Dissertations / Theses on the topic 'Explicit Approximated Model Predictive Control'

2009/2010
One of the more recent and promising approaches to control is the Receding Horizon one. Due to its intrinsic characteristics, this methodology, also know as Model Predictive Control, allows to easily face disturbances and model uncertainties: indeed at each sampling instant the control action is recalculated on the basis of the reached state (closed loop). More in detail, the procedure consists in the minimization of an adequate cost function with respect to a control input sequence; then the first element of the optimal sequence is applied. The whole procedure is then continuously reiterated. In this thesis, we will focus in particular on robust control of constrained systems. This is motivated by the fact that, in practice, every real system is subjected to uncertainties, disturbances and constraints, in particular on state and input (for instance, plants can work without being damaged only in a limited set of configurations and, on the other side, control actions must be compatible with actuators' physical limits). With regard to the first aspect, maintaining the closed loop stability even in presence of disturbances or model mismatches can result in an essential strategy: moreover it can be exploited in order to design an approximate stabilizing controller, as it will be shown. The control input values are obtained recurring to a Nearest Neighbour technique or, in more favourable cases, to a Neural Network based approach to the exact RH law, which can be then calculated off line: this implies a strong improvement related to the applicability of MPC policy in particular in terms of on line computational burden. The proposed scheme is capable to guarantee stability even for systems that are not stabilizable by means of a continuous feedback control law. Another interesting framework in which the study of the influence of uncertainties on stability can lead to significant contributions is the networked MPC one. In this case, due to the absence of physical interconnections between the controller and the systems to be controlled, stability can be obtained only taking into account of the presence of disturbances, delays and data losses: indeed this kind of uncertainties are anything but infrequent in a communication network. The analysis carried out in this thesis regards interconnected systems and leads to two distinct procedures, respectively stabilizing the linear systems with TCP protocol and nonlinear systems with non-acknowledged protocol. The core of both the schemes resides in the online solution of an adequate reduced horizon optimal control problem.
Una delle strategie di controllo emerse più recentemente, più promettenti e di conseguenza più studiate negli ultimi anni è quella basata sull'approccio Receding Horizon. Grazie alle caratteristiche che contraddistinguono questa tecnica, cui si fa spesso riferimento anche col nome di Model Predictive Control, risulta piuttosto agevole trattare eventuali disturbi e incertezze di modellazione; tale metodo prevede infatti il calcolo di un nuovo ingresso di controllo per ciascun istante di campionamento, in seguito alla minimizzazione ad ogni passo di un'opportuna funzione di costo rispetto ad una sequenza di possibili futuri ingressi, inizializzata sulla base del valore dello stato del sistema all'istante considerato. Il controllo è dato dal primo elemento di tale sequenza ottima; tutto questo viene continuamente ripetuto, il che comporta un aggiornamento costante del segnale di controllo. Gli inconvenienti di questa tecnica risiedono nelle elevate risorse computazionali e nei tempi di calcolo richiesti, così da ridurne drasticamente l'applicabilità specie nel caso di sistemi con elevata dinamica. In questa tesi ci si concentrerà sulle caratteristiche di robustezza del controllore: l'importanza di quest'analisi risiede nel fatto che ogni sistema reale è soggetto a incertezze e disturbi di varia origine cui bisogna far fronte durante le normali condizioni