**Title: Verified Estimation and Control of Chemical Processes**

**Project code:** APVV SK-CN-2015-0016

**Partners:**

- Slovak University of Technology in Bratislava (Radoslav Paulen, Michal Kvasnica, Juraj Oravec, Miroslav Fikar)
- ShanghaiTech University (Boris Houska, Xuhui Feng, Yanlin Zha, Mario Eduard Villanueva, Jiahe Shi, Kai Wang)

**Duration: 2018-2019**

**Abstract:**

The goal of this project is to bring together scientists who share common research interests in the development and application of verified estimation and control algorithms for dynamic systems in order to achieve greater energy- and material efficiency as well as safety of chemical production sites. The research team consists of students and professors with backgrounds in mathematics, control and engineering. The scientific goals of the cooperation are to develop a methodology for efficient guaranteed parameter and state estimation of nonlinear dynamic systems, which shall be synthesized with advanced model predictive control schemes. Software implementations will be delivered as part of this project. Moreover, this project aims at a demonstration of the developed tools by applying them to laboratory chemical process systems, membrane filtration system and distillation column.

**Project description:**

A safe and sustainable operation of chemical processes requires sensing of key process variables, estimation of unmeasured variables and disturbances, and application of actions that steer production plants’ behavior towards desired goals in an efficient manner. The proposed project studies advanced model-based approaches to estimation and control of dynamic systems, namely guaranteed estimation and model predictive control, and investigates the applications of these methodologies to chemical production systems.

Many process variables, such as chemical compositions of material streams or levels of degradation of the equipment, cannot be measured directly. Despite the availability of modern and cheap sensor technology, many process variables still need to be estimated by using sophisticated algorithms that simultaneously reveal statistically best options (estimates) for the values of the unmeasured variables and the confidence associated with these estimates.

The two biggest obstacles to gathering precise information about the unmeasured quantities are the typically nonlinear relations between measured and unmeasured variables and the presence of measurement noise in the obtained data. The current state of the art in estimation of unknown quantities in the industry relies mostly on linear models and Gaussian probability distributions, which lead to rather inaccurate linear regression or linear-quadratic maximum likelihood estimation. As chemical reactions in industrial process systems are typically highly nonlinear, the results of the industrially-applied state-of-the- art estimation technology are often unreliable or inaccurate, although nonlinear model based estimation frameworks could lead to better operation and management of the processing units. In the context of nonlinear estimation technology, the current rate of technological research-to-industry transfer is insufficient and, as a consequence, many industrial processes could benefit from tools that illustrate the available estimation potential.

Guaranteed estimation [1], often referred to as set-membership estimation, originated in early 1980s as a technique for estimation of parameters of linear mathematical models subject to unknown-but-bounded measurement errors. It thus represents a robust estimation technique that overcomes the limitations of maximum-likelihood approaches as it does not require the measurement noise to follow any particular shape and demands only the knowledge of the noise bounds, which are often known quite reliably in practice. Moreover this estimation principle is well suited to incorporation of nonlinear relationships between the process variables.

The appealing features of guaranteed estimation, however, come at a price of heavier computational burden [2]. The procedure of obtaining guaranteed estimates requires computation of enclosure (image) sets of the mathematical models of the involved systems. This requires significant effort on the numerical side as commonly used tools from the field of set arithmetics, such as standard interval arithmetic, tend to yield too conservative results when implicit and nonlinear relations are involved. In this project, we envision the use of advanced interval superposition arithmetics, a novel type of set arithmetics that is currently developed in the group of the project partners at ShanghaiTech University. A principal goal is to make this new tool available for the computation of the guaranteed state- and parameter estimates for nonlinear chemical processes. The project partners expect major improvements compared to the existing, pre-mature tools that are currently used for guaranteed parameter estimation.

