Merging process optimization and advanced control: novel
algorithms and performance monitoring strategies for
sustained economic e
fficiency
Corso di Dottorato in Ingegneria Industriale - Curriculum in Ingegneria Chimica e Materiali Relazione Finale
Dottorando: Marco Vaccari Relatore: Prof. Gabriele Pannocchia
Controrelatore: Prof. Claudio Scali March 10, 2019
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Introduction
In the process industries especially, the current paradigm for achieving overall economic objectives is to partition the information management, decision making, and control system into two layers. The first layer, often referred to as real-time optimization (RTO), performs a steady-state economic optimization of the plant’s variables, updated on a timescale of hours or days. The RTO sends the re-sults of its optimization as a setpoint to the second layer, usually referred to as the advanced process control system. It is the task of this layer to guide the plant’s transient state to the setpoint and, once arrived, to reject dynamic disturbances that enter the system. This process control layer is often im-plemented with model predictive control (MPC) because of its flexibility, performance, robustness, and its ability to directly handle hard constraints on both inputs and states.
However, there are an increasing number of problems for which the hierarchical separation of eco-nomic analysis and control is either inefficient or inappropriate. Hence, flexibility and efficiency are requirements the control system must address.
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Objectives
The macro objectives of this PhD thesis are twofold.
O1 Study nonlinear MPC algorithms which merge MPC and RTO into a single dynamic optimiza-tion and control module. We aimed at studying recent proposals, typically referred to as “eco-nomic MPC”, as well as defining new algorithms which included disturbance estimation to improve robustness and applicability in process control problems.
O2 Study the definition and implementation of suitable performance monitoring and diagnosis methods, aimed at keeping the actual performance of the process as high as possible. In par-ticular, we aim at understanding from data when a revamping of the algorithm is necessary. This can be necessary because the economic objectives could have changed along the process, because disturbances are not properly estimated, because the MPC model is no longer consis-tent with the actual process behavior as could be seen from corrections made by modifiers, or
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Activity of the first year
3.1 Literature analysis and formation
Preparation, literature investigation and course attending have been the focus of the first part of the year. Bases about MPC and system theory have been increased and consolidated. RTO liter-ature has also been deeply analyzed, with particular attention on economic offset problems. The major contributes about the economic MPC (EMPC) fundaments have been extensively investigated: formulation, stability definition, performance constraint and crucial topics have been assimilated. Attended courses have spaced firstly MPC basis and various formulations (AC8), then more specifi-cally the EMPC field (AC7) and lastly precise aspects of convex optimization (AC6).
From the literature investigation, a not solved problem has raised: actual algorithms cannot reach a robust offset-free EMPC formulation.
3.2 RTO and modifiers-adaptation technique research
Starting from May 2016 the attention has also moved on finding solution to the problem evidenced from the literature investigation. From the Real-Time Optimization (RTO) field has been extrapo-lated a technique named “Modifier-Adaptation Methodology” which aim is to adjust the optimiza-tion problem in order to reach a point that satisfies the Necessary Condioptimiza-tion of Optimality of the process and, under constraints satisfaction, corresponds to a local optimum of the real plant.
It has not been an obvious task to transfer the concept formulated for the RTO steady-state prob-lem to the MPC structure where not only the output, but also the state map is used. Based on the Karush-Kuhn-Tucker (KKT) conditions matching of both the target and dynamic optimization prob-lems, a modification of the state and output maps, instead of the the traditional modification, have been applied. Results obtained on an academic example give positive signals to pursue to develop this method. The examined example takes in consideration an isothermal CSTR with two consecu-tive reactions. The wanted product is the intermediate one and it is supposed to have uncertainties (γk2) on the kinetic constant of the degradation reaction. The simple offset-free EMPC does not reach the optimal economic value calculated analytically while used in combination with the above ex-posed technique, the steady-state trajectory is adjusted to the optimal value and the dynamic one is following it. Extensive results and description are collected in the paper for the Special Issue “Real-Time Optimization” ofProcesses (Vaccari, Pannocchia, JP4). In order to calculate the modification at
each iteration, it is mandatory to have knowledge of the real gradients of the system, which is not a trivial task. In this work, in order to calculate modifications from the KKT matching, it has been supposed to perfectly know the plant gradients at least at the steady-state points calculated by the target optimization module.
