This dissertation deals with some computational and analytic challenges for dynamic process operations using first-principles models. For processes with significant spatial variations, spatially distributed first-principles models can provide accurate physical descriptions, which are crucial for offline dynamic simulation and optimization. However, the large amount of time required to solve these detailed models limits their use for online applications such as nonlinear model predictive control (NMPC). To cope with the computational challenge, we develop computationally efficient and accurate dynamic reduced order models which are tractable for NMPC using temporal and spatial model reduction techniques. Then we introduce an input and state blocking strategy for NMPC to further enhance computational efficiency. To improve the overall economic performance of process systems, one promising solution is to use economic NMPC which directly optimizes the economic performance based on first-principles dynamic models. However, complex process models bring challenges for the analysis and design of stable economic NMPC controllers. To solve this issue, we develop a simple and less conservative regularization strategy with focuses on a reduced set of states to design stable economic NMPC controllers. In this thesis, we study the operation problems of a solid sorbent-based CO2 capture system with bubbling fluidized bed (BFB) reactors as key components, which are described by a large-scale nonlinear system of partial-differential algebraic equations. By integrating dynamic reduced models and blocking strategy, the computational cost of NMPC can be reduced by an order of magnitude, with almost no compromise in control performance. In addition, a sensitivity based fast NMPC algorithm is utilized to enable the online control of the BFB reactor. For economic NMPC study, compared with full space regularization, the reduced regularization strategy is simpler to implement and lead to less conservative regularization weights. We analyze the stability properties of the reduced regularization strategy and demonstrate its performance in the economic NMPC case study for the CO2 capture system.

This research work proposes two robust empirical model-based predictive control algorithms for nonlinear processes. Chemical process are generally highly nonlinear thus predictive control algorithms that explicitly account for the nonlinearity of the process are expected to provide better closed-loop performance as compared to algorithms based on linear models. Two types of models can be considered for control: first-principles and empirical. Empirical models were chosen for the proposed algorithms for the following reasons: (i) they are less complex for on-line optimization, (ii) they are easy to identify from input-output data and (iii) their structure is suitable for the formulation of robustness tests. One of the key problems of every model that is used for prediction within a control strategy is that some model parameters cannot be known accurately due to measurement noise and/or error in the structure of the assumed model. In the robust control approach it is assumed that processes can be represented by models with parameters' values that are assumed to lie between a lower and upper bound or equivalently, that these parameters can be represented by a nominal value plus uncertainty. When this uncertainty in control parameters is not considered by the controller the control actions might be insufficient to effectively control the process and in some extreme cases the closed-loop may become unstable. Accordingly, the two robust control algorithms proposed in the current work explicitly account for the effect of uncertainty on stability and closed-loop performance. The first proposed controller is a robust gain-scheduling model predictive controller (MPC). In this case the process is represented within each operating region by a state-affine model obtained from input-output data. The state-affine model matrices are used to obtain a state-space based MPC for every operating region. By combining the state-affine, disturbance and controller equations a closed-loop representation was obtained. Then, the resulting mathematical representation was tested for robustness with linear matrix inequalities (LMI's) based on a test where the vertices of the parameter box were obtained by an iterative procedure. The result of the LMI's test gives a measure of performance referred to as γ that relates the effect of the disturbances on the process outputs. Finally, for the gain-scheduling part of the algorithm a set of rules was proposed to switch between the available controllers according to the current process conditions. Since every combination of the controller tuning parameters results in a different value of γ, an optimization problem was proposed to minimize γ with respect to the tuning parameters. Accordingly, for the proposed controller it was ensured that the effect of the disturbances on the output variables was kept to its minimum. A bioreactor case study was presented to show the benefits of the proposed algorithm. For comparison purposes a non-robust linear MPC was also designed. The results show that the proposed algorithm has a clear advantage in terms of performance as compared to non-robust linear MPC techniques. The second controller proposed in this work is a robust nonlinear model predictive controller (NMPC) based on an empirical Volterra series model. The benefit of using a Volterra series model for this case is that its structure can be split in two sections that account for the nominal and uncertain parameter values. Similar to the previously proposed gain-scheduled controller the model parameters were obtained from input-output data. After identifying the Volterra model, an interconnection matrix and its corresponding uncertainty description were found. The interconnection matrix relates the process inputs and outputs and is built according to the type of cost function that the controller uses. Based on the interconnection representing the system a robustness test was proposed based on a structured singular value norm calculation (SSV). The test is based on a min-max formulation where the worst possible closed-loop error is minimized with respect to the manipulated variables. Additional factors that were considered in the cost function were: manipulated variables weighting, manipulated variables restrictions and a terminal condition. To show the benefits of this controller two case studies were considered, a single-input-single-output (SISO) and a multiple-input-multiple-output (MIMO) process. Both case studies show that the proposed controller is able to control the process. The results showed that the controller could efficiently track set-points in the presence of disturbances while complying with the saturation limits imposed on the manipulated variables. This controller was also compared against a non-robust linear MPC, non-robust NMPC and non-robust first-principles NMPC. These comparisons were performed for different levels of uncertainty and for different values of the suppression or control actions weights. It was shown through these comparisons that a tradeoff exists between nominal performance and robustness to model error. Thus, for larger weights the controller is less aggressive resulting in more sluggish performance but less sensitivity to model error thus resulting in smaller differences between the robust and non-robust schemes. On the other hand when these weights are smaller the controller is more aggressive resulting in better performance at the nominal operating conditions but also leading to larger sensitivity to model error when the system is operated away from nominal conditions. In this case, as a result of this increased sensitivity to model error, the robust controller is found to be significantly better than the non-robust one.