Model predictive control [3] is an advanced control strategy that is getting a wide attention in industrial process control due to its ability to cope with multi-input multi-output process systems under hard operational constraints. It uses a mathematical model of a dynamic system to predict the future system behavior and to derive the control actions that steer this behavior towards desired goals while respecting the constraints. Model predictive control is not yet standard in the industry but its growing presence in the industrial environment stands for a great example of penetration of advanced theoretical control methods into practice. However, in order to realize its full potential, the model predictive control should deal reliably with nonlinear, often uncertainty affected, dynamic nature of industrial processes. This calls for a so-called robust control approach within the model predictive control.

Unfortunately, existing robustification methodologies [4], which can deal with uncertainties in the context of model predictive control, are not yet real-time feasible for large-scale and complex systems and for systems with high sampling rate. In order to remedy this situation, the proposed project will improve the existent robust model predictive control approaches by a) increasing the speed of the solution methods by efficiently combining the best of the two worlds of explicit model predictive control and auto-generated model predictive controllers, b) decreasing the complexity of the control problems using the ideas from distributed optimization and c) further developing of promising techniques based on linear matrix inequalities.

The aim of the proposed project is to establish cooperation between Slovak University of Technology in Bratislava and ShaghaiTech University in estimation of nonlinear dynamic systems and strengthen and intensify the previously established collaboration in the domain of robust model predictive control. The scientific goals of the proposed collaboration project can be summarized as a set of actions towards:

1. development of efficient methodology for guaranteed estimation of high-order nonlinear dynamic systems

2. synthesis of advanced robust MPC design for uncertain dynamic systems

3. development of software packages that enable the transfer of theoretical developments into relevant applications

4. demonstration of the theoretical and software developments on a set of challenging case studies from the domain of chemical engineering and process systems engineering in order to promote wide acceptance by industry.

The software developed within the project will be made freely available and shall be tested on laboratory systems. The laboratory systems concern two typical down-stream separation processes, a membrane filtration system and a distillation column. Both these systems are energy-intensive processes that are widely applied in the chemical industry and both exhibit highly nonlinear behavior. Energy- and material- efficient operation of these systems is possible using model-based techniques [5, 6]. These techniques, however, require reliable information about the unmeasured state variables, which are chemical compositions of the material streams, and about the values of model parameters, which are usually unknown in practice. The employed models represent mass-transfer correlations, permeability of the membrane and vapour-liquid equilibria over the trays of the distillation column, whose parameters often vary between different pieces of equipment and different chemical systems so the estimation from measured data is the only possibility of finding these values. Only a reliable state and parameter estimation would make it possible that the operation of the process is feasible, i.e. the separation goal is met, and at the same time energy (for pressurizing, heating and cooling) and material (very clean solvent) are used efficiently.

The results of the project will be published in top-tier journals, at jointly organized conference sessions and workshops as well as on a project web page.

References:

[1] L. Jaulin and E. Walter. Set inversion via interval analysis for non-linear bounded-error estimation. Automatica 29 (4):1053–1064, 1993.

[2] R. Paulen, M. E. Villanueva and B. Chachuat. Guaranteed parameter estimation of non-linear dynamic systems using high-order bounding techniques with domain and CPU-time reduction strategies. IMA Journal of Mathematical Control and Information 33 (3):563–587, 2016.

[3] J. B. Rawlings and D. Q. Mayne. Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, WI, 2009.

[4] D. Q. Mayne. Model predictive control: Recent developments and future promise, Automatica 50 (12): 2967-2986, 2014.

[5] R. Paulen, M. Jelemenský, Z.Kovacs and M. Fikar. Economically optimal batch diafiltration via analytical multi-objective optimal control. Journal of Process Control 28: 73–82, 2015.

[6] J. Drgoňa, M. Klaučo, F. Janeček and M. Kvasnica. Optimal control of a laboratory binary distillation column via regionless explicit MPC, Computers & Chemical Engineering 96 (4): 139-148, 2017.

The planned activities of the project cover the actions foreseen in the call. A close collaboration will be established within the proposed project among the partner institutions by a) preparing joint publications and other outputs, such as software prototypes, b) actively participating at conferences and organizing joint scientific activities, c) mutually using special laboratory equipment, d) involving PhD students and young researchers (up to 35 years).

