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Graph-based Computation of Control Invariant Sets: Algorithms, Analysis and Applications
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- Author / Creator
- Decardi-Nelson, Benjamin
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Increasingly faced with sustainability and profitability objectives, chemical process plants have become very complex with many operating constraints. To achieve these objectives, a high level of automation is required. Unfortunately, the ability of the automated controllers to ensure that the control objectives are met at all future times is complicated by constraints on the available control energy and uncertainties present in the control system. Robust control invariant set (RCIS) and control invariant set (CIS) are fundamental tools used in the analysis of constrained, controlled dynamical systems. However, determining these sets is very difficult, especially in a nonlinear setting. This thesis tackled the problem of computing invariant sets in two directions. In the first part of this thesis, we developed several graph-based invariant set (GIS) tools for computing invariant sets of constrained, controlled dynamical systems and proved the convergence of the set to the largest RCIS. Specifically, we first presented algorithms that inner and outer approximate the largest RCIS (and by extension CIS) contained in the state constraint. Thereafter, we identified several bottlenecks in the GIS algorithm and proposed remedial strategies including adaptive subdivision, parallelization, and system decomposition. The improved GIS has a much improved scalability compared to the standard GIS algorithm. We demonstrated the efficacy of the proposed algorithms and remedial strategies using several numerical examples, including a six dimensional continuous stirred tank reactor (CSTR). In the second part of this thesis, we used the algorithms developed in the first part to develop a robust economic model predictive control with zone tracking (RZEMPC) framework for nonlinear systems. Because the zone to be tracked is not necessarily robust control invariant, we proposed to obtain an RCIS subset of the zone to be tracked and introduced the concept of risk factor in the controller design. This not only ensured the stability of the closed-loop system but also ensured guaranteed economic performance in the presence of uncertainties. We conducted rigorous stability analysis and demonstrated the efficacy of the RZEMPC framework using a nonlinear CSTR example. Thereafter, we further improved the applicability of the RZEMPC framework to higher dimensional systems by tracking an ellipsoidal control invariant set instead of a polytopic control invariant set. We demonstrated the suitability of the proposed RZEMPC algorithm to avoid solvent flooding and over-circulation in the absorption column of a post-combustion CO$_2$ capture plant.
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- Graduation date
- Fall 2022
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.