where high speed operation is needed. The oscillation usually occurs at stepping rates lower than 1000 pulse/s, and has been recognized as a mid-frequency instability or local instability 1, or a dynamic instability 2. In ad

9、dition, there is another kind of unstable phenomenon in stepper motors, that is, the motors usually lose synchronism at higher stepping rates, even though load torque is less than their pullout torque. This phenomenon is identified as high-frequency instability in this paper, because it appears at m

10、uch higher frequencies than the frequencies at which the mid-frequency oscillation occurs. The high-frequency instability has not been recognized as widely as mid-frequency instability, and there is not yet a method to evaluate it.Mid-frequency oscillation has been recognized widely for a very long

11、time, however, complete understanding of it has not been well established. This can be attributed to the nonlinearity that dominates the oscillation phenomenon and is quite difficult to deal with. 384 L. Cao and H. M. SchwartzMost researchers have analyzed it based on a linearized model l. Although

12、in many cases, this kind of treatments is valid or useful, a treatment based on nonlinear theory is needed in order to give a better description on this complex phenomenon. For example, based on a linearized model one can only see that the motors turn to be locally unstable at some supply frequencie

13、s, which does not give much insight into the observed oscillatory phenomenon. In fact, the oscillation cannot be assessed unless one uses nonlinear theory.Therefore, it is significant to use developed mathematical theory on nonlinear dynamics to handle the oscillation or instability. It is worth not

14、ing that Taft and Gauthier 3, and Taft and Harried 4 used mathematical concepts such as limit cycles and separatrices in the analysis of oscillatory and unstable phenomena, and obtained some very instructive insights into the socalled loss of synchronous phenomenon. Nevertheless, there is still a la

15、ck of a comprehensive mathematical analysis in this kind of studies. In this paper a novel mathematical analysis is developed to analyze the oscillations and instability in stepper motors.The first part of this paper discusses the stability analysis of stepper motors. Tt is shown that the mid-freque

16、ncy oscillation can be characterized as a bifurcation phenomenon (Hopf bifurcation) of nonlinear systems. One of contributions oT this paper is to relate the midfrequency oscillation to Hopf bifurcation, thereby, the existence of the oscillation is proved theoretically by Hopf theory. High-frequency

17、 instability is also discussed in detail, and a novel quantity is introduced to evaluate high-frequency stability. This quantity is very easyto calculate, and can be used as a criteria to predict the onset of the high-frequency instability. Experimental results on a real motor show the efficiency of

18、 this analytical tool.The second part of this paper discusses stabilizing control of stepper motors through feedback. Several authors have shown that by modulating the supply frequency 5, the midfrequencyinstability can be improved. In particular, Pickup and Russell 6, 7 have presented a detailed an

19、alysis on the frequency modulation method. In their analys is, Jacob i series was used to solve a ordi nary d i fferen t i al equali on, and a set of nonlinear algebraic equations had to be solved numerically. In addition, their analysis is undertaken for a two-phase motor, and therefore, their conc

20、lusions cannot applied directly to our situation, where a three phase motor will be considered. Here, we give a more elegant analysis for stabilizing stepper motors, where no complex mathematical manipulation is needed. In this analysis, a d q model of stepper motors is used. Because two-phase motor

21、s and three-phase motors have the same q- (/model and therefore, the analysis is valid for both two-phase and three-phase motors. Up to date, it is only recognized that the modulation method is needed to suppress the midfrequency oscillation. In this paper, it is shown that this method is not only v

22、alid to improve mid-frequency stability, but also effective to improve high-frequency stability. 2. Dynamic Model of Stepper MotorsThe stepper motor considered in this paper consists of a salient stator with two-phase or threephase windings, and a permanent-magnet rotor. A simplified schematic of a

23、three-phase motor with one pole-pair is shown in Figure 1. The stepper motor is usually fed by a voltage-source inverter, which is controlled by a sequence of pulses and produces square wave voltages Thismotor operates essentially on the same principle as that of synchronous motors. One of major ope

24、rating manner for stepper motors is that supplying voltage is kept constant and frequencyof pulses is changed at a very wide range. Under this operating condition, oscillation and instability problems usually arise.NSInverter Supply pulseNSInverter Supply command Figure 1. Schematic model of a three

