基于单片机的步进电机电路控制设计英文文献及翻译

The Stepper motor control circuit be based on Single chip microcomputer The AT89C51 is a low power high performance CMOS 8 bit microcomputer with 4K bytes of Flash programmable and erasable read only memory PEROM The device is manufactured using Atmel s high density nonvolatile memory technology and is compatible 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 combining a versatile 8 bit CPU with Flash on a monolithic chip the Atmel AT89C51 is a powerful microcomputer which provides a highly flexible and cost effective solution to many embedded control applications Function characteristic The 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 architecture a full duplex 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 port 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 next hardware reset Pin Description VCC Supply voltage GND Ground Port 0 Port 0 is an 8 bit open drain bi directional I O port As an output 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 multiplexed loworder address data bus during accesses to external program and data memory In this mode P0 has internal pullups Port 0 also receives the code bytes during Flash programming and outputs the code bytes during programverification External pullups are required during programverification Port 1 Port 1 is an 8 bit bi directional I O port with internal pullups The Port 1 output buffers can sink source four TTL inputs When 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 externally 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 verification Port 2 Port 2 is an 8 bit bi directional I O port with internal pullups The Port 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 externally being pulled low will source current because of the internal pullups Port 2 emits the high order address byte during fetches from external program memory and during accesses to external data memory that use 16 bit addresses In this application it uses strong internal pullupswhen emitting 1s During accesses to external 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 3 Port 3 is an 8 bit bi directional I O port with internal pullups The Port 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 externally being pulled low will source current IIL because of the pullups Port 3 also serves the functions of various special features of the AT89C51 as listed below Port 3 also receives some control signals for Flash programming and verification RST Reset input A high on this pin for two machine cycles while the oscillator is running resets the device ALE PROG Address Latch Enable output pulse for latching the low byte of the address during accesses to external 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 external timing or clocking purposes Note however that one ALE pulse is skipped during each access to external 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 MOVX or MOVC instruction Otherwise the pin is weakly pulled high Setting the ALE disable bit has no effect if the microcontroller is in external execution mode PSEN Program Store Enable is the read strobe to external program memory When the AT89C51 is executing code from external program memory PSEN is activated twice each machine cycle except that two PSEN activations are skipped during each access to external data memory EA VPP External Access Enable EA must be strapped to GND in order to enable the device to fetch code from external 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 should be strapped to VCC for internal program executions This pin also receives the 12 volt programming enable voltage VPP during Flash programming for parts that require12 volt VPP XTAL1 Input to the inverting oscillator amplifier and input to the internal clock operating circuit XTAL2 Output from the inverting oscillator amplifier Oscillator Characteristics XTAL1 and XTAL2 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 an external clock source XTAL2 should be left unconnected while XTAL1 is driven as shown in Figure 2 There are no requirements on the duty cycle of the external clock signal since the input to the internal clocking circuitry is through a divide by two flip flop but minimum and maximum voltage high and low time specifications must be observed Figure 1 Oscillator Connections Figure 2 External Clock Drive Configuration Idle Mode In 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 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 execution from where it left off up to two machine 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 unexpected write to a port pin when Idle is terminated by reset the instruction following the one that invokes Idle should not be one that writes to a port pin or to external memory Power down Mode In the power down mode the oscillator is stopped and the instruction that invokes power down is the last instruction executed The on chip RAM and Special Function Registers retain their values until the power down mode is terminated The only exit 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 to restart and stabilize Program Memory Lock Bits On 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 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 IntroductionIntroduction Stepper 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 can track any step position in open loop mode consequently no feedback 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 these properties have made 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 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 addition 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 pull out torque This phenomenon is identified as high frequency instability in this paper because it appears at much 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 time however a 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 Schwartz Most 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 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 frequencies 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 noting that Taft and Gauthier 3 and Taft and Harned 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 lack 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 It is shown that the mid frequency oscillation can be characterized as a bifurcation phenomenon Hopf bifurcation of nonlinear systems One of contributions of 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 instability is also discussed in detail and a novel quantity is introduced to evaluate high frequency stability This quantity is very easy to 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 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 midfrequency instability can be improved In particular Pickup and Russell 6 7 have presented a detailed analysis on the frequency modulation method In their analysis Jacobi series was used to solve a ordinary differential equation 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 conclusions 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 motors and three phase motors have the same q d 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 valid to improve mid frequency stability but also effective to improve high frequency stability 2 Dynamic Model of Stepper Motors The 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 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 This motor operates essentially on the same principle as that of synchronous motors One of major operating manner for stepper motors is that supplying voltage is kept constant and frequency of pulses is changed at a very wide range Under this operating condition oscillation and instability problems usually arise Figure 1 Schematic model of a three 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 va Ria L dia dt M dib dt M dic dt d pma dt vb Rib L dib dt M dia dt M dic dt d pmb dt vc Ric L dic dt M dia dt M dib dt d pmc 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 flux linkages of the phases due to the permanent magnet and can be assumed to be sinusoid functions of rotor position as follow pma 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 flux linkages are nonlinear functions of the rotor position By using the q d 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 8 For example voltages in the q d reference are given by In 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 above transformation to the voltage equations 1 the transferred voltage equation in the q d frame can be obtained as vq Riq L1 diq dt NL1id N 1 vd Rid L1 did dt NL1iq 5 Figure 2 a b c and d q reference frame where L1 D L CM and is the speed of the rotor It can be shown that the motor s torque has the following form 2 T 3 2N 1iq The equation of motion of the rotor is written as J d dt 3 2 N 1iq 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 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 following equation D 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 stepper 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 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 supply voltages are sinusoidal Under this assumption we can get vq and vd as follows vq Vmcos N vd Vmsin N where Vm 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 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 matrix form as follows F X u AX Fn X Bu 10 where X 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 matrix B is defined by The matrix A is the linear part of F and is given by Fn X represents the nonlinear part of F and is given by The input term u is independent of time and therefore Equation 10 is autonomous There are three parameters in F X 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 In practice stepper motors are usually driven in such a way that the supply frequency 1 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 parameter 1 3 Bifurcation and Mid Frequency Oscillation By setting D 0 the equilibria of Equation 10 are given as and is its phase angle defined by arctan 1L1 R 16 Equations 12 and 13 indicate that multiple equilibria exist which means that these equilibria can never be globally stable One can see that ther