where [V.sub.t] is the DC source voltage (V), [I.sub.a] is the armature current (A), [R.sub.a] is the armature resistance ([OMEGA]), [L.sub.aa] is the armature inductance (H), [k.sub.m] is the torque constant (V-s/rad), and [[omega].sub.m] is motor speed (rpm).
Parameters Value Armature voltage [V.sub.t] 105 V Armature Current [I.sup.a] 5.2 A Armature resistance [R.sub.a] 20 [ohm] Armature Inductance [L.sub.a] 1.06 mH Moment of inertia J 1.06 * [10.sup.-6] kg x [m.sup.2] Viscous friction 3.79 * [10.sup.-3] N x m x s/rad coefficient [B.sub.m] Constant [k.sub.m] 0.52 Table 6: Operating values for boost converter.
where [R.sub.a] is the armature resistance, [L.sub.a] is the armature inductance, [i.sub.a] and [v.sub.a] are the armature current and voltage, respectively, and [v.sub.emf] is the back-emf voltage.
In following experiments, the parameters of the FCS-MPC controller remained the same as in Section 7 and real values of inertia and armature resistance have been varied.
The following nominal values for the various parameters of a DC motor and mobile platform are used: [V.sub.in] = 12 V; motor torque constant, [K.sub.t] = 1.188 Nm/A; armature resistance
, [R.sub.a] = 0.156 [OMEGA]; armature inductance, [L.sub.a] = 0.82 H; geared-motor inertia, [J.sub.m] = 0.271 kg [m.sup.2], geared-motor viscous damping, [b.sub.m] = 0.271 N m s; motor back EMF constant, [K.sub.b] = 1.185 rad/s/V; gear ratio, n = 3; wheel radius, r = 0.075 m; wheelchair height, h = 0.920 m; wheelchair width, b = 0.580 m; the distance between wheels centers 0.4 m; the total equivalent inertia, [J.sub.equiv] and total equivalent damping, [b.sub.equiv] at the armature of the motor are, [J.sub.equiv] = 0.275 kg [m.sup.2], [b.sub.equiv] = 0.392 N m s.
where [R.sub.a], [L.sub.a] are motor armature resistance
and inductance, [R.sub.f], [L.sub.f] are motor field resistance and inductance, [V.sub.a], [V.sub.f] are armature and field coil voltages, [i.sub.a], [i.sub.f] are armature and field coil currents, [e.sub.a] is electromotive force (EMF) and P is the differential operator (d/dt)
Physical modeling approach divide model on several basic parts (for example armature resistance
, armature inductance etc.) and these parts has their own models.
15, 400020 Cluj-Napoca, Romania, E-mail: email@example.com Table DC motor parameters Armature resistance
Ra, ohm 0.334 Armature Inductance La, H 0.000085 Torque Coefficient Kt, Nm/A 0.0194 Back EMF Coefficient Kb, Vs/rad 0.0194 Gear Ratio Ng, rad/rad 4.8 Moment of Inertia of 0.00000676 Armature Ja, kg[m.sup.2] Moment of Inertia of Gear/Load 0.0000156175 Jg, kg[m.sup.2] Coefficient of viscous friction 0.000062 at armature Ba, Nms/rad Coefficient of viscous friction 0.00001 at gear Bg, Nms/rad Current saturation 4 coefficient Isat, A Friction dead zone 0.1 coefficient dz, Nms/rad
Most of these vibrators have an armature resistance
of at least 10 ohms and a terminal voltage of 1.3 volts.