25、-phase stepper motor. A mathematical model for a three-phase stepper motor is established using q- d framereference transformation. The voltage equations for three-phase windings are given by ， ，where R and L are the resistance and inductance of the phase windings, and M is the mutual inductance bet

26、ween the phase windings. _pma, _pmb and _pmc are the flux-linkages of thephases due to the permanent magnet, and can be assumed to be sinusoid functions of rotor position _ as followwhere Nis number of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that

27、 is, the flux-linkages are nonlinear functions of the rotor position.By using the q; (/transformation, the frame of reference is changed from the fixed phase axes to the axes moving with the rotor (refer to Figure 2). Transformation matrix from the a, b,c frame to the q,d frame is given by 8For exam

28、ple, voltages in the q; d reference are given byIn the a; b; c reference, only two variables are independent (ia C ib C ic D 0); therefore, the above transformation from three variables to two variables is allowable. Applying the abovetransformation to the voltage equations (l), the transferred volt

29、age equation in the q; d frame can be obtain as b q a c dFigure 2.a,h,c and d,q reference frame.where, and is the speed of the rotor.It can be shown that the motor s torque has the following form 2The equation of motion of the rotor is written aswhere Bf is the coefficient of viscous friction, and T

30、l represents load torque, which is assumed to be a constant in this paper.In order to constitute the complete state equation of the motor, we need another state variable that represents the position of the rotor. For this purpose the so called load angle _ 8 is usually used, which satisfies the foll

31、owing equationwhere /0 is steady-state speed of the motor. Equations (5), (7), and (8 constitute the statespace model of the motor, for which the input variables are the voltages and . As mentioned before, stepper motors are fed by an inverter, whose output voltages are not sinusoidal but instead ar

32、e square waves. However, because the nonsinusoida1 voltages do not change the oscillation feature and instability very much if compared to the sinusoidal case (as will be shown in Section 3, the oscillation is due to the nonlinearity of the motor), for the purposes of this paper we can assume the su

33、pply voltages are sinusoidal. Under this assumption, we can get vq and vd as followswhere is the maximum of the sine wave. With the above equation, we have changed the input voltages from a function of time to a function of state, and in this way we can represent the dynamics of the motor by a auton

34、omous system, as shown below. This will simplify the mathematical analysis.From Equations (5), (7), and (8), the state-space model of the motorcan be written in a matrix form as follows,(10)where is defined as the input, and is the supply frequency. The input matrix B is defined byThe matrix A is th

35、e linear part of F(.) and is given by represents the nonlinear part of F(.), and is given byThe input term u is independent of time, and therefore Equation (10) is autonomous.Thole are throe parameters in F(X,u) they are the supply frequency , the supply voltage magnitude and the load torque . These

36、 parameters govern the behaviour of the stepper motor. In practice, stepper motors are usually driven in such a way that the supply frequency is changed by the command pulse to control the motor s speed, while the supply voltage is kept constant. Therefore, we shall investigate the effect of paramet

37、er. 3. Bifurcation and Mid-Frequency Oscillation By setting , the equilibria of Equation (10) are given as , (11),(12) ,(13) , (14)where, n = 0,1,2.The term z is the transferred impedance given by , (15)Table1.The parameters of a three-phase stepper motorand is its phase angle defined by (16) Equati

38、ons (12) and (13) indicate that multiple equilibria exist, which means that these equilibria can never be globally stable. One can see that there are two groups of equilibria as shown in Equations (12) and (13). The first group represented by Equation (12) corresponds to the real operating condition

39、s of the motor. The second group represented by Equation (13) is always unstable and does not relate to the real operating conditions. In the following, we will concentrate on the equilibria represented by Equation (12).This application note illustrates the in-circuit programmability of the Atmel AT

40、89C51 Flash-based micro controller. Guidelines for the addition of in-circuit programmability to AT89C51 applications are presented along with an application example and the modifications to it required to support in-circuit programming. A method is then shown by which the AT89C51 microcontroller in

41、 the application can be reprogrammed remotely, over a commercial telephone line. The circuitry described in this application note supports five volt programming only, requiring the use of an AT89C51-XX-5. The standard AT89C51 requires 12 volts for programming. The software for this application may b

