I have a piezo actuator for a micro fatigue test which should give a sinusoidal load output. But I don't know how you go from displacement controlled to load controlled with the actuator. The actuator is closed loop via a strain gauge and there is a load cell to control the loads on the specimen.
For force control, you should design your control system based on the load cell output signal and first of all you need to find the relation between load cell output voltage and force, but in displacement control system your feedback sensor is strain gauge. I think you can't convert displacement control to force control directly.
You'll need to build a controller around it. Key methods are admittance control and impedance control.
e.g. a relatively simple method to implement: De Schutter J, Van Brussel H. Compliant Robot Motion II. A Control Approach Based on External Control Loops. The International Journal of Robotics Research. 1988;7(4):18-33. doi:10.1177/027836498800700402
here the difference between the measured force and the desired force is multiplied by the inverse of the modelled stiffness, multiplied by a control constant (units s^-1). This results in a velocity that is sent to the displacement actuator.
Here this is applied to a piezo-stepper:
M. Versteyhe, D. Reynaerts and H. Van Brussel, "A rigid and accurate piezo-stepper based on smooth learning hybrid force-position controlled clamping," Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146), Leuven, Belgium, 1998, pp. 3059-3064 vol.4, doi: 10.1109/ROBOT.1998.680895.
The Springer Handbook of Robotics also has sections on force control/impedance control.
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