Hej Kumarasemy,

To 1 and 4. When using a cascaded control, you have an inner control loop for the current and an outer control loop for the speed. The bandwidth of the current controller is usually determined by the switching frequency of your converter. The switching frequency should be at least ten times higher then the maximum fundamental frequency of the motor. The inner control loop should be about ten times faster than the outer control loop and, thus, the BW of the speed controller should be a tenth of the BW of the current controller.

2. In the paper below, I have derived the current controller gains using loop shaping. A similar approach should be used for the speed controller.

https://www.researchgate.net/publication/331137173_Fault_Detection_and_Localization_for_Limp_Home_Functionality_of_Three-Level_NPC_Inverters_With_Connected_Neutral_Point_for_Electric_Vehicles

3. The torque is usually defined as

T=1.5p×psi×iq+(Lsd-Lsq)isqisd .

Then you have to express isd and isq using sin and cos. With the help of

I=sqrt(isq^2+isd^2) you can express the torque just with the help of one of the currents and beta. Take the derivative and put it to zero, this will give the beta resulting in the minimum current.

However, you have to consider also the voltage limitations (ellipses) at field weakening and high speed.