In this study, the performance of the Model Predictive Controller (MPC) algorithm is investigated in two different reaction systems. The first case is a saponification reaction system where ethyl acetate reacts with sodium hydroxide to produce sodium acetate and ethanol in a CSTR. In the reactor, temperature and sodium acetate concentration are controlled by manipulating the flow rates of ethyl acetate and cooling water. The model of the reactor is developed considering first principal models. The experiments are done to obtain steady state data from the reaction system and these are compared with the model outputs to find the unknown parameters of the model. Then, the developed model is used for designing SISO and MIMO-MPC considering Singular Value Decomposition (SVD) technique for coupling. The second case is the reaction system used for the production of boric acid by the reaction of colemanite and sulfuric acid in four CSTR&rsquo / s connected in series. In the reactor, the boric acid concentration in the fourth reactor is controlled by manipulating the sulfuric acid flow rate fed to the reactor. The transfer functions of the process and disturbance (colemanite flow rate) are obtained experimentally by giving step changes to the manipulated variable and to the disturbance. A model-based and constrained SISO-MPC is designed utilizing linear step response coefficients. The designed controllers are tested for performance in set point tracking, disturbance rejection and robustness issues for the two case studies. It is found that, they are satisfactory except in robustness issues for disturbance rejection in boric acid system.

In this thesis, a reversible Lotka-Volterra model was proposed to study the nonlinear oscillation of the Belousov-Zhabotinsky(BZ) reaction in a closed isothermal chemical system. The reaction zone can be divided into two zones, oscillation zone and transition zone, where the oscillation time and the transition time and the number of the complete oscillations are estimated. By applying the geometric singular perturbation method, it was proved that there exist an oscillation axis in the oscillation zone, a strongly stable two-dimensional invariant manifold in transition zone, on which there is also a one-dimensional stable invariant manifold, which is the part of the central axis. There is no oscillation in the vicinity of the equilibrium, as indicated by Onsager's reciprocal symmetry relation. Furthermore, the damped oscillation is studied in terms of the action-action-angle variables. In the end, the model reference control technique is employed to control the oscillation amplitude in the BZ reaction.

Research Doctorate - Doctor of Philosophy (PhD) / This dissertation presents some new approaches to addressing the main issues encountered by practitioners in the implementation of linear model predictive control(MPC), namely, stability, feasibility, complexity and the size of the region of attraction. When stability guaranteeing techniques are applied nominal feasibility is also guaranteed. The most common technique for guaranteeing stability is to apply a special weighting to the terminal state of the MPC formulation and to constrain the state to a terminal region where certain properties hold. However, the combination of terminal state constraints and the complexity of the MPC algorithm result in regions of attraction that are relatively small. Small regions of attraction are a major problem for practitioners. The main approaches used to address this issue are either via the reduction of complexity or the enlargement of the terminal region. Although the ultimate goal is to enlarge the region of attraction, none of these techniques explicitly consider the upper bound of this region. Ideally the goal is to achieve the largest possible region of attraction which for constrained systems is the null controllable set. For the case of systems with a single unstable pole or a single non-minimum phase zero their null controllable sets are defined by simple bounds which can be thought of as implicit constraints. We show in this thesis that adding implicit constraints to MPC can produce maximally controllable systems, that is, systems whose region of attraction is the null controllable set. For higher dimensional open-loop unstable systems with more than one real unstable mode, the null controllable sets belong to a class of polytopes called zonotopes. In this thesis, the properties of these highly structured polytopes are used to implement a new variant of MPC, which we term reduced parameterisation MPC (RP MPC). The proposed new strategy dynamically determines a set of contractive positively invariant sets that require only a small number of parameters for the optimisation problem posed by MPC. The worst case complexity of the RP MPC strategy is polylogarithmic with respect to the prediction horizon. This outperforms the most efficient on-line implementations of MPC which have a worst case complexity that is linear in the horizon. Hence, the reduced complexity allows the resulting closed-loop system to have a region of attraction approaching the null controllable set and thus the goal of maximal controllability.

