自動(dòng)化專業(yè)外文翻譯---步進(jìn)電機(jī)的振蕩、不穩(wěn)定以及控制(編輯修改稿)
2025-06-25 18:44 本頁(yè)面
【文章內(nèi)容簡(jiǎn)介】 n this paper consists of a salient stator with twophase or three phase windings, and a permanentmag rotor. A simplified schematic of a threephase motor with one polepair is shown in Figure 1. The stepper motor is usually fed by a voltagesource inverter, which is controlled by a sequence of pulses and produces squarewave 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 threephase stepper motor. A mathematical model for a threephase stepper motor is established using q–d frame reference transformation. The voltage equations for threephase windings are given by va = Ria + L*dia /dt ? M*dib/dt ? M*dic/dt + dλpma/dt , vb = Rib + L*dib/dt ? M*dia/dt ? M*dic/dt + dλpmb/dt , vc = Ric + L*dic/dt ? M*dia/dt ? M*dib/dt + dλpmc/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 fluxlinkages of the phases due to the permanent mag, and can be assumed to be sinusoid functions of rotor position _ as follow λpma = λ1 sin(Nθ), λpmb = λ1 sin(Nθ ? 2 /3), λpmc = λ1 sin(Nθ 2 /3), where N is number of rotor teeth. The nonlinearity emphasized in this paper is represented by the above equations, that is, the fluxlinkages are nonlinear functions 咸寧學(xué)院本科畢業(yè)論文（設(shè)計(jì)）：外文翻譯 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 + NL1idω + Nλ1ω, vd=Rid + L1*did/dt ? NL1iqω, (5) Figure 2. a, b, c and d, q reference frame. where L1 D L CM, and ! is the speed of the can be shown that the motor’s torque has the following form [2] T = 3/2Nλ1iq The equation of motion of the rotor is written as J*dω/dt = 3/2*Nλ1iq ? Bfω – Tl , 咸寧學(xué)院本科畢業(yè)論文（設(shè)計(jì)）：外文翻譯 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 purpose the so called load angle _ [8] is usually used, which satisfies the following equation Dδ/dt = ω?ω0 , where !0 is steadystate 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 nonsinusoidal 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
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