The generalization of feedforward control for a periodic motion system

A comparison of data-driven methods

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A repetitive motion system supporting nano meter precision is positioned at high accelerations, which produces a force that disturbs the demanded accuracy requirements. Iterative learning control is used to learn optimal feedforward control signals for the attenuation this disturbance force. The iterative method comes with a limitation, as it has to learn the compensation signals one by one. In this study, a data-driven approach is taken to design a feedforward controller that generalizes the control action, by finding a model that fits the learned optimal compensation signals. The multi-objective evolutionary algorithm genetic programming is used for its unique ability to search directly in the
program space, therefore returning compact analytic equations as feedforward controller. Feedforward artificial neural networks with the ReLU and tanh activation function are used, due to their excellent approximation qualities. sherlock is a tool that efficiently computes the maximum and minimum output off a ReLU network for a compact input set. The tool is used to find a guaranteed output range for the feedforward controller constructed from ReLU networks, which is desirable from a safety perspective. Finally, the designed controller are compared based on their attenuation of the disturbance force
and their model size. The designed feedforward controllers are capable of reducing the disturbance force by at least 40.01%. The analytic controllers found with genetic programming provide the user with insights in the control problem, cost less memory storage and come with a faster computation time.