di funzionamento. Inoltre, la capacità di gestire errori di modellazione, come si vedrà, può essere sfruttata per ottenere un notevole incremento delle prestazioni nella stima del valore da fornire in ingresso all'impianto: si tratta di ripartire l'errore complessivo in modo da garantirsi dei margini che consentano di lavorare con un'approssimazione della legge di controllo, come specificato più avanti. In tutto il lavoro si considereranno sistemi vincolati: l'interesse per questa caratteristica dipende dal fatto che nella pratica vanno sempre tenuti in considerazione eventuali vincoli su stato e ingressi: basti pensare al fatto che ogni impianto è progettato per lavorare solo all'interno un determinato insieme di configurazioni, determinato ad esempio da vincoli fisici su attuatori, sensori e così via: non riporre sufficiente attenzione in tali restrizioni può risultare nel danneggiamento del sistema di controllo o dell'impianto stesso. Le caratteristiche di stabilità di un sistema controllato mediante MPC dipendono in modo determinante dalla scelta dei parametri e degli attributi della funzione di costo da minimizzare; nel seguito, con riferimento al caso dei sistemi non lineari, saranno forniti suggerimenti e strumenti utili in tal senso, al fine di ottenere la stabilità anche in presenza di disturbi (che si assumeranno opportunamente limitati). Successivamente tale robustezza verrà sfruttata per la progettazione di controllori stabilizzanti approssimati: si dimostrerà infatti che, una volta progettato adeguatamente il sistema di controllo “esatto” basato su approccio RH e conseguentemente calcolati off-line i valori ottimi degli ingressi su una griglia opportunamente costruita sul dominio dello stato, il ricorso a una conveniente approssimazione di tali valori non compromette le proprietà di stabilità del sistema complessivo, che continua per di più a mantenere una certa robustezza. Da notare che ciò vale anche per sistemi non stabilizzabili mediante legge di controllo feedback continua: la funzione approssimante può essere ottenuta in questo caso con tecniche di tipo Nearest Neighbour; qualora invece la legge di controllo sia sufficientemente regolare si potrà far ricorso ad approssimatori smooth, quali ad esempio le reti neurali. Tutto ciò comporta un notevole miglioramento delle prestazioni del controllore RH sia dal punto di vista del tempo di calcolo richiesto che (nel secondo caso) della memoria necessaria ad immagazzinare i parametri del controllore, risultando nell'applicabilità dell'approccio basato su MPC anche al caso di sistemi con elevata dinamica. Un altro ambito in cui lo studio dell'influenza delle incertezze e dei disturbi sulla stabilità richiede una notevole attenzione è quello dei sistemi networked; anche in questo caso il ricorso all'MPC può portare a ottimi risultati di stabilità robusta, a patto di individuare un' opportuna struttura per il sistema complessivo ed effettuare scelte adeguate per il problema di ottimizzazione. In particolare, si considererà il caso di trasmissione di dati tra un controllore centralizzato e le varie parti dell'impianto in assenza di collegamento fisico diretto. Lo studio della stabilità dovrà allora tenere in considerazione la presenza di perdite di pacchetti o ritardi di trasmissione, condizioni tutt'altro che infrequenti per le reti. Saranno quindi proposte due distinte procedure, che si dimostreranno essere in grado di garantire robustezza a sistemi rispettivamente lineari comunicanti con protocolli di tipo TCP e non lineari in presenza di protocolli UDP. Questo secondo caso è senz'altro il più complesso ma allo stesso tempo il più concreto tra i due. Il nucleo del controllo è ancora basato su una tecnica MPC, ma stavolta il controllore è chiamato a risolvere il problema di ottimizzazione su un orizzonte “ridotto”, che consente la gestione dei ritardi e di eventuali perdite di pacchetto su determinati canali. La lunghezza dell'orizzonte dipenderà dalla presenza o meno dei segnali di ricezione del pacchetto (acknowledgement).
XXIII Ciclo
1977