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Activity of the second year
4.1 Academic Collaboration
From January 2017 since October 2017 I worked in collaboration with prof. James B. Rawlings vis-iting his research group at the University of Wisconsin - Madison. During this period meantime various topics have been analyzed:
• Research on economic MPC and how offset-free condition can be reached without the assump-tion of knowing plant gradients.
• Finding an application in the field of chemical engineering of the offset-free economic MPC. • Comparison and integration of the MPC code I developed with the one developed by Prof.
Rawling’s group. In particular we focused on the Moving Horizon Estimation (MHE) technique implementation for non linear systems.
State estimation is one of the fundamental module of the MPC, and usually it is not a simple task due to difficulties in modeling, insufficient available measurements, noises. The most used state estima-tion technique for non-linear systems is the Extended Kalman Filter, that uses a local linearizaestima-tion of the system. Unfortunately, in case of a poor a priori estimate, this method cannot always converge to
the real process value; this lack is mainly due to two causes: a process that has multiple steady-states and the impossibility to apply any constraints. This can often lead to non physical solution e.g. neg-ative concentrations/pressures, that affect negneg-atively the estimate.
On the other hand MHE is a state and parameter estimation method based on optimization problem. Based on the so called Full Information problem, MHE has the computational advantage, on the lat-ter, of considering a fixed length (N ) time horizon that is shifted forward at each time step. In order to well approximate a full information problem, a prior weight has to be added to the standard ob-jective function. The covariance of this prior weight can be updated in two fashions: a filtering way where at step k information collected up to k − N are used, or in a smoothing way where information used to properly estimated the covariance are the ones collected up to k − 1.
Literature review and theory research about the MHE technique has been constantly analyzed in order to deeply understand the estimation problem with a focus on the update of its prior weight. In particular, time has been spent to develop the correct analytical formula for the filtering and the smoothing update of the state covariance in the prior weighting in case of non-linear systems. This method is seen as the best method currently used for state estimation in case of non-linear MPC as the one used in my research field. MHE is a wide open field because many questions and behaviors have still to be answered.
Furthermore, in that contest, I also contributed to the realization of the second edition of the book “Model Predictive Control: Theory, Computation and Design” by Rawlings J.B., Maine D.Q. and Diehl M.M.. I provided a correct implementation of MHE problem that has been integrated into the code package that will be released with the online version of the book.
The class CBE 770 (AC5) has also been attended in order to better consolidate my knowledge on MPC and advanced control in general.
As part of the Prof. Rawlings research group I have also took part at the First American Summer School on Model Predictive Control (MPC) held in July 25-28 (AC4). In that occasion I had the pos-sibility to have meetings, among the others, with Prof. David Angeli (Imperial College London, UK) and Dr. Thomas A. Badgwell (ExxonMobil Engineering and Research).
Finally, results of the work on the MHE technique developed in the past months have been shown during the semestral “Texas - Wisconsin - California Control Consortium” (AC3) held at UW Madi-son where I had the possibility to interact with industrial practitioners and understand better what is required by the industrial world. A talk and a poster presentation have been my contributions.
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Activity of the third year
5.1 A steady-state plant gradient estimation method
Following the first year work and the open issues and assumptions left in the paper JP4, the plant gradient estimation methods have been studied. Using the knowledge in the identification system field acquired working on paper CP3, a new methodology has been developed. Collecting transient output and input data an identification method has been applied to identify a local linearized model of the non-linear process. In particular, the identification tool used in this developed technique, is the one described in the paper CP2. The linearized model is then used to obtain the system gain, hence the plant gradient approximation. Also the Moving Horizon Estimation (MHE) studied dur-ing the second year has been used to better estimate the system states and disturbances. The new methodology performances have been then compared to the one obtained in JP4 and the offset-free economic MPC is achieved for the tested example. Results and the analysis of this work can be found in the paper CP3 and they have been discussed in August 2018 at the NMPC 2018 conference, where my contribution was a poster.
