Control design for finite element model

[xlxc34]

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I am coding up a non-linear dynamic simulation of some wind turbine blade test equipment. The blade is cantilevered from a mounting structure and fatigue tested by reciprocating a large mass that is mounted to the blade at the resonant frequency of the system. The blade and its mounting structure can be simplified to the system inside the red box in the picture.

In the finite element model, the displacements are solved for based on externally applied forces. I therefore need to calculate what force needs to be applied in order to get the displacement d(t) to follow a prescribed sinusoidal path given by d(t)=A*sin(2*pi*f*t) where A is the amplitude, f is the resonant frequency of the system and t is time. I intend to model the hydraulic actuator as a beam element with length l and a very low axial stiffness, and apply a force F(t) to the mass and the structure so that l follows the equation above.

My question is: given all of the above information, how do I calculate what force to apply at the next time step, given the desired length at the new time step (d(t)), the length at the previous time step (l) and the equivalent model of the blade given by K, C and M?

Any help will be much appreciated!