Python Function:

A piecewise multivariable polynomial regression was created from the publicly available T-200 data (attached in this repository), including fitting to a zero band between 1460 and 1560. The coefficients for the PWM values above and below this zero band are then printed out (with values in between set to zero), as well as an MSE value for error. Plots of the error, polyfit at each voltage, and the plot of the actual values from the dataset are also made for visual representation of the plot.

MATLAB Function:

The coefficients are taken from the Python function and put into a function centered at 1500. This MATLAB function can then take a value for voltage and PWM to output a corresponding force value, with piecewise components based on the PWM (created as an upper and lower index for the function, including an index between -40 and 40 for the zeroband for 12V, and -28 to 28 for 16V). The base function is below, and the 3D plot is found below.

MSE for 16V: 0.0007741950422248906

MSE for 10V (Largest 0 band): 0.0007903323001878588

Function for Voltage V and PWM Centered at 1500 P (Using 12V Zero Band):

P < -40
force = 0.18450859598294592 - 0.03877245224750089 * V + 0.00437326839182978 * V^2 - 0.00014159192815009454 * V^3 + 0.0047430745735151875 * P - 0.0011779727652119001 * P * V
+ 0.00012626694389350853 * P * V^2 - 3.6521719807495034e-06 * P * V^3 - 3.394361152608232e-05 * P^2 + 7.081135717273334e-06 * P^2 * V - 6.937006893095161e-07 * P^2 * V^2
+ 1.7574133886452198e-08 * P^2 * V^3 - 1.0125491849106606e-07 * P^3 + 2.3956832126051456e-08 * P^3 * V - 2.0262771883546578e-09 * P^3 * V^2 + 5.312516822050221e-11 * P^3 * V^3

P > 40
force = - 2.2103591356566494 + 0.5020761226661944 * V - 0.038894245021323104 * V^2 + 0.0009685515042413979 * V^3 + 0.04287528029632993 * P - 0.010018667907150527 * P * +
0.0007918978226055346 * P * V^2 - 1.965296626711245e-05 * P * V^3 - 0.00015245579360787697 * P^2 + 3.5803548508328624e-05 * P^2 * V - 2.3976087919487086e-06 * P^2 * V^2 +
5.395703879569961e-08 * P^2 * V^3 + 1.3322303527138988e-07 * P^3 - 2.9258256623955067e-08 * P^3 * V + 1.7469073167777621e-09 * P^3 * V^2 - 3.0349724016130765e-11 * P^3 * V^3

-40 < P < 40
force = 0