In this master thesis, a real-time control system that stabilizes the rotational rates of a tri-copter, has been studied. The tricopter is a rotorcraft with three rotors. The tricopter has been modelled and identified, using system identification algorithms. The model has been used in a Kalman filter to estimate the state of the system and for design ofa model based controller. The control approach used in this thesis is a model predictive controller, which is a multi-variable controller that uses a quadratic optimization problem to compute the optimal con-trol signal. The problem is solved subject to a linear model of the system and the physicallimitations of the system. Two different types of algorithms that solves the MPC problem have been studied. These are explicit MPC and the fast gradient method. Explicit MPC is a pre-computed solution to the problem, while the fast gradient method is an online solution. The algorithms have been simulated with the Kalman filter and were implemented on themicrocontroller of the tricopter.

This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.

This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.

The contributions of this thesis are organised in two parts. Part I presents a mathematical model for drug distribution and drug effect of volatile anaesthesia. Part II presents model predictive control strategies for depth of anaesthesia control based on the derived model. Closed-loop model predictive control strategies for anaesthesia are aiming to improve patient's safety and to fine-tune drug delivery, routinely performed by the anaesthetist. The framework presented in this thesis highlights the advantages of extensive modelling and model analysis, which are contributing to a detailed understanding of the system, when aiming for the optimal control of such system. As part of the presented framework, the model uncertainty originated from patient-variability is analysed and the designed control strategy is tested against the identified uncertainty. An individualised physiologically based model of drug distribution and uptake, pharmacokinetics, and drug effect, pharmacodynamics, of volatile anaesthesia is presented, where the pharmacokinetic model is adjusted to the weight, height, gender and age of the patient. The pharmacodynamic model links the hypnotic depth measured by the Bispectral index (BIS), to the arterial concentration by an artificial effect site compartment and the Hill equation. The individualised pharmacokinetic and pharmacodynamic variables and parameters are analysed with respect to their influence on the measurable outputs, the end-tidal concentration and the BIS. The validation of the model, performed with clinical data for isoflurane and desflurane based anaesthesia, shows a good prediction of the drug uptake, while the pharmacodynamic parameters are individually estimated for each patient. The derived control design consists of a linear multi-parametric model predictive controller and a state estimator. The non-measurable tissue and blood concentrations are estimated based on the end-tidal concentration of the volatile anaesthetic. The designed controller adapts to the individual patient's dynamics based on measured data. In an alternative approach, the individual patient's sensitivity is estimated on-line by solving a least squares parameter estimation problem.

New and exciting possibilities in vehicle control are revealed by the consideration of topography through the combination GPS and three dimensional road maps. This thesis explores how information about future road slopes can be utilized in a heavy truck with the aim at reducing the fuel consumption over a route without increasing the total travel time.

A model predictive control (MPC) scheme is used to control the longitudinal behavior of the vehicle, which entails determining accelerator and brake levels and also which gear to engage. The optimization is accomplished through discrete dynamic programming. A cost function is used to define the optimization criterion. Through the function parameters the user is enabled to decide how fuel use, negative deviations from the reference velocity, velocity changes, gear shifts and brake use are weighed.

Computer simulations with a load of 40 metric tons shows that the fuel consumption can be reduced with 2.5% with a negligible change in travel time, going from Link¨oping to J¨onk¨oping and back. The road slopes are calculated by differentiation of authentic altitude measurements along this route. The complexity of the algorithm when achieving these results allows the simulations to run two to four times faster than real time on a standard PC, depending on the desired update frequency of the control signals.

Model predictive control (MPC) is a paradigm within automatic control notable for its ability to handle constraints. This ability come at the cost of high computational demand, which until recently has limited use of MPC to slow systems. Recent advances have however enabled MPC to be used in embedded applications, where its ability to handle constraints can be leveraged to reduce wear, increase efficiency and improve overall performance in everything from cars to wind turbines. MPC controllers can be made even faster by precomputing the resulting policy and storing it in a lookup table. A method known as explicit MPC. An alternative way of leveraging precomputation is to train a neural network to approximate the policy. This is an attractive proposal both due to neural networks ability to imitate policies for nonlinear systems, and results that indicate that neural networks can efficiently represent explicit MPC policies. Limited work has been done in this area. How the networks are setup and trained therefore tends to reflect recent trends in other application areas rather than being based on what is known to work well for approximating MPC policies. This thesis attempts to alleviate this situation by evaluating how some common neural network architectures and training methods performs when used for this purpose. The evaluations are carried out through a literature study and by training several networks with different architectures to replicate the policy of a nonlinear MPC controller tasked with stabilizing an inverted pendulum. The results suggest that ReLU activation functions give better performance than hyperbolic tangent and SELU functions; and that dropout and batch normalization degrades the ability to approximate policies; and that depth significantly increases the performance. However, the neural network controllers do occasionally exhibit problematic behaviors, such as steady state errors and oscillating control signals close to constraints.
Modell-prediktiv reglering (MPC, efter engelskans Model Predictive Control) är ett paradigm inom reglertekniken som på ett effektivt sätt kan hantera begränsningar i systemet som ska regleras. Den här egenskapen kommer på bekostnad av att MPC kräver mycket datorkraft. Tidigare har  användning av den här typen av kontroller därför varit begränsad till långsamma system. På senare tid har framsteg inom hård- och mjukvara dock möjliggjort användning av MPC på inbyggda system. Där kan dess förmåga att hantera begränsningar användas för att minska slitage, öka effektivitet och förbättra prestanda inom allt från bilar till vindkraftverk. Ett sätt att minska beräkningsbördan ytterligare är att beräkna MPC-policyn i förväg och spara den i en tabell. Det här tillvägagångssättet kallas explicit MPC. Ett alternativt tillvägagångssätt är att träna ett neuralt nätverk till att approximera policyn. Potentiellt har det här fördelarna att ett neuralt nätverk inte är begränsat till att efterlikna policys för system med linjär dynamik, och att det finns resultat som pekar på att neurala nätverk är väl lämpade för att lagra policys för explicit MPC. En begränsad mängd arbete har gjorts inom det här området. Hur nätverken designas och tränas tenderar därför att reflektera trender inom andra applikationsområden för neurala nätverk istället för att baseras på vad som fungerar för att implementera MPC. Det här examensarbetet försöker avhjälpa det här problemet. Dels genom en litteraturstudie och dels genom att undersöka hur olika arkitekturer för neurala nätverk beter sig när de tränas för att efterlikna en ickelinjär MPC-kontroller som ska stabilisera en inverterad pendel. Resultaten tyder på att nätverk med ReLU-aktivering ger bättre prestanda än motsvarande nätverk som använder SELU eller tangens hyperbolicus som aktiveringsfunktion. Resultaten visar också att batch noralization och dropout försämmrar nätverkens förmåga att lära sig policyn och att prestandan blir bättre om antalet lager i nätverket ökar. De neurala nätverken uppvisar dock i vissa fall kvalitativa problem, så som statiska fel och oscillerande kontrollsignaler nära begränsningar.

