1、-The Stepper motor control circuit be based on Single chip microputerThe AT89C51 is a low-power, high-performance CMOS 8-bit microputer with 4K bytes of Flash programmable and erasable read only memory (PEROM). The device is manufactured using Atmels high-density nonvolatile memory technology and is

2、 patible with the industry-standard MCS-51 instruction set and pinout. The on-chip Flash allows the program memory to be reprogrammed in-system or by a conventional nonvolatile memory programmer. By bining a versatile 8-bit CPU with Flash on a monolithic chip, the Atmel AT89C51 is a powerful micropu

3、ter which provides a highly-fle*ible and cost-effective solution to many embedded control applications.Function characteristicThe AT89C51 provides the following standard features: 4K bytes of Flash, 128 bytes of RAM, 32 I/O lines, two 16-bit timer/counters, a five vector two-level interrupt architec

4、ture, a full duple* serial port, on-chip oscillator and clock circuitry. In addition, the AT89C51 is designed with static logic for operation down to zero frequency and supports two software selectable power saving modes. The Idle Mode stops the CPU while allowing the RAM, timer/counters, serial por

5、t and interrupt system to continue functioning. The Power-down Mode saves the RAM contents but freezes the oscillator disabling all other chip functions until the ne*t hardware reset.Pin DescriptionVCC：Supply voltage.GND：Ground.Port 0：Port 0 is an 8-bit open-drain bi-directional I/O port. As an outp

6、ut port, each pin can sink eight TTL inputs. When 1s are written to port 0 pins, the pins can be used as highimpedance inputs.Port 0 may also be configured to be the multiple*ed loworder address/data bus during accesses to e*ternal program and data memory. In this mode P0 has internal pullups.Port 0

7、 also receives the code bytes during Flash programming,and outputs the code bytes during programverification. E*ternal pullups are required during programverification.Port 1Port 1 is an 8-bit bi-directional I/O port with internal pullups.ThePort 1 output buffers can sink/source four TTL inputs.When

8、1s are written to Port 1 pins they are pulled high by the internal pullups and can be used as inputs. As inputs,Port 1 pins that are e*ternally being pulled low will source current (IIL) because of the internal pullups.Port 1 also receives the low-order address bytes during Flash programming and ver

9、ification.Port 2Port 2 is an 8-bit bi-directional I/O port with internal pullups.ThePort 2 output buffers can sink/source four TTL inputs.When 1s are written to Port 2 pins they are pulled high by the internal pullups and can be used as inputs. As inputs,Port 2 pins that are e*ternally being pulled

10、low will source current, because of the internal pullups.Port 2 emits the high-order address byte during fetches from e*ternal program memory and during accesses to e*ternal data memory that use 16-bit addresses. In this application, it uses strong internal pullupswhen emitting 1s. During accesses t

11、o e*ternal data memory that use 8-bit addresses, Port 2 emits the contents of the P2 Special Function Register.Port 2 also receives the high-order address bits and some control signals during Flash programming and verification.Port 3Port 3 is an 8-bit bi-directional I/O port with internal pullups.Th

12、ePort 3 output buffers can sink/source four TTL inputs.When 1s are written to Port 3 pins they are pulled high by the internal pullups and can be used as inputs. As inputs,Port 3 pins that are e*ternally being pulled low will source current (IIL) because of the pullups.Port 3 also serves the functio

13、ns of various special features of the AT89C51 as listed below:Port 3 also receives some control signals for Flash programming and verification.RSTReset input. A high on this pin for two machine cycles while the oscillator is running resets the device.ALE/PROGAddress Latch Enable output pulse for lat

14、ching the low byte of the address during accesses to e*ternal memory. This pin is also the program pulse input (PROG) during Flash programming.In normal operation ALE is emitted at a constant rate of 1/6 the oscillator frequency, and may be used for e*ternal timing or clocking purposes. Note, howeve

15、r, that one ALE pulse is skipped during each access to e*ternal Data Memory.If desired, ALE operation can be disabled by setting bit 0 of SFR location 8EH. With the bit set, ALE is active only during a MOV* or MOVC instruction. Otherwise, the pin is weakly pulled high. Setting the ALE-disable bit ha

16、s no effect if the microcontroller is in e*ternal e*ecution mode.PSENProgram Store Enable is the read strobe to e*ternal program memory.When the AT89C51 is e*ecuting code from e*ternal program memory, PSEN is activated twice each machine cycle, e*cept that two PSEN activations are skipped during eac

17、h access to e*ternal data memory.EA/VPPE*ternal Access Enable. EA must be strapped to GND in order to enable the device to fetch code from e*ternal program memory locations starting at 0000H up to FFFFH. Note, however, that if lock bit 1 is programmed, EA will be internally latched on reset.EA shoul

18、d be strapped to VCC for internal program e*ecutions.This pin also receives the 12-volt programming enable voltage(VPP) during Flash programming, for parts that require12-volt VPP.*TAL1Input to the inverting oscillator amplifier and input to the internal clock operating circuit.*TAL2Output from the