This research work proposes two robust empirical model-based predictive control algorithms for nonlinear processes. Chemical process are generally highly nonlinear thus predictive control algorithms that explicitly account for the nonlinearity of the process are expected to provide better closed-loop performance as compared to algorithms based on linear models. Two types of models can be considered for control: first-principles and empirical. Empirical models were chosen for the proposed algorithms for the following reasons: (i) they are less complex for on-line optimization, (ii) they are easy to identify from input-output data and (iii) their structure is suitable for the formulation of robustness tests. One of the key problems of every model that is used for prediction within a control strategy is that some model parameters cannot be known accurately due to measurement noise and/or error in the structure of the assumed model. In the robust control approach it is assumed that processes can be represented by models with parameters' values that are assumed to lie between a lower and upper bound or equivalently, that these parameters can be represented by a nominal value plus uncertainty. When this uncertainty in control parameters is not considered by the controller the control actions might be insufficient to effectively control the process and in some extreme cases the closed-loop may become unstable. Accordingly, the two robust control algorithms proposed in the current work explicitly account for the effect of uncertainty on stability and closed-loop performance. The first proposed controller is a robust gain-scheduling model predictive controller (MPC). In this case the process is represented within each operating region by a state-affine model obtained from input-output data. The state-affine model matrices are used to obtain a state-space based MPC for every operating region. By combining the state-affine, disturbance and controller equations a closed-loop representation was obtained. Then, the resulting mathematical representation was tested for robustness with linear matrix inequalities (LMI's) based on a test where the vertices of the parameter box were obtained by an iterative procedure. The result of the LMI's test gives a measure of performance referred to as γ that relates the effect of the disturbances on the process outputs. Finally, for the gain-scheduling part of the algorithm a set of rules was proposed to switch between the available controllers according to the current process conditions. Since every combination of the controller tuning parameters results in a different value of γ, an optimization problem was proposed to minimize γ with respect to the tuning parameters. Accordingly, for the proposed controller it was ensured that the effect of the disturbances on the output variables was kept to its minimum. A bioreactor case study was presented to show the benefits of the proposed algorithm. For comparison purposes a non-robust linear MPC was also designed. The results show that the proposed algorithm has a clear advantage in terms of performance as compared to non-robust linear MPC techniques. The second controller proposed in this work is a robust nonlinear model predictive controller (NMPC) based on an empirical Volterra series model. The benefit of using a Volterra series model for this case is that its structure can be split in two sections that account for the nominal and uncertain parameter values. Similar to the previously proposed gain-scheduled controller the model parameters were obtained from input-output data. After identifying the Volterra model, an interconnection matrix and its corresponding uncertainty description were found. The interconnection matrix relates the process inputs and outputs and is built according to the type of cost function that the controller uses. Based on the interconnection representing the system a robustness test was proposed based on a structured singular value norm calculation (SSV). The test is based on a min-max formulation where the worst possible closed-loop error is minimized with respect to the manipulated variables. Additional factors that were considered in the cost function were: manipulated variables weighting, manipulated variables restrictions and a terminal condition. To show the benefits of this controller two case studies were considered, a single-input-single-output (SISO) and a multiple-input-multiple-output (MIMO) process. Both case studies show that the proposed controller is able to control the process. The results showed that the controller could efficiently track set-points in the presence of disturbances while complying with the saturation limits imposed on the manipulated variables. This controller was also compared against a non-robust linear MPC, non-robust NMPC and non-robust first-principles NMPC. These comparisons were performed for different levels of uncertainty and for different values of the suppression or control actions weights. It was shown through these comparisons that a tradeoff exists between nominal performance and robustness to model error. Thus, for larger weights the controller is less aggressive resulting in more sluggish performance but less sensitivity to model error thus resulting in smaller differences between the robust and non-robust schemes. On the other hand when these weights are smaller the controller is more aggressive resulting in better performance at the nominal operating conditions but also leading to larger sensitivity to model error when the system is operated away from nominal conditions. In this case, as a result of this increased sensitivity to model error, the robust controller is found to be significantly better than the non-robust one.