Agile autonomous systems are emerging, such as unmanned aerial vehicles (UAVs), that must robustly perform tightly coordinated time-critical missions; for example, military surveillance or search-and-rescue scenarios. In the space domain, execution of temporally flexible plans has provided an enabler for achieving the desired coordination and robustness, in the context of space probes and planetary rovers, modeled as discrete systems. We address the challenge of extending plan execution to systems with continuous dynamics, such as air vehicles and robot manipulators, and that are controlled indirectly through the setting of continuous state variables.Systems with continuous dynamics are more challenging than discrete systems, because they require continuous, low-level control, and cannot be controlled by issuing simple sequences of discrete commands. Hence, manually controlling these systems (or plants) at a low level can become very costly, in terms of the number of human operators necessary to operate the plant. For example, in the case of a fleet of UAVs performing a search-and-rescue scenario, the traditional approach to controlling the UAVs involves providing series of close waypoints for each aircraft, which incurs a high workload for the human operators, when the fleet consists of a large number of vehicles.Our solution is a novel, model-based executive, called Sulu, that takes as input a qualitative state plan, specifying the desired evolution of the state of the system. This approach elevates the interaction between the human operator and the plant, to a more abstract level where the operator is able to “coach” the plant by qualitatively specifying the tasks, or activities, the plant must perform. These activities are described in a qualitative manner, because they specify regions in the plant’s state space in which the plant must be at a certain point in time. Time constraints are also described qualitatively, in the form of flexible temporal constraints between activities in the state plan. The design of low-level control inputs in order to meet this abstract goal specification is then delegated to the autonomous controller, hence decreasing the workload per human operator. This approach also provides robustness to the executive, by giving it room to adapt to disturbances and unforeseen events, while satisfying the qualitative constraints on the plant state, specified in the qualitative state plan.Sulu reasons on a model of the plant in order to dynamically generate near-optimal control sequences to fulfill the qualitative state plan. To achieve optimality and safety, Sulu plans into the future, framing the problem as a disjunctive linear programming problem. To achieve robustness to disturbances and maintain tractability, planning is folded within a receding horizon, continuous planning and execution framework. The key to performance is a problem reduction method based on constraint pruning. We benchmark performance using multi-UAV firefighting scenarios on a real-time, hardware-in-the-loop testbed. / SM thesis

