外文文献原稿和译文关于自动巡航消防下车的设计.docx

1、外文文献原稿和译文关于自动巡航消防下车的设计外文文献原稿和译文原 稿Oscillation,Instability,and Control of Stepper Motors Abstract: A novel approach to analyzing instability in permanent-magnet stepper motors is presented. It is shown that there are two kinds of unstable phenomena in this kind of motor: mid-frequency oscillation and

2、 high-frequency instability. Nonlinear bifurcation theory is used to illustrate the relationship between local instability and mid-frequency oscillatory motion. A novel analysis is presented to analyze the loss of synchronism phenomenon, which is identified as high-frequency instability. The concept

3、s of separatrices and attractors in phase-space are used to derive a quantity to evaluate the high-frequency instability. By using this quantity one can easily estimate the stability for high supply frequencies. Furthermore, a stabilization method is presented. A generalized approach to analyze the

4、stabilization problem based on feedback theory is given. It is shown that the mid-frequency stability and the high-frequency stability can be improved by state feedback. Keywords: Stepper motors; instability; nonlinearity; state feedback1. IntroductionStepper motors are electromagnetic incremental-m

5、otion 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 moto

6、rs 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 driver

7、s 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 oscill

8、ation usually occurs at stepping rates lower than 1000 pulse/s, and has been recognized as a mid-frequency instability or local instability , or a dynamic instability . In addition, there is another kind of unstable phenomenon in stepper motors, that is, the motors usually lose synchronism at higher

9、 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

10、 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

11、dominates the oscillation phenomenon and is quite difficult to deal with. Most researchers have analyzed it based on a linearized model . 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

12、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 theor

13、y.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 , and Taft and Harned used mathematical concepts such as limit cycles and separatrices in the analysis of oscillatory and unst

14、able 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

15、 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

16、 mid-frequency 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,

17、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 mo

18、dulating the supply frequency the mid-frequency.Instability can be improved. In particular, Pickup and Russell 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

19、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, wher

20、e no complex mathematical manipulation is needed. In this analysis, a dq model of stepper motors is used. Because two-phase motors and three-phase motors have the same qd model and therefore, the analysis is valid for both two-phase and three-phase motors. Up to date, it is only recognized that the

21、modulation method is needed to suppress the mid-frequency 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 MotorsThe stepper motor considered in this paper

22、 consists of a salient stator with two-phase or three phase 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 pr

23、oduces 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, oscil

24、lation 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 qd frame reference transformation. The voltage equations for three-phase windings are given byva = Ria + L*dia /dt M*dib/dt

25、 M*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 , (1)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 th

26、e phases due to the permanent magnet, and can be assumed to be sinusoid functions of rotor position _ as followpma = 1 sin(N),pmb = 1 sin(N ),pmc = 1 sin(N - ), (2)where N is number of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that is, the flux-lin

27、kages 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 (3)For example, voltages

28、 in the q; d reference are given by (4)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 equa

29、tion in the q; d frame 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 frame.where L1 D L CM, and ! is the speed of the rotor.It can be shown that the motors torque has the following form T = 3/2N1iq , (6) The equation of motion

30、of the rotor is written asJ*d/dt = 3/2*N1iq Bf Tl , (7)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 p

31、osition of the rotor. For this purpose the so called load angle is usually used, which satisfies the following equationD/dt = 0 , (8)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 v

32、q 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 followsvq = Vmcos(N) ,vd = Vmsin(N) , (9)