This thesis presents a robust nonlinear model predictive controller (RNMPC), nominal nonlinear model predictive controller (NMPC) and single-loop proportional-integral-derivative (PID) controllers that are applied to a nonlinear model of a run-of-mine (ROM) ore milling circuit. The model consists of nonlinear modules for the individual process units of the milling circuit (such as the mill, sump and cyclone), which allow arbitrary milling circuit configurations to be modelled easily. This study aims to cast a complex problem of a ROM ore milling circuit into an RNMPC framework without losing the flexibility of the modularised nonlinear model and implement the RNMPC using open-source software modules. The three controllers are compared in a simulations study to determine the performance of the controllers subject to severe disturbances and model parameter variations. The disturbances include changes to the feed ore hardness, changes in the feed ore size distributions and spillage water being added to the sump. The simulations show that the RNMPC and NMPC perform better than the PID controllers with regard to the economic objectives, assuming full-state feedback is available, especially when actuator constraints become active. The execution time of the RNMPC, however, is much too long for real-time implementation and would require further research to improve the efficiency of the implementation. / Thesis (PhD)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

Increased safety and productivity are driving factors for the trend in the mining industry where equipment and machines increasingly get automated. An example is the load-haul-dump vehicle, which is a machine that is used for transport of ore in underground mines. The cyclic load-haul-dump process is well suited for automation and automated loaders are commercially available today. Recent advances in autonomous driving have raised questions if there are efficiency gains that can be made by improving the path following algorithms that are used in the control. The aim of this thesis is to investigate the usage of model predictive control for path following for center-articulated mining vehicles. Two path following nonlinear model predictive controllers are designed and implemented. One controller is based on an error dynamics model, formulated as a regulation problem and implemented with the open source NMPC-library GRAMPC. The second controller is based on a kinematic model, formulated as a reference tracking NMPC problem and implemented using the embedded-MPC software tool FORCESPRO. The controllers are simulated on the same hardware that is used in real load-haul-dump vehicles, in a simulation environment provided by Epiroc Rock Drills AB. The results from the simulations show that both controllers can successfully follow a path, with a similar level of path error and less aggressive control actions compared to the current path following controller. The implemented controllers perform the control computations within a range of milliseconds on the embedded hardware, which is fast enough for real-time operation of the load-haul-dump vehicle.

This thesis focuses on the possibilities of application of nonlinear model predictive control for electric drives. Specifically, for drives with a permanent magnet synchronous motor. The thesis briefly describes the properties of this type of drive and presents its mathematical model. After that, a nonlinear model of predictive control and methods of nonlinear optimization, which form the basis for the controller output calculation, are described. As it is used in the proposed algorithm, the Active set method is described in more detail. The thesis also includes simulation experiments focusing on the choice of the objective function on the ability to control the drive. The same effect is examined for the different choices of the length of the prediction horizon. The end of the thesis is dedicated to the comparison between the proposed algorithm and commonly used field oriented control. The computational demands of the proposed algorithm are also measured and compared to the used sampling time.