Moving horizon estimation (MHE) is a class of estimation methods in which the system state and disturbance estimates are obtained by solving a constrained optimization problem. The main advantage of MHE is that information about the system can be explicitly considered in the form of constraints and hence improve the estimates. In stochastic systems the estimation error will inevitably be non-zero and the controller needs to explicitly account for it to prevent constraint violations. In order for the controller to be robustified against the estimation error, bounds on the error need to be known. These bounds can be calculated if the dynamics that govern the estimation error are known. This work presents those dynamics for the unconstrained and the constrained case of the moving horizon estimator with a linear time-invariant model, and also discusses how the bounds on the estimation error can be obtained with set-theoretical methods. Those bounds are then used for robust output-feedback model predictive control (MPC). The MHE and the MPC are derived explicitly through multi-parametric programming. The complete framework is demonstrated using simultaneous MHE and tubebased MPC. The possibility of solving MPC explicitly is very appealing for flight control of small unmanned aerial vehicles (UAVs) because the behaviour of the controller is known in advance and can be guaranteed. Flight control is a challenging task that involves a multi-layer control structure where each decision influences the other layers and the overall performance. This work investigates the requirements on the different layers and their cross-effects. A linear model of the UAV is derived such that it captures the wind which is the most challenging disturbance for UAV flight. Particular focus is placed on the design of a model predictive controller as the autopilot and on in-flight wind estimation.

To reduce fossil fuel consumption and carbon emission in the building sector, renewable and low carbon energy technologies are integrated in building energy systems to supply all or part of the building energy demand. In this research, an optimal supervisory controller is designed to optimize the operational cost and the CO2 emission of the integrated energy systems. For this purpose, the building energy system is defined and its boundary, components (subsystems), inputs and outputs are identified. Then a mathematical model of the components is obtained. For mathematical modelling of the energy system, a unified modelling method is used. With this method, many different building energy systems can be modelled uniformly. Two approaches are used; multi-period optimization and hybrid model predictive control. In both approaches the optimization problem is deterministic, so that at each time step the energy consumption of the building, and the available renewable energy are perfectly predicted for the prediction horizon. The controller is simulated in three different applications. In the first application the controller is used for a system consisting of a micro-combined heat and power system with an auxiliary boiler and a hot water storage tank. In this application the controller reduces the operational cost and CO2 emission by 7.31 percent and 5.19 percent respectively, with respect to the heat led operation. In the second application the controller is used to control a farm electrification system consisting of PV panels, a diesel generator and a battery bank. In this application the operational cost with respect to the common load following strategy is reduced by 3.8 percent. In the third application the controller is used to control a hybrid off-grid power system consisting of PV panels, a battery bank, an electrolyzer, a hydrogen storage tank and a fuel cell. In this application the controller maximizes the total stored energies in the battery bank and the hydrogen storage tank.