19、inverting oscillator amplifier.Oscillator Characteristics*TAL1 and *TAL2 are the input and output, respectively,of an inverting amplifier which can be configured for use as an on-chip oscillator, as shown in Figure 1.Either a quartz crystal or ceramic resonator may be used. To drive the device from

20、an e*ternal clock source, *TAL2 should be left unconnected while *TAL1 is driven as shown in Figure 2.There are no requirements on the duty cycle of the e*ternal clock signal, since the input to the internal clocking circuitry is through a divide-by-two flip-flop, but minimum and ma*imum voltage hig

21、h and low time specifications must be observed.Figure 1. Oscillator Connections Figure 2. E*ternal Clock Drive ConfigurationIdle ModeIn idle mode, the CPU puts itself to sleep while all the onchip peripherals remain active. The mode is invoked by software. The content of the on-chip RAM and all the

22、special functions registers remain unchanged during this mode. The idle mode can be terminated by any enabled interrupt or by a hardware reset.It should be noted that when idle is terminated by a hard ware reset, the device normally resumes program e*ecution,from where it left off, up to two machine

23、 cycles before the internal reset algorithm takes control. On-chip hardware inhibits access to internal RAM in this event, but access to the port pins is not inhibited. To eliminate the possibility of an une*pected write to a port pin when Idle is terminated by reset, the instruction following the o

24、ne that invokes Idle should not be one that writes to a port pin or to e*ternal memory.Power-down ModeIn the power-down mode, the oscillator is stopped, and the instruction that invokes power-down is the last instruction e*ecuted. The on-chip RAM and Special Function Registers retain their values un

25、til the power-down mode is terminated. The only e*it from power-down is a hardware reset. Reset redefines the SFRs but does not change the on-chip RAM. The reset should not be activated before VCC is restored to its normal operating level and must be held active long enough to allow the oscillator t

26、o restart and stabilize.Program Memory Lock BitsOn the chip are three lock bits which can be left unprogrammed (U) or can be programmed (P) to obtain the additional features listed in the table below.When lock bit 1 is programmed, the logic level at the EA pin is sampled and latched during reset. If

27、 the device is powered up without a reset, the latch initializes to a random value, and holds that value until reset is activated. It is necessary that the latched value of EA be in agreement with the current logic level at that pin in order for the device to function properly.IntroductionStepper mo

28、tors are electromagnetic incremental-motion devices which convert digital pulseinputs to analog angle outputs. Their inherent stepping ability allows for accurate positioncontrol without feedback. That is, they can track any step position in open-loop mode, consequentlyno feedback is needed to imple

29、ment position control. Stepper motors deliver higherpeak torque per unit weight than DC motors; in addition, they are brushless machines andtherefore require less maintenance. All of these properties have made stepper motors a veryattractive selection in many position and speed control systems, such

30、 as in puter hard diskdrivers and printers, *Y-tables, robot manipulators, etc.Although stepper motors have many salient properties, they suffer from an oscillation orunstable phenomenon. This phenomenon severely restricts their open-loop dynamic performanceand applicable area where high speed opera

31、tion is needed. The oscillation usuallyoccurs at stepping rates lower than 1000 pulse/s, and has been recognized as a mid-frequencyinstability or local instability 1, or a dynamic instability 2. In addition, there is anotherkind of unstable phenomenon in stepper motors, that is, the motors usually l

32、ose synchronismat higher stepping rates, even though load torque is less than their pull-out torque. This phenomenonis identified as high-frequency instability in this paper, because it appears at muchhigher frequencies than the frequencies at which the mid-frequency oscillation occurs. Thehigh-freq

33、uency 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 time, however, aplete understanding of it has not been well established. This can be attributed to thenon

34、linearity 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 1. Although in many cases,this kind of treatments is valid or useful, a treatment based on nonlinear theory is neededin o

35、rder to give a better description on this ple* phenomenon. For e*ample, based on alinearized model one can only see that the motors turn to be locally unstable at some supplyfrequencies, which does not give much insight into the observed oscillatory phenomenon. Infact, the oscillation cannot be asse

36、ssed unless one uses nonlinear theory.Therefore, it is significant to use developed mathematical theory on nonlinear dynamics tohandle the oscillation or instability. It is worth noting that Taft and Gauthier 3, and Taft andHarned 4 used mathematical concepts such as limit cycles and separatrices in

37、 the analysis ofoscillatory and unstable phenomena, and obtained some very instructive insights into the socalledloss of synchronous phenomenon. Nevertheless, there is still a lack of a prehensivemathematical analysis in this kind of studies. In this paper a novel mathematical analysis isdeveloped t

38、o analyze the oscillations and instability in stepper motors.The first part of this paper discusses the stability analysis of stepper motors. It is shownthat the mid-frequency oscillation can be characterized as a bifurcation phenomenon (Hopfbifurcation) of nonlinear systems. One of contributions of

39、 this paper is to relate the midfrequencyoscillation to Hopfbifurcation, thereby, the e*istence of the oscillation is provedtheoretically by Hopf theory. High-frequency instability is also discussed in detail, and anovel quantity is introduced to evaluate high-frequency stability. This quantity is v