Les dernières années ont permis des développements très rapides, tant au niveau de l’élaboration que de l’application, d’algorithmes de commande prédictive non linéaire (CPNL), avec une gamme relativement large de réalisations industrielles. Un des obstacles les plus significatifs rencontré lors du développement de cette commande est lié aux incertitudes sur le modèle du système. Dans ce contexte, l’objectif principal de cette thèse est la conception de lois de commande prédictives non linéaires robustes vis-à-vis des incertitudes sur le modèle. Classiquement, cette synthèse peut s’obtenir via la résolution d’un problème d’optimisation min-max. L’idée est alors de minimiser l’erreur de suivi de la trajectoire optimale pour la pire réalisation d'incertitudes possible. Cependant, cette formulation de la commande prédictive robuste induit une complexité qui peut être élevée ainsi qu’une charge de calcul importante, notamment dans le cas de systèmes multivariables, avec un nombre de paramètres incertains élevé. Pour y remédier, une approche proposée dans ces travaux consiste à simplifier le problème d’optimisation min-max, via l’analyse de sensibilité du modèle vis-à-vis de ses paramètres afin d’en réduire le temps de calcul. Dans un premier temps, le critère est linéarisé autour des valeurs nominales des paramètres du modèle. Les variables d’optimisation sont soit les commandes du système soit l’incrément de commande sur l’horizon temporel. Le problème d’optimisation initial est alors transformé soit en un problème convexe, soit en un problème de minimisation unidimensionnel, en fonction des contraintes imposées sur les états et les commandes. Une analyse de la stabilité du système en boucle fermée est également proposée. En dernier lieu, une structure de commande hiérarchisée combinant la commande prédictive robuste linéarisée et une commande par mode glissant intégral est développée afin d’éliminer toute erreur statique en suivi de trajectoire de référence. L'ensemble des stratégies proposées est appliqué à deux cas d'études de commande de bioréacteurs de culture de microorganismes. / The last few years have led to very rapid developments, both in the formulation and the application of Nonlinear Model Predictive Control (NMPC) algorithms, with a relatively wide range of industrial achievements. One of the most significant challenges encountered during the development of this control law is due to uncertainties in the model of the system. In this context, the thesis addresses the design of NMPC control laws robust towards model uncertainties. Usually, the above design can be achieved through solving a min-max optimization problem. In this case, the idea is to minimize the tracking error for the worst possible uncertainty realization. However, this robust approach tends to become too complex to be solved numerically online, especially in the case of multivariable systems with a large number of uncertain parameters. To address this shortfall, the proposed approach consists in simplifying the min-max optimization problem through a sensitivity analysis of the model with respect to its parameters, in order to reduce the calculation time. First, the criterion is linearized around the model parameters nominal values. The optimization variables are either the system control inputs or the control increments over the prediction horizon. The initial optimization problem is then converted either into a convex optimization problem, or a one-dimensional minimization problem, depending on the nature of the constraints on the states and commands. The stability analysis of the closed-loop system is also addressed. Finally, a hierarchical control strategy is developed, that combines a robust model predictive control law with an integral sliding mode controller, in order to cancel any tracking error. The proposed approaches are applied through two case studies to the control of microorganisms culture in bioreactors.

No / A novel threefold optimization algorithm is proposed to simultaneously solve the nonlinear model predictive control and dynamic real-time optimization for batch processes while optimizing the batch operation time. Object-oriented programming and parallel computing are exploited to make the algorithm effective to handle industrial cases. A well-known literature case is selected to validate the algorithm.

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.

The world's energy demand has been rapidly increasing and is projected to continue growing for at least the next two decades. With increasing global energy demand and competition from renewable energy, the oil and gas industry is striving for more efficient petroleum production. Many technical breakthroughs have enabled the drilling industry to expand the exploration to more difficult drilling such as deepwater drilling and multilateral directional drilling. For example, managed pressure drilling (MPD) offers ceaseless operation with multiple manipulated variables (MV) and wired drill pipe (WDP) provides two-way, high-speed measurements from bottom hole and along-string sensors. These technologies have maximum benefit when applied in an automation system or as a real-time advisory tool. The objective of this study is to investigate the benefit of nonlinear model-based control and estimation algorithms with various types of models. This work presents a new simplified flow model (SFM) for bottomhole pressure (BHP) regulation in MPD operations. The SFM is embedded into model-based control and estimation algorithms that use model predictive control (MPC) and moving horizon estimation (MHE), respectively. This work also presents a new Hammerstein-Wiener nonlinear model predictive controller for BHP regulation. Hammerstein-Wiener models employ input and output static nonlinear blocks before and after linear dynamics blocks to simplify the controller design. The control performance of the new Hammerstein-Wiener nonlinear controller is superior to conventional PID controllers in a variety of drilling scenarios. Conventional controllers show severe limitations in MPD because of the interconnected multivariable and nonlinear nature of drilling operations. BHP control performance is evaluated in scenarios such as drilling, pipe connection, kick attenuation, and mud density displacement and the efficacy of the SFM and Hammerstein-Wiener models is tested in various control schemes applicable to both WDP and mud pulse systems. Trusted high-fidelity drilling simulators are used to simulate well conditions and are used to evaluate the performance of the controllers using the SFM and Hammerstein-Wiener models. The comparison between non-WDP (semi-closed loop) and WDP (full-closed loop) applications validates the accuracy of the SFM under the set of conditions tested and confirms comparability with model-based control and estimation algorithms. The SFM MPC maintains the BHP within ± 1 bar of the setpoint for each investigated scenario, including for pipe connection and mud density displacement procedures that experience a wider operation range than normal drilling.