We need to do a matlab script code with these requirements:

Script files:

$-->$ There will be one script file dedicated for the physics of the problem. The physics needs to be solved with ode$45.($code A$)$

$-->$ There will be one script file dedicated for the cost function. This script file will call ode$45,$ and calculate the cost. $($code B$)$

$-->$ There will be one script file dedicated for the optimization routine. $($code C$)$

$-->$ Therefore; code A will call code B$.$ Code B will call code C$.$

Pyhsics of the system:

Here is a very brief description of the case and the physical system:

$-->$ You are a researcher to build a test setup for a specific experiment. In this experiment you want to rotate a small spherical object immersed in a viscous fluid.

$-->$ Sphere, which is immersed in silicone oil, will be rotated by a DC$-$motor. DC$-$motor is powered up with a Li$-$Po battery.

$-->$ The experiment will last till the battery is depleted.

$-->$ The motor is doing work against internal friction torque and the friction torque of the liquid exerted on the sphere.

$-->$ The battery is doing work against overall resistance of the system and the back$-$emf effect.

$-->$ Everything is coupled.

Expectations:

$-->$ You want to achieve the fastest rotation rate but the flow must remain laminar. $($Reynolds number $<mtext\; id="EditorElement\_1797946"></mtext><mn\; id="EditorElement\_1797947">0</mn><mn\; id="EditorElement\_1797948">.</mn><mn\; id="EditorElement\_1797949">1</mn><mi\; id="EditorElement\_1797950">)</mi>$

$-->$ You want to conduct the experiment as long as possible but the battery has a capacity limit

$($Ah x V x $3600[$Joules$])$

$-->$ Therefore you face two objectives and two constraints.

$-->$ There are two variables $($potantiometer$/$adjustable resistance$),$ connected in series and in parallel, in the circuit to modify the current passing through the circuit. These are what you are supposed to optimize.

$-->$ Therefore you have two optimization variables to play with.

Cost Function:

$-->$ The cost function has two separate objectives.

$-->$ Objectives might be imbalanced in magnitude; therefore, might need to be scaled to weigh equally.

$-->$ The objectives could be determined with the help of the constraints and$/$or educated guesses.

$-->$ Constraints can directly be embedded in the cost functions $($if$/$when it makes sense.$)$

Variables and Bounds:

$-->$ The variables $($adjustable variables$)$ cannot be negative.

$-->$ You will see that it will be most logical to assume that both cannot be equal to zero.

$-->$ Variables will be embeded in the equations as in $$equivalent value$$ of resistances.

$-->$ initial guesses should be justifiable. The choice of very small or very large values, if used, should be explained carefully.

Further details $($physics modeling, geometric properties, material specific constants$)$ on the problem are available in the $.$tiff files