The main topic of this thesis is model predictive control (MPC) of an unstable fighter aircraft. When flying it is important to be able to reach, but not exceed the aircraft limitations and to consider the physical boundaries on the control signals. MPC is a method for controlling a system while considering constraints on states and control signals by formulating it as an optimization problem. The drawback with MPC is the computational time needed and because of that, it is primarily developed for systems with a slowly varying dynamics. Two different methods are chosen to speed up the process by making simplifications, approximations and exploiting the structure of the problem. The first method is an explicit method, performing most of the calculations offline. By solving the optimization problem for a number of data sets and thereafter training a neural network, it can be treated as a simpler function solved online. The second method is called fast MPC, in this case the entire optimization is done online. It uses Cholesky decomposition, backward-forward substitution and warm start to decrease the complexity and calculation time of the program. Both methods perform reference tracking by solving an underdetermined system by minimizing the weighted norm of the control signals. Integral control is also implemented by using a Kalman filter to observe constant disturbances. An implementation was made in MATLAB for a discrete time linear model and in ARES, a simulation tool used at Saab Aeronautics, with a more accurate nonlinear model. The result is a neural network function computed in tenth of a millisecond, a time independent of the size of the prediction horizon. The size of the fast MPC problem is however directly affected by the horizon and the computational time will never be as small, but it can be reduced to a couple of milliseconds at the cost of optimality.

Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.
Numeriska algoritmer för att effektivt lösa optimala styrningsproblem är en viktig komponent i avancerade regler- och estimeringsstrategier som exempelvis modellprediktiv reglering (eng. model predictive control (MPC)) och glidande horisont estimering (eng. moving horizon estimation (MHE)). MPC är en reglerstrategi som kan användas för att styra system med flera styrsignaler och/eller utsignaler samt ta hänsyn till exempelvis begränsningar i styrdon. Den grundläggande principen för MPC och MHE är att styrsignalen och de estimerade variablerna kan beräknas genom att lösa ett optimalt styrningsproblem. Detta optimeringsproblem måste lösas inom en kort tidsram varje gång som en styrsignal ska beräknas eller som variabler ska estimeras, och således är det viktigt att det finns effektiva algoritmer för att lösa denna typ av problem. Två vanliga sådana är inrepunkts-metoder (eng. interior-point (IP)) och aktivmängd-metoder (eng. active-set (AS)), där optimeringsproblemet löses genom att lösa ett antal enklare delproblem. Ett av huvudfokusen i denna avhandling är att beräkna lösningen till dessa delproblem på ett tidseffektivt sätt genom att utnyttja strukturen i delproblemen. Lösningen till ett delproblem beräknas genom att lösa ett linjärt ekvationssystem. Detta ekvationssystem kan man exempelvis lösa med generella metoder eller med så kallade Riccatirekursioner som utnyttjar strukturen i problemet. När man använder en AS-metod för att lösa MPC-problemet så görs endast små strukturerade ändringar av ekvationssystemet mellan varje delproblem, vilket inte har utnyttjats tidigare tillsammans med Riccatirekursionen. I denna avhandling presenteras ett sätt att utnyttja detta genom att bara göra små förändringar av Riccatirekursionen för att minska beräkningstiden för att lösa delproblemet. Idag har behovet av  parallella algoritmer för att lösa MPC och MHE problem ökat. Att algoritmerna är parallella innebär att beräkningar kan ske på olika delar av problemet samtidigt med syftet att minska den totala verkliga beräkningstiden för att lösa optimeringsproblemet. I denna avhandling presenteras parallella algoritmer som kan användas i både IP- och AS-metoder. Algoritmerna beräknar lösningen till delproblemen parallellt med ett förutbestämt antal steg, till skillnad från många andra parallella algoritmer där ett okänt (ofta stort) antal steg krävs. De parallella algoritmerna utnyttjar problemstrukturen för att lösa delproblemen effektivt, och en av dem har utvärderats på parallell hårdvara. Linjära MPC problem kan också lösas genom att utnyttja teori från multiparametrisk kvadratisk programmering (eng. multiparametric quadratic programming (mp-QP)) där den optimala lösningen beräknas i förhand och lagras i en tabell, vilket benämns explicit MPC. I detta fall behöver inte MPC problemet lösas varje gång en styrsignal beräknas, utan istället kan den förberäknade optimala styrsignalen slås upp. En nackdel med mp-QP är att det krävs mycket plats i minnet för att spara lösningen. I denna avhandling presenteras en strukturutnyttjande algoritm som kan minska behovet av minne för att spara lösningen, vilket kan öka det praktiska användningsområdet för mp-QP och explicit MPC.