5.2 A monitoring strategies for EMPC
My last research period has been dedicated to the work on O2. A new performance diagnosis method-ology has been analyzed. The goal was to exploit optimization problem parameters, in particular sensitivity analysis, and identification error indices. Based on the EMPC algorithm developed in the paper CP3, we have proposed a novel performance monitoring technique based on event-triggered identification. In presence of disturbances or time-varying plant dynamics, the plant gradient esti-mation procedure described in CP3 can fail because of a weekly informative set of data. As result the identification procedure cannot guarantee a good quality gradient approximation. This lead to a poor functioning of the modifier-adaptation strategy and so of the all EMPC implementation. Hence, the monitoring algorithm exploits a sort of sensitivity analysis of the KKT optimality conditions of the plant and consequently is able to evaluate if a new data collection is needed or not. The event-triggering mechanism is then well described and tested any time conditions apply. We applied the monitoring methodology to the CSTR example in CP3, testing various state and disturbance estima-tion methods. Results shows how the proposed methodology can overcome plant-model mismatch and time varying disturbances, converging always to the best economic equilibrium. Selected the algorithm with the MHE method with smoothing updating, it is shown how the monitoring tech-nique is particularly efficient versus its counterpart non monitored. This techtech-nique seems to mark a positive step into a more reliable and robust EMPC formulation nearer to the industrial panorama needs. Extensive results and methods can be found in the paper CP1.
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MPC code developing
Simultaneously to the literature review, a sufficient competence in using the software Python have been achieved: this has been necessary to implement an MPC algorithm code. This code first purpose has been to serve as the main tool for this PhD research over the three years; thereafter its intention is to be an open-source, multipurpose, easy-to-use code for MPC design, analysis and simulation. The code is able to represent both tracking and economic MPC with the possibility to have an “offset-free” control. The code has been firstly presented in the contest of the European Conference on Computational Optimization (EUCCO) with an abstract submission and a session talk on September 2016 (Vaccari, Pannocchia [CP6]).
With the ongoing of my research, many features have been added to the original structure. During the second year, as the studying of MHE theory and methods has started, implementation of the MHE problem on the code has begun. This has been tested for obtaining the best performances and has opened the opportunity to test the application of MHE to the economic MPC problem developed in JP4.
The last year, with two new techniques formulated, the code has been further updated. Both the gradient estimation method through system identification and the monitoring procedure have been implemented. In the end, in May 2018, the code has been finally published on GitHub as a public repository and can be found at https://github.com/CPCLAB-UNIPI/MPC-code.
The past and current applications of this code are various.
• The code is used as didactics support and exercise tool for the following teaching:
– “Controllo dei Processi Tecnologici” held by Prof. Alberto Landi in the Master Degree course of Robotics and Automatic Engineering.
– “Controllo dei Processi” held by Prof. Gabriele Pannocchia in the Master Degree course of Chemical Engineering.
• Application of the code can be found in the collaboration with Dr. Bacci di Capaci (Bacci di Capaci, Vaccari, Pannocchia [CP5 and JP2]). In this works the code has been used to simulate the controller of a non linear process with control valves affected by stiction. Implementation of the problem into the code and similar technical support have been my contributes.
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Other Works
In January 2017, we also completed a full paper for the Special Issue “Efficient Energy Management” of Journal of Process Control (Vaccari et al., JP3). This paper collects all my Master thesis work and
overall the work done in collaboration with ENEL Ingegneria ed Ricerca. This work presents a soft-ware tool able to optimize the decision variables of various electrical, thermal and/or storage devices in a Hybrid Renewable Energy System (HRES). Controlling the HRES in an economic efficient fash-ion is the aim of this software. It is also shown how this tool has been applied to a real energy system in Tuscany giving positive results.
This work is also being written with a gained literature knowledge in the control field that let us explain what is one possible connection of the tool developed with a dynamic RTO. In this way I can see it also very near to my research topics.
The MPC code has been also used in another project in collaboration with Dr. Bacci di Capaci. After the work done in CP5 and JP2, we focused on the system identification area. An optimiza-tion problem has been formulated in order to identify the process dynamics under uncertainties and noise. In particular this approach has been applied firstly to SISO systems ([CP4]) and then extended to MIMO systems in order to quantify, with a certain accuracy, the stiction parameters characteriz-ing the system valves. Problem formulation, algorithm implementation and support have been my contributions. Analysis, results and discussions are presented in Bacci di Capaci, Vaccari, Scali, Pan-nocchia [JP1].