Στην προκειμένη εργασία μελετάται όλο το θεωρητικό υπόβαθρο για τον προβλεπτικό έλεγχο για τις δύο κατηγορίες συστημάτων (Single Input-Single Output SISO, Multiple Input-Multiple Output MIMO). Αρχικά μελετάται η πρώτη μορφή προβλεπτικού ελέγχου που ήταν ο δυναμικός έλεγχος μητρών (DMC). Στην συνέχεια ακολουθεί το πρόβλημα του βέλτιστου προβλεπτικού ελέγχου διακριτού χρόνου όπως αυτό παρουσιάζεται και αναλύεται στην θεωρία του κ. Μaciejowski. Αμέσως μετά μελετάται πάλι το πρόβλημα εύρεσης βέλτιστου προβλεπτικού ελέγχου διακριτού χρόνου αλλά με την χρησιμοποίηση των διακριτών ορθοκανονικών συναρτήσεων βάσης Laguerre όπως αναλύεται από τον κ. Wang στο βιβλίο του. Στις δύο επόμενες ενότητες παρουσιάζονται οι ορθοκανονικές συναρτήσεις βάσης Laguerre συνεχούς χρόνους καθώς και μια άλλη κατηγορία, οι συναρτήσεις Κautz και αναλύεται ο τρόπος που υπολογίζεται ο προβλεπτικός έλεγχος συνεχούς χρόνου με τη χρήση αυτών. Αφού ο αναγνώστης αποκτήσει τις γνώσεις που χρειάζονται πάνω στον προβλεπτικό έλεγχο, ακολουθεί μια πρακτική εφαρμογή πάνω σε ένα ελικόπτερο 2 βαθμών ελευθερίας της Quanser. Εκεί αρχικά αφού περιγραφεί πλήρως η διάταξη μελετάμε τα προβλήματα ελέγχου πρώτα με Pole Placement στην συνέχεια με LQR καθώς και με την χρησιμοποίηση εκτιμητών κατάστασης όπως κάποιο παρατηρητή (observer) ή φίλτρο Kalman πάντα με τη βοήθεια του Μatlab και του Simulink. Επίσης όλη η θεωρία του ΜPC που μελετήσαμε έχει εφαρμοσθεί επιτυχώς σε προσομοίωση στο Μatlab και Simulink. Παρουσιάζονται ο κώδικας που χρειάζεται κάθε φορά καθώς και ενδιαφέροντα αποτέλεσματα για την απόκριση της διεργασίας. Επιπλέον μελετήθηκε το toolbox του Matlab για τον προβλεπτικό έλεγχο (MPC Toolbox). Τέλος οι παραπάνω έλεγχοι εφαρμόσθηκαν κατευθείαν στην πραγματική διεργασία (μη γραμμική) και τα αποτελέσματα ήταν ικανοποιητικά. / This work presents all the necessary theory for the Model Predictive Control for both system categories (Single Input-Single Output SISO, Multiple Input-Multiple Output MIMO). To start, the earliest form of MPC called dynamic matrix control (DMC) is studied. Then the optimal Model Predictive Control for discrete time is analyzed based on the theory that Maciejowski presented. Afterwards the same problem is studied using the discrete time Laguerre orthonormal base functions and the optimal Model Predictive Control is computed as presented in Wang’s theory. In the next two chapters the reader will be guided through the continuous time Laguerre and Kautz orthonormal base functions and how they are used in computing the optimal continuous time Model Predictive Control. Since the reader has acquired all the necessary knowledge about MPC, a practical approach on the Quanser’s two degrees of freedom helicopter follows. Initially, after we have fully described the plant and all its components, we study the control problems using the pole placement and LQR techniques along with state estimators such as observers and Kalman filter, always in the Matlab and Simulink enviroment. Next, the MPC approaches we’ve studied are applied successfully, again using Matlab and Simulink. In every case, all the necessary programs and results are presented in detail. Addionally, the Matlab MPC Toolbox is studied along with its results for the problem. Finally all those controls are applied directly to the real nonlinear plant successfully and the results are discussed.

This thesis presents the work conducted during a three year research project in the field of Control Systems and Biomaterials Engineering. The findings are presented over seven chapters, starting with a thorough literature review of the existing methods and key technologies, and following through by highlighting the existing problems with the current methods and how they have been overcome. The data is presented in tables, figures and photographs to enhance understanding and clarification. The research focuses on two relatively new manufacturing methods in the field of Tissue Engineering. Both of the methods are used for creating materials for regeneration of human and animal tissue, with the aim of replacing the current surgical methods. The methods are viewed from a control systems perspective and improvements have been made with the implementation of new technologies and methods. Additionally, further advancements are presented on the theoretical modelling field of control systems, where the shortfalls of existent modelling methods are highlighted and solutions proposed.

