【正文】 i n(n ps3mp2p1 ?????? ????? － ???dtd Here LS is the selfinductance of a stator winding, M is the coefficient of mutual inductance between the phases, Km is the torque/backemf constant (so that KM = Km/req is the force/backemf constant in the linear motor), RS the resistance of a stator winding, np is the number of pole pairs (or the number of rotor teeth for a stepper motor). If the phases were perfectly coupled, one would have M = 21 LS. The threephase to twophase transformations for currents and voltages are defined by ??????????????????????????????????3210 212121232302121132SSSsbsaiiiiii which transforms the original model into the equivalent model 外文翻譯（ 原 文） 5 busV2?)s i n(23)( ?? pmsaSsasas nKiRvdtdiML ???? )s i n(23)( ?? pmsaSsasbs nKiRvdtdiML ???? For a balanced threephase system assumed here, it follows that v0=(vs1+vs2+vs3)/ 3 =0, i0=(vs1+vs2+vs3)/ 3 =0 so that one obtains the twophase equivalent model given by sapeqsaSsa vnKiRdtdiL ???? )s i n( ?? sbpeqsbS vnKiRdtdi bL ???? )c os ( ?? Here L= Ls + M(≈23 Ls),Keq = 23 Km ia and ib are the equivalent currents in phases a and b, respectively. Letting Vbus denote the bus voltage into a threephase inverter. The maximum voltage out of the inverter is obtained when it is run in six step mode and the peak of the fundamental of the sixstep waveform is vmax = This is taken to be the maximum limit of the phase voltage. Finally, with i max, vmax denoting the limits of the phase currents and voltages of the threephase motor, the corresponding limits Imax,Vmax for the equivalent twophase motor are then The directquadrature or dq transformation is defined by where id, iq and vd, vq are the transformed currents and voltages, respectively in the dq (for direct and quadrature) reference frame. The definition of the dq reference system assumes that the daxis is aligned with the rotor,s magic axis when ? = that ???????????????????? sbsapp ppqd iinn nnii )c os ()s i n( )s i n()c os ( ?? ?? 外文翻譯（ 原 文） 6 ???????????????????? sbsapp ppqd vvnn nnvv )c os ()s i n( )s i n()c os ( ?? ?? when ? =0, the daxis is aligned the iaaxis which in turn is the same as the iS1axis. The statespace model in the dq coordinates is ???dtd (5) This model assumes that the rotor is smooth (nonsalient) and that the magics are linear. 3. Motor specifications The motor parameters are specified for a linear motor and are converted to an equivalent rotary motor. The linear motor parameters are stator inductance LS = , stator resistance RS = ? , coefficient of mutual inductance M = = , motor mass m = kg, force constant KM = , distance between poles dp = , np = 1 (no. of primary polepairs). The maximum dc bus voltage to the inverter is Vmax = 320V resulting in a peak fundamental waveform to the motor of vmax = Vma x= phase currents are limited to Imax = 10A (peak) and the maximum (linear) force put out by the motor is 320N. The radius of an equivalent rotary motor satisfies 2preq = np2dp ? req = . The torque constant of an equivalent threephase rotary motor is found from the linear force constant by setting Km = req KM = ()(32)Nm/A = and the moment of inertia is J =r2eqm =() =? 103kgm2. The parameters LS, M, RS, np are the same as for the linear motor. Here x = 0 for the linear motor corresponds to the magic axis of its rotor phase a being lined up with the magic axis of stator phase a and similarly for the equivalent rotary motor. The corresponding equivalent twophase parameters are then L = LS + M = , RS = ? , Keq = 23 Km=, Imax (continuous) = 23 imax =,Vmax= 23 vmax= linear force put out by this motor is F = Keq iq / req= 23 Km iq / req . 外文翻譯（ 原 文） 7 . Door model The door model is from the technical report of He [4] and is of the form dx/dt = Ax+bu y =Cx where A ? R8? 8 , b?R8 , C?R8? 8 . The values of the triple {A,b,C} are given in [4]. Here x1 is the door position, x2 is the door speed and the input u to the door is the linear force F = Keq iq / req put out by the motor. The state variables x1, x2 are the two measured/puted state variables so that the output matrix is simply ??????? 00000010 00000001C The mass of the door is denoted by Mc so that the total mass of the door/motor bination is Mc + m. The observability matrix ? ?765432 CACACACACACACAC has rank 4 while the controllability matrix ? ?b765432 AbAbAbAbAbAAbb has rank 5. However, A is stable. The control approach is to feed back x, ?(? = x/req,ω=?/req) treating the transfer function from input u = F to x as a double integrator. The resolution of the linear position feedback from the wall to the door control system is . The maximum door speed is ?max = 1m=s, the maximum acceleration is αmax = , and the jerk rate is limited to j max = distance traveled by each door is 555mm. . Standard controller 外文翻譯（ 原 文） 8 A straightforward way to do servo control of this motor for the standard controller in which there is one inverter for each motor is to choose the linear force as ))()()(( 0012 dtxxKxxKxvKMu t r e fr e fr e fr e fc ???????? ? dtiiKiiKv t qqr e fIqqr e fpq ? ???? 0 )()( dtiiKiiKv t ddr e fIddr e fpq ? ???? 0 )()( where the reference trajectories xref, vref, αref, iqref are as shown in Section and idref is typically taken to be zero [1–3]. 4. Two motors and one inverter The interest here is to control the motor using a single inverter and the approach to independently control the quadrature current in each motor which in turn requires leaving the direct currents uncontrolled. One approach to controlling two PM synchronous motors using one inverter would be to just control the two motors identically. Specifi