Parameter Value Voltage 310V dc Speed 4600 rpm Torque 2.2 Nm Stall current 4.52 A Poles number 4 Voltage constant (Ke) 51 V [krpm.sup.-1] Torque constant
(Kt) 0.49 Nm [A.sup.-1] Ph/ph resistance 3.07 [OMEGA] Ph/ph inductance 6.57 mH Moment of inertia (Jm) 1.8 kg [cm.sup.2] Encoder 2000 ppr Table 2.
[beta] - Dynamic frictional torque constant
(Nm x s x [rad.sup.-1])
PMSM torque constant
is defined as [k.sub.t] = c[PSI]PM.
where [T.sub.e] denotes the generated electromagnetic torque, [i.sub.a], [i.sub.b], and [i.sub.c] denote the phase currents, [k.sub.t] is the phase torque constant
, and [[theta].sub.r] denotes the rotor electrical angle.
To calculate this current, divide the desired torque by the torque constant
(Kt) of the motor.
where R is the motor winding resistance, [L.sub.d] and [L.sub.q] are the motor winding inductances, p is the number of pole-pairs, [k.sub.t] is the motor torque constant
, [lambda] is the rotor flux linkage, J is the total drive inertia, [i.sub.d], [i.sub.q] and [u.sub.d], [u.sub.q] are the motor current and voltage components, [[omega].sub.r] and [[omega].sub.r] are the rotor speed and position, [T.sub.l] is the load torque, [B.sub.[omega]] is the viscous friction coefficient and p is the number of pole pairs.
where [F.sub.o[omega]] - transfer function of the speed control loop; [F.sub.R[omega]] - transfer function of the speed controller; [F.sub.Ci] - transfer function of the closed current control loop; [i.sub.m] - magnetizing current; J - total moment of inertia; [K.sub.AD] - transfer constant of the A/D converter; [K.sub.I] - transfer constant of the current sensor; [K.sub.IS] - transfer constant of the incremental sensor IS; [K.sub.T] - torque constant
; [T.sub.S[omega]] - sampling period of the speed CL.
where: [u.sub.a] - armature supply voltage; [R.sub.a], [L.sub.a] - armature resistance and inductivity, respectively; [i.sub.a] - current in the armature circuit; k - motor torque constant
; m - electromagnetic torque developed by the motor; [m.sub.r] - useful resistant torque produced by load (working machine driven by the motor) that means the perturbing size of the system; [m.sub.f] - friction torque; J - inertia moment of the masses at rotation motion; [OMEGA] - armature angular speed.
where [K.sub.M], [C.sub.T], and [I.sub.M] are the gear box gear ratio, torque constant
, and the armature winding current.
where [K.sub.t] is the torque constant
, [i.sub.a] is the armature current, [T.sub.load] is load torque, [T.sub.[alpha]] is torque due to acceleration ([T.sub.[alpha]] = [J.sub.m][d.sup.2][theta]/[dt.sup.2]), [T.sub.[omega]] is torque due to velocity ([T.sub.[omega]] = [b.sub.m]d[theta]/dt).
and the torque constant
kT is stated as in Equation (28).