Mechatronics: DC Motor Position Control

[ConnorM]

Homework Statement

Write down the equations of motion and develop the continuous-time system.

Homework Equations

See my word doc. or PNG's.

The Attempt at a Solution

See my word doc. or PNG's.

I assumed that there was no friction as no information was given.
I can easily get the transfer function relating angular position to voltage, however, I'm just unsure about what I did in order to account for the inertia of the 5kg mass and the inertia of the lead screw.

The main equation that I am unsure about is [7].
Does it look correct, or where did I go wrong?

 

[KataKoniK]

I would like to provide some feedback on your solution. Overall, your approach seems correct and your equations of motion are well-written. However, there are a few things to consider and clarify:

1. Assumptions: It is important to clearly state any assumptions made in your solution, as they can greatly affect the accuracy of your results. In this case, assuming no friction may not be a realistic assumption, as friction can significantly affect the motion of the system. It would be better to state that your solution is for an idealized system with no friction, and then discuss the potential impact of friction on the results.

2. Inertia terms: In equation [7], the inertia terms for the 5kg mass and the lead screw are not correct. The inertia of the 5kg mass should be represented by I2, not I1, and the inertia of the lead screw should be added to the denominator of the transfer function. This will result in a more accurate representation of the system's dynamics.

3. Transfer function: It is important to note that the transfer function you have derived is for the angular position of the system, not the voltage. If you want to relate the voltage to the angular position, you will need to take the inverse Laplace transform of the transfer function to get the time-domain equation.

4. Continuous-time system: Your solution is correct for a continuous-time system, but it would be helpful to also provide a discrete-time representation of the system, as many practical systems are implemented using digital control.

Overall, your solution is a good start, but it would be beneficial to clarify the assumptions made and correct the inertia terms in equation [7]. Additionally, providing a discrete-time representation of the system would make your solution more complete. Keep up the good work!