The time frame of the project duration is 24 months with the following schedule:

- Month 1-9: Development of theoretical concepts. a) Formulation of guaranteed estimation in the framework of interval superposition arithmetic and tailoring of interval superposition arithmetics to guaranteed state- and parameter estimation. b) Development of approaches for reliable robust model predictive control based on explicit model predictive control and by using linear matrix inequalities. Towards the end of this period the first batch of PhD students and young scientists will be exchanged in order to finalize the theoretical developments, assess the applicability of the theoretical results, propose further developments, if needed, and prepare the software implementation strategy and plan the demonstration of the theoretical concepts on the case studies.

- Month 10-15: Work on software implementation. This phase is initiated by an exchange of scientific staff (PhD students and young scientists) in the previous period. Both partner institutions will work jointly on the software implementation of the theoretical developments. Also a first set of disseminating publications will be prepared in this phase of the project.

- Month 16-24: Demonstration and dissemination. The developed methodologies will be demonstrated in challenging simulations and on laboratory chemical processes; membrane filtration system and distillation column. For this aim the second batch of researchers (PhD students and young scientists) will be exchanged. This period also concludes the activities of the project by joint preparation of the scientific publications.

**Scientific exchanges during the project**

Dr. Mario
Eduardo Villanueva spent three days at STU in Bratislava in July 2018. He presented
the recent research progress of the group from ShaghaiTech University
and has been involved in discussions on
research topics that would be further pursued in the project.

Prof. Miroslav Fikar a Dr. Radoslav Paulen spent one week at ShaghaiTech University in July 2018. They have been involved in the scientific discussions with researchers in the group of Prof. Houska a they have actively participated in the workshop "International Workshop on Advanced Methods for Control and Estimation of Dynamic Systems" that was jointly organized by STU in Bratislava and ShanghaiTech University Link

Prof. Boris Houska, Jiahe Shi and Kai Wang spent one week at Slovak University of Technology in Bratislava from October, 1 2018 to October, 7 2018. They were involved in numerous scientific discussions with the researchers from Slovak University of Technology in Bratislava. New research ideas were discussed, presently pursued research goals were crystallized, and future research directions were set up. Moreover, Prof. Houska gave a scientific seminar on "Gram-Charlier expansions and their use in control".

Mrs. Petra Valiauga spent the period 25.3.-5.4.2019 at ShanghaiTech University. During the stay university she discussed several topics in area of Guaranteed Parameter Estimation and its implementation on dynamic problems. She has presented recent research in Moving-Horizon Guaranteed Parameter Estimation.

- J. Su – Y. Zha – K. Wang – M. Villanueva – R. Paulen – B. Houska:
**Interval Superposition Arithmetic for Guaranteed Parameter Estimation**. In*12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems DYCOPS 2019*, Elsevier, pp. 574–579, 2019. - C. E. Valero – R. Paulen:
**Set-Theoretic State Estimation for Multi-output Systems using Block and Sequential Approaches**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 22nd International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 268–273, 2019. - P. Valiauga – R. Paulen:
**Moving-horizon Guaranteed Parameter Estimation: Influence of the Measurement Error**. Editor(s): M. Fikar and M. Kvasnica, In*Proceedings of the 22nd International Conference on Process Control*, Slovak Chemical Library, Štrbské Pleso, Slovakia, pp. 256–261, 2019. - M. Villanueva – X. Feng – R. Paulen – B. Chachuat – B. Houska:
**Convex Enclosures for Constrained Reachability Tubes**(in ). In*12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems DYCOPS 2019*, Elsevier, pp. 118–123, 2019.

- J. Su – Y. Zha – K. Wang – M. Villanueva – R. Paulen – B. Houska:
**Interval Superposition Arithmetic for Guaranteed Parameter Estimation**(in ). 2018.

Responsibility for content: doc. Ing. Radoslav Paulen, PhD.

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