Les centaines de millions de véhicules du parc automobile mondial nous rappellent à quel point notre société dépend du moteur à combustion interne. Malgré des progrès significatifs en termes d’émissions polluantes et de consommation, les moteurs à essence et diesel demeurent l’une des principales sources de pollution de l’air des centres urbains modernes. Ce constat motive les autorités à renforcer les normes anti-pollution, qui tendent à complexifier la définition technique des moteurs. En particulier, un nombre croissant d’actionneurs fait aujourd’hui, du contrôle de la chaîne d’air, un challenge majeur. Dans un marché de plus en plus mondialisé et où le temps de développement de moteurs se doit d’être de plus en plus court, ces travaux entendent proposer une solution aux problèmes liés à cette augmentation de la complexité. La proposition repose sur une approche en trois étapes et combine : modélisation physique du moteur, contrôle prédictif non linéaire et programmation multiparamétrique. Le cas du contrôle de la chaîne d’air d’un moteur à essence suralimenté sert de fil conducteur au document. Dans son ensemble, les développements présentés ici fournissent une approche quasi-systématique pour la synthèse du contrôle de la chaîne des moteurs à essence suralimentés. Intuitivement, le raisonnement doit pouvoir être étendu à d’autres boucles de contrôle et au cas des moteurs diesel
The hundreds of millions of passenger cars and other vehicles on our roads emphasize our society’s reliance on internal combustion engines. Despite striking progress in terms of pollutant emissions and fuel consumption, gasoline and diesel engines remain one of the most important sources of air pollution in modern urban areas. This leads the authorities to lay down increasingly drastic pollutant emission standards, which entail ever more complex engine technical definitions. In particular, due to an increasing number of actuators in the past few years, the air path of internal combustion engines represents one of the biggest challenges of engine control design. The present thesis addresses this issue of increasing engine complexity with respect to the continuous reduction in development time, dictated by a more and more competitive globalized market. The proposal consists in a three-step approach that combines physics-based engine modeling, nonlinear model predictive control and multi-parametric nonlinear programming. The latter leads to an explicit piecewise affine feedback control law, compatible with a real-time implementation. The proposed approach is applied to the particular case of the control of the air path of a turbocharged gasoline engine. Overall, the developments presented in this thesis provide a quasi-systematic approach for the synthesis of the control of the air path of turbocharged gasoline engines. Intuitively, this approach can be extended to other control loops in both gasoline and diesel engines

Avec le développement des technologies de pile à combustible (PàC) et d’électrolyse de l’eau, l’hydrogène électrolytique devient un pilier de la transition énergétique, substitut aux ressources fossiles et outil d’intégration des sources d’énergies renouvelables (SER) intermittentes. À l'échelle de micro-réseaux isolés ou îlotables, cette transition repose sur le développement de systèmes hybrides, couplant des panneaux photovoltaïques (PV) et des électrolyseurs pour la production de l'hydrogène, des systèmes de stockage — réservoirs d'hydrogène (H2) et batteries (Bat) — et des PàC pour la production de l’électricité. Cette étude présente des stratégies de contrôle pour un système PV-H2-Bat-PàC afin d'optimiser la gestion de l'énergie PV intermittente tout en respectant les conditions de fonctionnement des électrolyseurs et des PàC. Premièrement, une commande de type MPPT (Maximum Power Point Tracking) est développée pour assurer le fonctionnement des PV à puissance maximale, et une stratégie de contrôle basée sur des commandes prédictives est mise en œuvre pour définir un courant de référence pour la PàC, l'électrolyseur et les batteries. Deuxièmement, des contrôleurs IP sont utilisés pour réguler ces courants. Troisièmement, un problème d’optimisation permet de définir un plan d’engagement afin d’utiliser la PàC et l’électrolyseur en tenant compte de l’offre, de la demande et des stocks d’énergie
With the development of fuel cell (FC) and water electrolysis technologies, electrolytic hydrogen is becoming a pillar of the energy transition, a substitute for fossil resources and a tool for integrating intermittent renewable energy sources (RES). On the scale of isolated or islandable microgrids, this transition is based on the development of hybrid systems, coupling photovoltaic (PV) panels and electrolyzers for hydrogen production, storage systems - hydrogen (H2) tanks and batteries (Bat) - and FC for electricity production. This study presents control strategies for a PV-H2-Bat-FC system to optimize intermittent PV energy management while respecting the operating conditions of electrolyzers and FC. First, a MPPT (Maximum Power Point Tracking) control system is developed to ensure the operation of PV at maximum power, and a control strategy based on Model Predictive Control is implemented to define a current reference for the FC, the electrolyzer and the batteries. Secondly, IP controllers are used to regulate these currents. Thirdly, an optimization problem makes it possible to define a commitment plan to use the FC and the electrolyser taking into account energy supply, demand and stocks

