Closed loop system means that you have a physical measurement brought back to the controller showing the actual position of the motor shaft you are trying to control. Then you would typically have a PID software control program running on your controller. The input variable for this PID would be the external position signal, the setpoint would be the desired position you want the motor to go to and the output signal of the PID (often called the error output, would be sent to typically a H-drive controller to command the motor direction and speed such the the position signal is driven to equal the setpoint value where the motor would stop. While that is a simple concept there is a ton of details to get a real world example functioning correcting. There are tuning value to come up with for the PID algorithm to use, Scaling of the position input signal, proper scaling of the error output to be compatible with the motor H-drive circuitry you are using.
A hobby type servo is a closed loop system, it's just that the PID type control, position feedback signal and motor H-drive are all included inside the servo, the signal you send it is the desired 'setpoint' position you desire and it will drive until it's final position equals the setpoint you are sending it. I would consider this an advanced DIY project to take on even if you do have some prior software and hardware experience.
Many people are able to build pan and tilt assembly using hobby type servos as such servos come in many torque and speed and quality choices. You kind of get what you pay for, and you have to have the mechanics correct for the servo to control axis's, no slop or backlash allowed if using gear or belt coupling. I'm sure if you look around the web you can find examples of good pan and tilt projects using standard R/C servos and that would give you a much better chance at success rather then trying to build your own closed-loop servo assemblies.
Lefty