40、ery easyto calculate, and can be used as a criteria to predict the onset of the high-frequency instability.E*perimental results on a real motor show the efficiency of this analytical tool.The second part of this paper discusses stabilizing control of stepper motors throughfeedback. Several authors h

41、ave shown that by modulating the supply frequency 5, the midfrequencyinstability can be improved. In particular, Pickup and Russell 6, 7 have presenteda detailed analysis on the frequency modulation method. In their analysis, Jacobi series wasused to solve a ordinary differential equation, and a set

42、 of nonlinear algebraic equations hadto be solved numerically. In addition, their analysis is undertaken for a two-phase motor,and therefore, their conclusions cannot applied directly to our situation, where a three-phasemotor will be considered. Here, we give a more elegant analysis for stabilizing

43、 stepper motors,where no ple* mathematical manipulation is needed. In this analysis, a dq model ofstepper motors is used. Because two-phase motors and three-phase motors have the sameqd model and therefore, the analysis is valid for both two-phase and three-phase motors.Up to date, it is only recogn

44、ized that the modulation method is needed to suppress the midfrequencyoscillation. In this paper, it is shown that this method is not only valid to improvemid-frequency stability, but also effective to improve high-frequencystability.2. Dynamic Model of Stepper MotorsThe stepper motor considered in

45、this paper consists of a salient stator with two-phase or threephasewindings, and apermanent-magnet rotor. A simplified schematic of a three-phase motorwith one pole-pair is shown in Figure 1. The stepper motor is usually fed by a voltage-sourceinverter, which is controlled by a sequence of pulses a

46、nd produces square-wave voltages. Thismotor operates essentially on the same principle as that of synchronous motors. One of majoroperating 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, osc

47、illation andinstability problems usually arise.Figure 1. Schematic model of a three-phase stepper motorA mathematical model for a three-phase stepper motor is established using qd framereference transformation. The voltage equations for three-phase windings are given byva= Ria+ L*dia /dt M*dib/dt M*

48、dic/dt + dpma/dt ,vb= Rib+ L*dib/dt M*dia/dt M*dic/dt + dpmb/dt ,vc= Ric+ L*dic/dt M*dia/dt M*dib/dt + dpmc/dt ,where R and L are the resistance and inductance of the phase windings, and M is the mutual inductance between the phase windings. _pma, _pmb and _pmc are the flu*-linkages of thephases due

49、 to the permanent magnet, and can be assumed to be sinusoid functions of rotor position _ as followpma= 1 sin(N),pmb= 1 sin(N 2/3),pmc= 1 sin(N - 2/3),where N is number of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that is, the flu*-linkages are non

50、linear functions of the rotor position.By using the q; d transformation, the frame of reference is changed from the fi*ed phase a*es to the a*es moving with the rotor (refer to Figure 2). Transformation matri* from the a; b; c frame to the q; d frame is given by 8For e*ample, voltages in the q; d re

51、ference 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 (1), the transferred voltage equation in the q; d fra

52、me can be obtained asvq= Riq+ L1*diq/dt + NL1id + N1,vd=Rid + L1*did/dt NL1iq, (5)Figure 2. a, b, c and d, q reference framewhere L1 D L CM, and ! is the speed of the rotor.It can be shown that the motors torque has the following form 2T = 3/2N1iqThe equation of motion of the rotor is written asJ*d/

53、dt = 3/2*N1iq Bf Tl ,where Bf is the coefficient of viscous friction, and Tl represents load torque, which is assumed to be a constant in this paper.In order to constitute the plete state equation of the motor, we need another state variable that represents the position of the rotor. For this purpos

54、e the so called load angle _ 8 is usually used, which satisfies the following equationD/dt = 0 ,where !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 vq and vd. As mentioned before, steppe

55、r motors are fed by an inverter, whose output voltages are not sinusoidal but instead are square waves. However, because the non-sinusoidal voltages do not change the oscillation feature and instability very much if pared to the sinusoidal case (as will be shown in Section 3, the oscillation is due

56、to the nonlinearity of the motor), for the purposes of this paper we can assume the supply voltages are sinusoidal. Under this assumption, we can get vq and vd as followsvq = Vmcos(N) ,vd = Vmsin(N) ,where Vm is the ma*imum of the sine wave. With the above equation, we have changed the input voltage

57、s from a function of time to a function of state, and in this way we can represent the dynamics of the motor by a autonomous system, as shown below. This will simplify the mathematical analysis.From Equations (5), (7), and (8), the state-space model of the motor can be written in a matri* form as fo

58、llows = F(*,u) = A* + Fn(*) + Bu , (10)where * D Tiq id ! _UT , u D T!1 TlUT is defined as the input, and !1 D N!0 is the supply frequency. The input matri* B is defined byThe matri* A is the linear part of F._/, and is given byFn.*/ represents the nonlinear part of F._/, and is given byThe input term u is independent of time, and therefore Equation (10) is autonomous.There are three parameters in F.*;u/, they are the supply frequency !1, the supply voltage magnitude Vm and the load torque Tl . These parameters govern the behaviour of the stepper motor. I