Un des plus grands défis dans la commande des robots est de combler l'écart entre la capacité de mouvement de l'humain et des robots humanoïdes. La difficulté réside dans la complexité des systèmes dynamiques représentant les robots humanoïdes: la non linéarité, le sous-actionnement, le comportement non-lisse en raison de collisions et de frottement, le nombre élevé de degrés de liberté. De plus, les robots humanoïdes sont censés opérer dans des environnements non-déterministes, qui exigent une commande temps réel avancée.L'approche qui prévaut actuellement pour faire face à ces difficultés est d'imposer diverses restrictions sur les mouvements et d'employer des modèles approximatifs des robots. Dans cette thèse, nous suivons la même ligne de recherche et proposons une nouvelle approche pour la conception de contrôleurs corps entier qui préservent l'équilibre. L'idée principale est de tirer parti des avantages des modèles approximatifs et de corps entier en les mélangeant dans un seul problème de contrôle prédictif avec des objectifs strictement hiérarchisés.La préservation de l'équilibre est l'une des principales préoccupations dans la commande des robots humanoïdes. Des recherches antérieures ont déjà établi que l'anticipation des mouvements est essentiel à cet effet. Nous préconisons que l'anticipation est utile dans ce sens comme un moyen de maintenir la capturabilité du mouvement, i.e., la capacité de s'arrêter. Nous soulignons que capturabilité des mouvements prévus peut être imposée avec des contraintes appropriées. Dans la pratique, il est fréquent d'anticiper les mouvements du robot à l'aide de modèles approximatifs afin de réduire l'effort de calcul, par conséquent, un contrôleur séparé de mouvement du corps entier est nécessaire pour le suivi. Au lieu de cela, nous proposons d'introduire l'anticipation avec un modèle approximatif directement dans le contrôleur corps entier. En conséquence, les mouvements du corps entier générés respectent les contraintes de capturabilité et les mouvements anticipes du modèle approximatif prennent en compte les contraintes et les tâches désirées pour le corps entier. Nous posons nos contrôleurs du mouvement du corps entier comme des problèmes d'optimisation avec des objectifs strictement hiérarchisés. Bien que cet ordre de priorité soit commun dans la littérature, nous croyons qu'il est souvent mal exploité.Par conséquent, nous proposons plusieurs exemples de contrôleurs, où la hiérarchisation est utile et nécessaire pour atteindre les comportements souhaités. Nous évaluons nos contrôleurs dans deux scénarios simulés, où la tâche du corps entier du robot influence la marche et le robot exploite éventuellement un contact avec la main pour maintenir son équilibre en étant debout. / One of the greatest challenges in robot control is closing the gap between themotion capabilities of humans and humanoid robots. The difficulty lies in thecomplexity of the dynamical systems representing the said robots: theirnonlinearity, underactuation, discrete behavior due to collisions and friction,high number of degrees of freedom. Moreover, humanoid robots are supposed tooperate in non-deterministic environments, which require advanced real timecontrol. The currently prevailing approach to coping with these difficulties isto impose various limitations on the motions and employ approximate models ofthe robots. In this thesis, we follow the same line of research and propose anew approach to the design of balance preserving whole body motion controllers.The key idea is to leverage the advantages of whole body and approximate modelsby mixing them within a single predictive control problem with strictlyprioritized objectives.Balance preservation is one of the primary concerns in the control of humanoidrobots. Previous research has already established that anticipation of motionsis crucial for this purpose. We advocate that anticipation is helpful in thissense as a way to maintain capturability of the motion, i.e., the ability tostop. We stress that capturability of anticipated motions can be enforced withappropriate constraints. In practice, it is common to anticipate motions usingapproximate models in order to reduce computational effort, hence, a separatewhole body motion controller is needed for tracking. Instead, we propose tointroduce anticipation with an approximate model into the whole body motioncontroller. As a result, the generated whole body motions respect thecapturability constraints and the anticipated motions of an approximate modeltake into account whole body constraints and tasks. We pose our whole bodymotion controllers as optimization problems with strictly prioritizedobjectives. Though such prioritization is common in the literature, we believethat it is often not properly exploited. We, therefore, propose severalexamples of controllers, where prioritization is useful and necessary toachieve desired behaviors. We evaluate our controllers in two simulatedscenarios, where a whole body task influences walking motions of the robot andthe robot optionally exploits a hand contact to maintain balance whilestanding.

abstract: Contemporary methods for dynamic security assessment (DSA) mainly re-ly on time domain simulations to explore the influence of large disturbances in a power system. These methods are computationally intensive especially when the system operating point changes continually. The trajectory sensitivity method, when implemented and utilized as a complement to the existing DSA time domain simulation routine, can provide valuable insights into the system variation in re-sponse to system parameter changes. The implementation of the trajectory sensitivity analysis is based on an open source power system analysis toolbox called PSAT. Eight categories of sen-sitivity elements have been implemented and tested. The accuracy assessment of the implementation demonstrates the validity of both the theory and the imple-mentation. The computational burden introduced by the additional sensitivity equa-tions is relieved by two innovative methods: one is by employing a cluster to per-form the sensitivity calculations in parallel; the other one is by developing a mod-ified very dishonest Newton method in conjunction with the latest sparse matrix processing technology. The relation between the linear approximation accuracy and the perturba-tion size is also studied numerically. It is found that there is a fixed connection between the linear approximation accuracy and the perturbation size. Therefore this finding can serve as a general application guide to evaluate the accuracy of the linear approximation. The applicability of the trajectory sensitivity approach to a large realistic network has been demonstrated in detail. This research work applies the trajectory sensitivity analysis method to the Western Electricity Coordinating Council (WECC) system. Several typical power system dynamic security problems, in-cluding the transient angle stability problem, the voltage stability problem consid-ering load modeling uncertainty and the transient stability constrained interface real power flow limit calculation, have been addressed. Besides, a method based on the trajectory sensitivity approach and the model predictive control has been developed for determination of under frequency load shedding strategy for real time stability assessment. These applications have shown the great efficacy and accuracy of the trajectory sensitivity method in handling these traditional power system stability problems. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012

