Abstract
This chapter describes systems and control theory for advanced manufacturing. These processes have (1) high to infinite state dimension; (2) probabilistic parameter uncertainties; (3) time delays; (4) unstable zero dynamics; (5) actuator, state, and output constraints; (6) noise and disturbances; and (7) phenomena described by combinations of algebraic, ordinary differential, partial differential, and integral equations (that is, generalizations of descriptor/singular systems). Model predictive control formulations are described that have the flexibility to handle dynamical systems with these characteristics by employing polynomial chaos theory and projections. Implementations of these controllers on multiple advanced manufacturing processes demonstrate an order-of-magnitude improved robustness and decreased computational cost. Some promising directions are proposed for future research.
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Paulson, J.A., Harinath, E., Foguth, L.C., Braatz, R.D. (2018). Control and Systems Theory for Advanced Manufacturing. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_5
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