In the end, I also contributed to the paper CP2 that describes an open-source package for MIMO system identification. The software has been originally developed by Armenise, a former master student in Chemical Engineering. I also helped him with the code publication and maintained it over the last six months. The code can be found at https://github.com/CPCLAB-UNIPI/SIPPY.
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Possible future directions
A comparison between the developed modifier-adaptation based method on the EMPC and an MPC algorithm where there is no more the distinction between target and control optimization problem could be interesting. Of course this last implementation will maintain the hierarchical separation between MPC and RTO, and the intention is also to see if and where this is still acceptable.
Further studies on feasibility, stability and reliability of the proposed EMPC algorithm can analyze its convergence properties and guarantee (or not) a possible real usage into industrial plants.
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Journal Papers
JP1 Bacci di Capaci R., Vaccari M., Pannocchia G., Scali C. 2018. “Enhancing MPC formulations by identification and estimation of valve stiction”.Submitted Paper
JP2 Bacci di Capaci R., Vaccari M., Pannocchia G., 2018. “Model predictive control design for multivariable processes in the presence of valve stiction”. Journal of Process Control, 71,
pp.25-34.
JP3 Vaccari M., Mancuso G.M., Riccardi J., Cant `u M., Pannocchia G., 2017. “A Sequential Linear Programming Algorithm for Economic Optimization of Hybrid Renewable Energy Systems”.
Journal of Process Control. In press
JP4 Vaccari, M., Pannocchia, G., 2016. “A Modifier-Adaptation Strategy towards Offset-Free Eco-nomic MPC”.Processes, 5(1), p.2.
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Conference Papers
oper-28, 2019.Accepted for presentation
CP2 Armenise G., Bacci di Capaci R., Vaccari M., Pannocchia G.: “An open-source System Identi-fication Package for multivariable processes”. 2018 UKACC 12th International Conference on Control (CONTROL 2018), Sheffield, United Kingdom, September 5 - 7, 2018. In Proceedings
CP3 Vaccari M., Pannocchia G.: “Implementation of an economic MPC with robustly optimal steady-state behavior”. 6th IFAC Conference on Nonlinear Model Predictive Control (NMPC 2018),
Madison WI, USA, August 19 - 22, 2018.In Proceedings
CP4 Bacci di Capaci R., Vaccari M., Pannocchia G., Scali C.: “Identification and estimation of valve stiction by the use of a smoothed model”. 10th IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM-2018), Shenyang, China, July 25 - 27, 2018. In Proceedings
CP5 Bacci di Capaci R., Vaccari M., Pannocchia G.: “A valve stiction tolerant formulation of MPC for industrial processes”. IFAC 2017 World Congress, Toulouse, France, The 20thWorld Congress of the International Federation of Automatic Control, July 9-14, 2017.In Proceedings
CP6 Vaccari M., Pannocchia G.: “A multipurpose, easy-to-use Model Predictive Control design and simulation code”. 4th European Conference on Computational Optimization (EUCCO-2016),
Leuven, Belgio, September 12-14, 2016.http://easychair.org/smart-program/EUCCO2016/
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Attended Courses and Conferences
AC1 “GRICU PhD NATIONAL SCHOOL” organized by GRICU in Pisa; May 16 - 19, 2018.
AC2 “Fundamentals of optimization” held by Prof. Gabriele Pannocchia, Alessio Artoni e Prof. Marco Gabiccini at DICI, UniPI; February 5 - March 16, 2018.
AC3 “Texas - Wisconsin - California Control Consortium (TWCCC)” held at the UW Madison; Septem-ber 18 - 19, 2017.
AC4 “First American Summer School on Model Predictive Control” organized by Dr. Saˇsa V. Rakovi´c, Prof. James B. Rawlings and Prof. Ilya V. Kolmanovsky at the UW Madison; July 25-28, 2017. AC5 “Advanced Process Dynamics and Control” held by Prof. James B. Rawlings at the UW
Madi-son; January-May 2017.
AC6 “Convex Otimization” held by Prof.Stephen Boyd at the IMT Alti Studi Lucca; May 2016. AC7 “Advanced topics in control systems” held by Dott. Pantelis Sopasakis at the IMT Alti Studi
Lucca; February 2016.
AC8 “Model predictive control” held by Prof. Alberto Bemporad at the IMT Alti Studi Lucca; November 2015.
