How to draw MTPA curve on torque contours

Hi, I have drawn torque contours using contour command as shown below

How can I add maximum torque per ampere (MTPA) curve to my graph i.e. minimum current for i_f and i_t combination for each torque curve? An example is shown below.

Answer 1

[Raghunath Rachabattuni]

To know how to draw the MTPA curves, and also other constraint curves of the PMSM, pls refere to the following link.

PMSM Constraint Curves and Their Application - MATLAB & Simulink Example - MathWorks India

This page also shows the commands that can be used to draw the curves for a given operating torque and operating speed.