  The increasing demand on precision and throughput within high-precision
mechatronics industries requires a new generation of feedforward controllers
with higher accuracy than existing, physics-based feedforward controllers. As
neural networks are universal approximators, they can in principle yield
feedforward controllers with a higher accuracy, but suffer from bad
extrapolation outside the training data set, which makes them unsafe for
implementation in industry. Motivated by this, we develop a novel
physics-guided neural network (PGNN) architecture that structurally merges a
physics-based layer and a black-box neural layer in a single model. The
parameters of the two layers are simultaneously identified, while a novel
regularization cost function is used to prevent competition among layers and to
preserve consistency of the physics-based parameters. Moreover, in order to
ensure stability of PGNN feedforward controllers, we develop sufficient
conditions for analyzing or imposing (during training) input-to-state stability
of PGNNs, based on novel, less conservative Lipschitz bounds for neural
networks. The developed PGNN feedforward control framework is validated on a
real-life, high-precision industrial linear motor used in lithography machines,
where it reaches a factor 2 improvement with respect to physics-based
mass-friction feedforward and it significantly outperforms alternative neural
network based feedforward controllers.