A crescente demanda pela melhoria operacional dos processos aliada ao desenvolvimento da tecnologia da informação tornam a utilização de controladores preditivos baseados em modelos (MPC) uma prática comum na indústria. Estes controladores estimam, a partir dos dados de planta e de um modelo do processo, uma sequência de ações de controle que levam as variáveis ao valor desejado de forma otimizada. Dessa forma, dentre os parâmetros de configuração de um MPC, a baixa qualidade do modelo é, indiscutivelmente, a mais importante fonte de degradação de seu desempenho. Este trabalho propõe uma série de metodologias para a avaliação da qualidade do modelo do controlador preditivo, as quais consideram sua velocidade em malha fechada. Tais metodologias são baseadas na filtragem dos erros de simulação a partir função nominal de sensibilidade, e possuem a capacidade de informar o impacto dos problemas de modelagem no desempenho do sistema, além de localizar as variáveis controladas que estão com tais problemas e se os mesmos são provenientes de uma discrepância no modelo ou de um distúrbio não medido. As técnicas ainda possuem a vantagem de serem independentes do setpoint, o que as torna flexível de também serem utilizadas em controladores nos quais as variáveis são controladas por faixas. A abordagem proposta foi testada em dois estudos de caso simulados, sendo eles: a Fracionadora de Óleo Pesado da Shell e a Planta de Quatro tanques Cilíndricos. As técnicas também foram avaliadas em dados de processo da Unidade de Coqueamento Retardado de uma refinaria. Os resultados indicam que as mesmas apresentam resultados coerentes, corroborando seu elevado potencial de aplicação industrial. / The growing demand for operational improvement and the development of information technology make the use of model predictive controllers (MPCs) a common practice in industry. This kind of controller uses past plant data and a process model to estimate a sequence of control actions to lead the variables to a desired value following an optimal policy. Thus, the model quality is the most important source of MPC performance degradation. This work proposes a series of methods to investigate the controller model quality taking into account its closed loop performance. The methods are based on filtering the simulation errors using the nominal sensitivity function. They are capable detect the impact of modeling problems in the controller performance, and also to locate the controlled variables that have such problems and if it is caused by a model-plant mismatch or unmeasured disturbance. The techniques have the advantage to be setpoint independent, making them flexible to be also used in MPCs with controlled variables working by range. The proposed approach was tested in two simulated case studies The Shell Heavy Oil Fractionator Process and The Quadruple-tanks Process. The methods are also evaluated in process data of the Delayed Coking Unit of a Brazilian refinery. Results indicate that the method is technically coherent and has high potential of industrial application.

Recently, photovoltaic (PV) generation is becoming increasingly popular in industrial applications. As a renewable and alternative source of energy they feature superior characteristics such as being clean and silent along with less maintenance problems compared to other sources of the energy. In PV generation, employing a Maximum Power Point Tracking (MPPT) method is essential to obtain the maximum available solar energy. Among several proposed MPPT techniques, the Perturbation and Observation (P&O) and Model Predictive Control (MPC) methods are adopted in this work. The components of the MPPT control system which are P&O and MPC algorithms, PV module and high gain DC-DC boost converter are simulated in MATLAB Simulink. They are evaluated theoretically under rapidly and slowly changing of solar irradiation and temperature and their performance is shown by the simulation results, finally a comprehensive comparison is presented.