Can you derive this electromagnetic equation?

I have an electromagnet inside another electromagnet, and their magnetic fields oppose each other so that the outer electromagnet pushes the inner electromagnet down. The inner electromagnet is tied to a thin rope that is pulled with a constant force upward. The goal of this contraption is to keep constant the force that is required to pull this inner electromagnet upwards. The force needed to pull this inner electromagnet upwards CAN NOT CHANGE. So, let's say the pulling force must be 10 [N] of force. You would need to create an equation that determines the amount of current flowing through each electromagnet so that the pulling force must be 10[N] in order to move the magnet upwards. But this is where things get tricky. As the inner electromagnet is pulled upwards, it induces a current on the outer electromagnet and therefore the current going through the outer electromagnet must change in order to keep the magnetic force between the magnets the same. So, the real goal of this project is to derive two equations that determines the currents on the wire as a function of the speed of the inner electromagnet and the pulling force that is desired. The pulling force will always be constant, and chosen before any movement occurs. So really, once you know "F", the current equation will only depend on the speed at which the inner electromagnet is pulled. So once you know the pulling force, the current equation will depend on 1 variable, not 2. I have attached two pictures to kind of give you an idea of what the outer electromagnet might look like (see [login to view URL]) and how the inner electromagnet might look like (see [login to view URL]). I am willing to pay whatever it takes to solve this problem.