This thesis proposes, validates, and compares low-complexity algorithms for the fast-and-safe charge and balance of Li-ion batteries both for the single cell case and for the case of a serially-connected string of battery cells. The proposed algorithms are based on a reduced-order electrochemical model (Equivalent Hydraulic Model, EHM), and make use of constrained-control strategies to limit the main electrochemical degradation phenomena that may accelerate aging, namely: Lithium plating in the anode and solvent oxidation inthe cathode. To avoid the computational intensiveness of solving an online optimization as in the Model Predictive Control (MPC) framework, this thesis proposes the use of Reference Governor schemes. Variants of both the Scalar Reference Governors (SRG) and the Explicit Reference Governors (ERG) are developed to deal with the non-convex admissible region for the charge of a battery cell, while keeping a low computational burden. To evaluate the performance of the proposed techniques for the single cell case, they are experimentallyvalidated on commercial Turnigy LCO cells of 160 mAh at four different constant temperatures (10, 20, 30 and 40 °C). In the second part of this thesis, the proposed charging strategies are extended to take into account the balance of a serially-connected string of cells. To equalize possible mismatches, a centralized policy based on a shunting grid (active balance) connects or disconnects the cells during the charge. After a preliminary analysis, a simple mixed-integer algorithm was proposed. Since this method is computationally inefficient due to the high number of scenarios to be evaluated, this thesis proposes a ratio-based algorithm based on a Pulse-Width Modulation (PWM) approach. This approach can be used within both MPC and RG schemes. The numerical validations of the proposed algorithms for the case of a string of four battery cells are carried out using a simulator based on a full-order electrochemical model. Numerical validations show that the PWM-like approach charges in parallel all the cells within the pack, whereas the mixed-integer approach charges the battery cells sequentially from the battery cell with the lowest state of charge to the ones with the highest states of charge. On the basis of the simulations, an algorithm based on a mixed logic that allows to charge in a “sequential parallel” approach is proposed. Some conclusions and future directions of research are proposed at the end of the thesis.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished

Actuellement la nécessité des systèmes d'alimentation d'énergie, capables d'assurer un fonctionnement stable dans des domaines de fonctionnement assez larges avec des bonnes performances dynamiques (rapidité du système, variations limitées de la tension de sortie en réponse aux perturbations de charge ou de tension d'alimentation), devient de plus en plus importante. De ce fait, cette thèse est orientée sur la commande des convertisseurs de puissance DC-DC représentés par des modèles hybrides.En tenant compte de la structure variable de ces systèmes à commutation, un modèle hybride permet de décrire plus précisément le comportement dynamique d'un convertisseur dans son domaine de fonctionnement. Dans cette optique, l'approximation PWA est utilisée afin de modéliser les convertisseurs DC-DC. A partir des modèles hybrides développés, on s'est intéressé à la stabilisation des convertisseurs au moyen des correcteurs à gains commutés élaborés sur la base de fonctions de Lyapunov PWQ, et à l'implantation d'une commande prédictive explicite, en considérant des contraintes sur l'entrée de commande. La méthode de modélisation et les stratégies de commande proposées ont été appliquées sur deux topologies : un convertisseur buck, afin de mieux maîtriser le réglage des correcteurs et un convertisseur flyback avec filtre d'entrée. Cette dernière topologie nous a permis de répondre aux difficultés du point de vue de la commande (comportement à déphasage non-minimal) rencontrées dans la majorité des convertisseurs DC-DC. Les performances des commandes élaborées ont été validées en simulation sur les topologies considérées et expérimentalement sur une maquette du convertisseur buck.