Robustly stabilizing control of an open loop oscillatory crystallization process is considered. The crystallizer is described by a population balance model. From this distributed parameter model an irrational transfer function is obtained which has infinitely many poles and thus represents the infinite-dimensional nature of the system. An infinite-dimensional Hoc controller synthesis method is applied to solve the weighted mixed sensitivity problem for this transfer function. This procedure results in an irrational controller. For practical implementation, the controller needs to be approximated by a rational transfer function . The effectiveness of the controller is demonstrated in simulations.
In this article it is shown that moment models for batch crystallization processes are orbitally flat. The state dependent time scaling involved in orbital flatness is physically meaningful and leads to a notion of time that is very natural for the crystallization process. A procedure is presented to check if a desired final crystal size distribution (CSD) is achievable and to compute the temporal temperature profile that produces this desired CSD. Furthermore, the problem of dynamic optimization of the crystallizer operation is reformulated based on the system's flatness property such that the differential equations are eliminated from the optimization problem. In a case study the effectiveness of this optimization is demonstrated.
We present a quantum algorithm for the computation of the irrational period lattice of a function on Z n which is periodic in a relaxed sense. This algorithm is applied to compute the unit group of finite extensions of Q. Execution time for fixed field degree over Q is polynomial in the discriminant of the field. Our algorithms generalize and improve upon Hallgren's work [9] for the one-dimensional case corresponding to real-quadratic fields.
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