A three-phase permanent magnet (PM) synchronous motor (PMSM) is Y-connected in the stator windings. The motor has the following parameters: Number of pole pairs p=4 Stator d-axis inductance Ld=5.25 mH Stator q-axis inductance Lq-12 mH Stator resistance Rs=0.958 ohm PM flux linkage -0.1827 Wb Inertia: J=0.003 kg*m^2 Damping coefficient: B=0.008 N*m*s Rated torque TN-10 Nm Rated speed n=1000 rpm DC bus voltage Udc=311 V Using the FOC strategy, the motor is started with no-load to 1000 rpm. At t=0.2 s, a torque of 10 Nm is applied. In your assignment report, please provide: (1) Briefly state the control theory and basic analytical formulas for motor performance analysis. (2) Calculate some steady-state performance using the analytical formulae, e.g. the maximum back EMF at rated speed, and phase current at full-load. Note that these results might be used to validate your Simulink simulations later. (3) Build a Simulink model of FOC for controlling the motor speed as required. Report your model and machine and control parameters. The models should be attached for checking if they functions well. (4) Report various dynamic and steady-state performance, e.g. the speed curve, torque profile, phase current waveforms, output power profile, etc. (5) Analyse and validate your simulated results. (6) Any further analyses for improvement.