What are the functions that can the integrated encoder modules can perform? Are they able to control and maintain the rpm of motors?
You have to write your program to do that. All the integrated encoders do is measure rotation of your motors. However, you do need to use IMEs or the optical shaft encoders to implement speed control.
To be more specific, the IMEs count the number of Ticks that the motor has moved. The VEX product page has the details on how many ticks make up one revolution of the output shaft.
So from taking basic measurements of time and change in ticks over an interval, you can using programming to for example calculate the speed of the output shaft or use control loops such as PID or TBH in your programming.
One thing to note is that regular optical shaft encoders are often preferred over IMEs in some applications as the IMEs are known to have issues with static electricity and the possibility of temporarily resetting the Cortex CPU, resulting is a variety of possible disasters. You can search the forum for more details on that.
Thank you. After I program the desired rpm into the program, would this not be affected by battery voltage? Moreover, regardless of what time during the match it is, will the motor still perform at the same rate even though the battery level may fluctuate?
Yes, it is correct that battery voltage affects the speed of the motor. However, this is exactly what your programming and use of IMEs or Shaft Encoders is there to counter, because you are adjusting the motor power based on what the actual output speed is, regardless of battery power. Put really simply, you start with a full battery and a motor power of i.e. 90, and as the battery power reduces the motor output slows down, therefore you increase the motor power so that in the end the same output RPM is maintained.