Stochastic nonlinear model predictive control for chemical batch processes
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The chemical industry is a vital part of the world economy transforming raw materials into crucial intermediary products. Batch processes are common in many sectors of the chemical industry, which are gaining in importance due to the increasing emphasis on fine and speciality chemicals that are mostly produced employing batch processes. The main advantage of batch processes is their relative ease of design and inherent flexibility to produce different products and product grades. The control of batch processes is challenging, since these are operated at unsteady state and are often highly nonlinear. Nonlinear model predictive control (NMPC) is therefore a promising approach that can handle nonlinearity and constraints on manipulated and controlled variables. Most batch process models are however affected by significant uncertainties, which need to be taken into account to prevent performance deterioration and constraint violations. This thesis focuses on the development of NMPC formulations for batch processes that explicitly consider stochastic uncertainties to trade-off risk with economic performance. The work presented in this thesis is divided into two parts: - Stochastic nonlinear model predictive control using uncertainty propagation - Gaussian process dynamic modelling and nonlinear model predictive control The first part deals with the formulation of stochastic NMPC (SNMPC) algorithms by propagating the stochastic uncertainty through nonlinear transformations within the optimal control problem (OCP). Stochastic uncertainties considered include both time invariant parametric and additive uncertainties. The estimated statistics at each time step, such as mean and variance are utilised to ensure the satisfaction of chance constraints, while optimizing a nonlinear economic objective in expectation. Initially it is shown how the Unscented transformation and polynomial chaos expansions (PCEs) can be exploited to propagate stochastic uncertainties resulting from state estimates, parametric uncertainties, and additive disturbances to formulate the SNMPC algorithm. In addition, these are exploited to update the state estimates given available measurements. Next a novel application of Gaussian processes (GPs) is introduced for uncertainty propagation in SNMPC similar to PCEs. Given the outstanding performance of GPs and PCEs to capture the required statistics, a new approach for uncertainty propagation is proposed next combining PCEs and GPs. This combination is shown to be superior to either GPs and PCEs alone. All of the proposed SNMPC algorithms are shown to lead to a robust and reliable solution for batch processes and show superior performance to their nominal NMPC counterparts. The second part applies GPs to model batch processes from noisy input/output data. Commonly, dynamic models for batch processes are derived from first principles, which often have high development costs and are frequently too complex to be utilised online. Using GPs for black-box identification is therefore an appealing alternative. GPs in this regard are especially useful, since these quantify the residual uncertainty from the identification of a dynamic model. This uncertainty measure can be exploited to obtain more reliable optimization and control solutions. Firstly, it is illustrated how GPs are able to accurately simulate a bioprocess from experimental data and capture the model uncertainty by propagation of the uncertainty measure. Further, it is shown that the predictive quality of GPs is overall comparable to that of ANNs. Given the excellent predictive quality of GPs, an algorithm is then proposed to employ the GP as an approximate plant model for NMPC. It is crucial to account for the plant-model mismatch of the GP to avoid constraint violations. The proposed algorithm generates Monte Carlo samples of the GP offline for constraint tightening using back-offs. It is shown how probabilistic guarantees can be derived based on the number of constraint violations of these samples. Further, the approach is able to account for both online learning and state dependency of the uncertainty explicitly to alleviate conservativeness. Lastly, computational times could be shown to be relatively low. Often for batch processes it is possible to derive major parts of the plant models from first principles, however certain parts of the model are very difficult to determine from physical laws alone. It is therefore proposed to extend the previous algorithm to this case, for which the GP is exploited to model only the parts of the dynamic system that are difficult to describe using first principles alone.
Består avPaper 1: Bradford, Eric Christopher; Imsland, Lars Struen. Expectation constrained stochastic nonlinear model predictive control of a batch bioreactor. I: 27 European Symposium on Computer Aided Process Engineering. Elsevier 2017 ISBN 978-0-444-63965-3. s. 1621-1626. © 2017 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Paper 2: Bradford, Eric; Imsland, Lars Struen. Stochastic NMPC of Batch Processes Using Parameterized Control Policies. Computer-aided chemical engineering 2018 ; Volum 44. s. 625-630. © 2018 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Paper 3: Bradford, Eric; Imsland, Lars Struen. Stochastic nonlinear model predictive control of a batch fermentation process. Computer-aided chemical engineering 2019 ; Volum 46. s. 1237-1242. © 2019 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Paper 4: Bradford, Eric; Reble, Marcus; Bouaswaig, Ala; Imsland, Lars Struen. Economic stochastic nonlinear model predictive control of a semi-batch polymerization reaction. IFAC-PapersOnLine 2019 ; Volum 52.(1) s. 667-672. © 2019 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Paper 5: Bradford, Eric; Reble, Marcus; Imsland, Lars Struen. Output feedback stochastic nonlinear model predictive control of a polymerization batch process. I: 2019 18th European Control Conference (ECC). IEEE 2019 ISBN 978-3-907144-00-8. s. 3144-3151. © 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.