1. ME457 Mechatronic Systems 1 Permanent-magnet motor model iaia eaea + > ,, PMMOTOR eaea iaia  

2. ME457 Mechatronic Systems 2 Electromechanical coupling F, force; V, velocity; e, voltage; i, current B F i F= i x BL e = V x BL...physics....engineering. F= (BL)*i e = (BL)*V B V e +

3. ME457 Mechatronic Systems 3 PM Motor model: schematic (Ref.: Introduction to System Dynamics, by Shearer, Murphy, and Richardson, Figure 2-38.)

4. ME457 Mechatronic Systems 4 Harnessing e-m coupling in a motor (“a” denotes the armature) F R B V + B rotor F = BL*i a e a = BL*V  = R*F V = R*  ,, armature windings magnetic field, B

5. ME457 Mechatronic Systems 5 Typical “circuit” schematic

6. ME457 Mechatronic Systems 6 Ideal PM Motor model GY (BLR) eiei  K m = BLR  = K m *i e = K m *  Efficiency = ?

7. ME457 Mechatronic Systems 7 PM Motor model with losses Ra: electrical resistance of the windings. Rm: mechanical friction. GY (K m ) 1e 1m RaRa RmRm eaiaeaia  electrical …. conversion …. mechanical ebeb ii

8. ME457 Mechatronic Systems 8 PM Motor loss model: equations

9. ME457 Mechatronic Systems 9 PM Motor model with dynamics Electrical inductance and resistance of the windings. Mechanical inertia of the rotor and friction. GY (K m ) 1e 1m IeIe RaRa ImIm RmRm eaiaeaia  electrical conversion mechanical

10. ME457 Mechatronic Systems 10 PM Motor model with losses and dynamics: equations

11. ME457 Mechatronic Systems 11 PM Motor model: i/o equations State equations: Inputs: e a and  L Outputs: i a and 

12. ME457 Mechatronic Systems 12 DC Motor model: variable field Constant B-field (BLR) GY MGY ifif i f -controlled B-field (B(i f )LR) 1f IfIf RfRf efef  eaiaeaia eaiaeaia 