I am not able to understand how to implement this into simulink.

This is a stator current and Rotor angle (Beta) look up table under working condition.

How can I implement a look up table in simulink to decide the optimum points.

Answer 1

[Peter O]

Fortunately, that current map looks very smooth. Consider using the 2D lookup block: https://www.mathworks.com/help/simulink/slref/2dlookuptable.html

Use one block for beta and another for magnitude, same inputs to each.

You will need to decide how you want it to handle edge cases where the inputs don't map inside the table boundaries.

[Varun Nair]

I did not get the point ?

[Peter O]

The lookup table is computed ahead of time -- that optimization algorithm generates the surfaces for it. Offline, you will feed the optimizer a grid of operating points (speed, torque), and the golden search will return the optimal combination of current angle and magnitude for each (Speed, Torque) point in the grid.

So after running the optimizer, you have two surfaces: and . In MATLAB those will appear as matrices of dimension N x M, where N is the number of points used for and M is the number of points used for τ. Set each matrix as the data source for its 2D lookup block and the grid values for and τ as the breakpoints. Then, in the Simulink model, the speed and torque inputs at each time point will look at the surface and linearly interpolate to find the space where they need to be to fit on that optimal surface.

Does that make it clearer?

[Varun Nair]

Yes so should I use the Model Caliberation Toolbox for this?

[Peter O]

I'm not sure if you'll need the Model Calibration Toolbox. Golden section search is a way of locating the optimum point along a curve by taking steps in a division driven by the golden ratio. This is a complicated problem, so I would recommend approaching it with several smaller steps.

1. Formulate your golden section search algorithm code. Test its performance on a simple optimization function to which you know the "true" solution.
2. Formulate the Simulink model of the motor, drive, and current controller. Verify its performance in open-loop by supplying a known current magnitude, angle, and speed. You can solve the steady-state formulation analytically to verify your model is outputting the correct information.
3. Your cost function on the optimizer is probably to maximize the system efficiency.
4. Sweep the operating domain of speed and torque points into the steady-state analytical formulation. The optimizer will report back the "best" current angle and magnitude for each power point.
5. Collect these optimal values into the 2D lookup table that the "torque command" block area feeds to establish the full model with dynamic control. The PI controller in that block will probably also need some tuning to get the system to respond at the right level of agressiveness.

[Varun Nair]

It looks bit complicated with the time frame I have with me now.