42、e obtained by downloading from AtmelsGeneral ConsiderationsCircuitry added to support AT89C51 incircuit programming should appear transparent to the application when programming is not taking place. EA/VPP must be held high during programming. In applications which do not utilize external program me

43、mory, this pin may be permanently strapped to VCC. Applications utilizing external program memory require that this pin be held low during normal operation. RST must be held active during programming. A means must be provided for overriding the application reset circuit, which typically asserts RST

44、only briefly after power is applied.PSEN must be held low during programming, but must not be driven during normal operation.ALE/PROG is pulsed low during programming, but must not be driven during normal operation.During programming, AT89C51 I/O ports are used for the application of mode select, ad

45、dresses and data, possibly requiring that the controller be isolated from the application circuitry. How this is done is application dependent and will be addressed here only in general terms.Port Used for InputDuring programming, the controller must be isolated from signals sourced by the applicati

46、on circuitry. A buffer with threestate outputs might be inserted between the application circuitry and the controller, with the buffer outputs three-stated when programming is enabled. Alternately, a multiplexer might be used to select between signal sources, with signals applied to the controller b

47、y either the application circuitry or the programmer circuitry.Port Used for OutputNo circuit changes are required if the application circuitry can tolerate the state changes which occur at the port during programming. If the prior state of the application circuitry must be maintained during program

48、ming, a latch might be inserted between the controller and the application circuitry. The latch is enabled during programming, preserving the state of the application circuitry. An Application ExampleThe AT89C51 application shown in Figure 1 is an implementation of a moving display. This application

49、 was selected for its simplicity and ability to show graphically the results of in-circuit reprogramming. The text to be displayed is programmed into the controller as part of its firmware, and cannot be changed without reprogramming the device.The displayed text is presented in one of two modes sel

50、ected by the four-position DIP switch. In the first mode, one character at a time enters the display from the right and moves quickly to the left through each element of the display to its final position in the assembled message. In the second mode, the message moves through the display, from right

51、to left, with the display acting as a window onto the message. This mode is familiar as the method often used in displays of stock prices.The output consists of four DL1414T, four-digit, 17-segment alphanumeric displays with integral decoders and drivers. This yields 16 total display elements, each

52、capable of displaying digits 0-9, the upper case alphabet, and some punctuation characters. The displayable character codes are ASCII 20H-5FH.A power-on reset circuit and a 6-MHz crystal oscillator complete the application. Neither external program memory nor external data memory is used.Modificatio

53、ns to the Application to SupportIn-Circuit Programming Figure 2 shows the application modified for in-circuit programming. It is assumed that the programmer, when inactive, will neither drive nor excessively load the application. Since the application does not use external program memory, EA/VPP on

54、the controller is connected to VCC. This meets the requirement for programming.The reset circuit has been modified by the addition of twotransistors, which allow RST on the controller to be forced high by the programmer.PSEN and ALE/PROG, unused in the basic application, areunder the direct control

55、of the programmer.Programming requires programmer access to all of the four AT89C51 I/O ports, as documented in the data sheet. The programmer is connected directly to those controller pins which are unused by the application, while access to pins used by the application requires special treatment,

56、as explained in the following paragraphs. The least significant four bits of the address generated by the programmer are multiplexed onto port one of the controller with the data from the DIP switch. Note that the four resistors added at the switch are not required in the basic application, since th

57、e AT89C51 provides internal pull-ups on port one.During the normal operation of the application, controller ports zero and two provide data and control signals (respectively) to the displays. During programming and program verification, the programmer asserts control of port zero and part of port tw

58、o. The programmer is connected to ports zero and two without buffering, since, when inactive, its presence does not affect the normal operation of the application.A transparent latch has been added between port two of the controller and the display control inputs. The latch holds the display control

59、 signals inactive during programming, which eliminates erratic operation of the displays due to programmer activity on ports zero and two. No isolation ofthe display data inputs is required, since data applied to the inputs is ignored when the control signals are inactive.The AT89C51 reset circuit,

60、input multiplexer and output latch are controlled by a single signal generated by the programmer. During programming, reset is asserted, the multiplexer switches inputs, and the latch freezes the display control lines.To ensure that the display control lines are in a known state before they are latc