LPV models for jet-printed heightmap control

The technological development of microscale additive manufacturing requires automated control of material deposition to build a desired 3D structure. This paper considers 3D structures as heightmaps and presents a novel, linear parameter-varying (LPV) model of heightmap evolution for control. Three model identification methods are proposed, each using numerical simulations of liquid drop wetting on nonflat surfaces to obtain the model's time- and space-varying impulse response. First, a method using online numerical simulations is developed for high accuracy at high computational expense. Second, a method using regression to a precomputed dataset of numerical simulations is developed for computationally constrained applications. Third, a spatially invariant version of the second method is developed for compatibility with methods of fast, frequency domain, control computation. For fast numerical simulations, the solver Surface Evolver is used. In simulation, the LPV models identified by the three proposed methods show improved accuracy and precision over a standard linear model. The fast-to-identify and more accurate LPV heightmap evolution models improve the foundation for automated control of microscale additively manufactured structures.