Model free real-time optimization for vapor compression systems

A vapor compression system's optimal input settings vary according to changes in environmental conditions. Tracking these optimal input trajectories can be challenging when insufficient information for a reliable system model is available. An alternative set of optimization approaches use system measurements. This thesis focuses on one such approach, extremum seeking control, which uses performance index measurements to determine optimal system settings. Forgoing system model knowledge and relying exclusively on data allows an optimization approach to function well on many different plants. However, this added adaptivity comes at a performance cost. Using prior system model knowledge can be helpful for ensuring that a controller design works from the start of operation and inputs can be changed as soon as information about environmental conditions is updated. By contrast, data based methods may require the control designer to spend a time generating data in order to obtain enough information about the system to make good decisions online. A central theme of this work is addressing the trade off between using prior system model knowledge and ensuring sufficient adaptability of the extremum seeking optimization approach. Two main factors in the extremum seeking design are considered: the choice of extremum seeking control law and the choice of extremum seeking control input. Extremum seeking control laws come from the field of mathematical optimization; this thesis considers the pros and cons of choosing between gradient descent and Newton descent. Both simulations and experimental results show that while Newton descent extremum seeking is less reliant on model knowledge, but slower to find optimal inputs than gradient descent extremum seeking. Because of extremum seeking's adaptability to different plants, many different inputs can be chosen for implementation. However, using an approach known as self-optimizing control, knowledge about the plant's behavior can help choose set points with optimal values that are insensitive to changes in environmental conditions. Finding these special inputs turns the input tracking problem into a regulation problem. Both simulation and experimental results confirm that combining self-optimizing control and extremum seeking control can help improve tracking even as environmental conditions change

Modélisation dynamique et commande optimale d'un système de réfrigération à base d'éjecteur

Recently, the ejector-based refrigeration system (ERS) has been widely used in the cooling industry as an appropriate alternative to the compressor-based cooling systems. However, the advantages of ERS such as the reliable operation and low operation and maintenance costs are overshadowed by its low efficiency and design complexity. In this context, this thesis presents the efforts to develop a control model enabling the ERS to operate in its optimal operational conditions. The extensive experimental studies of ERS revealed that at a fixed condenser inlet condition, there exists an optimal primary stream mass flow rate (generating pressure) that simultaneously maximizes the compression ratio (Cr) and exergy efficiency and minimizes the evaporating pressure. Then, the steady state models of the heat exchangers were developed and used to investigate the influence of the increase in generating pressure on the coefficient of performance (COP) of the system and it showed that increasing the generating pressure reduces the COP, linearly. In order to predict the choking regime of the ejector and explain the reasons of observed physical phenomenon, the 1D model of a fixed geometry ejector installed within an R245fa ERS was developed. The developed model demonstrated that the ejector operates in the subcritical mode when the generating pressure is below the Cr optimum point, while it operates in critical mode at or above the optimum generating pressure. Next, a dynamic model of the ERS was built to evaluate the ERS transient response to an increase in the primary stream mass flow rate. Since the ERS dynamics is mainly dominated by the thermal dynamics of the heat exchangers, the dynamic models of the heat exchangers were developed using the moving boundary approach and connected to the developed models of the ejector and steady state models of the pump and expansion valve to build a single dynamic model of the system. The built dynamic model of an ERS was used to estimate the time response of the system in the absence of accurate experimental data of the system’s dynamics. Finally, a control model was designed to drive an ERS towards its optimal operation condition. A self-optimizing, model-free control strategy known as Extremum seeking control (ESC) was adopted to minimize evaporating pressure in a fixed condenser thermal fluid inlet condition. The innovative ESC model named batch phasor ESC (BPESC) was proposed based on estimating the gradient by evaluating the phasor of the output, in batch time. The simulation results indicated that the designed BPESC model can seek and find the optimum evaporating pressure with good performance in terms of predicting the steady state optimal values and the convergence rates.Récemment, le système de réfrigération à éjecteur (SRE) a été largement utilisé dans l'industrie du refroidissement en tant que solution de remplacement appropriée aux systèmes de refroidissement à compresseur. Cependant, les avantages du SRE, tels que le fonctionnement fiable et les faibles couts d'exploitation et de maintenance, sont éclipsés par son faible rendement et sa complexité de conception. Dans ce contexte, ce projet de recherche de doctorat a détaillé les efforts déployés pour développer une stratégie de commande permettant au système de fonctionner dans ses conditions opérationnelles optimales. Les études expérimentales approfondies du SRE ont révélé que, dans une condition d'entrée de condensateur constante, il existe un débit massique optimal du flux primaire (générant une pression) qui maximise simultanément le taux de compression (Cr) et l'efficacité exergétique, et minimise la pression d’évaporation. Ensuite, les modèles à l’état d’équilibre des échangeurs de chaleur ont été développés et utilisés pour étudier l’influence de l’augmentation de la pression générée sur le coefficient de performance (COP) du système et il en ressort que l'augmentation de la pression génératrice réduit le COP de manière linéaire. Afin de prédire le régime d'étouffement de l'éjecteur et d'expliquer les raisons du phénomène physique observé, le modèle 1D d'un éjecteur à géométrie fixe installé dans un système SRE R245fa a été développé. Le modèle développé a démontré que l'éjecteur fonctionne en mode sous-critique lorsque la pression génératrice est inférieure au point optimal de Cr, alors qu'il fonctionne en mode critique à une pression égale ou supérieure à la pression génératrice optimale. Ensuite, un modèle dynamique du SRE a été développé pour étudier la réponse transitoire du SRE lors d’une augmentation du débit massique du flux primaire. Puisque la dynamique du SRE est principalement dominée par la dynamique thermique des échangeurs de chaleur, les modèles dynamiques des échangeurs de chaleur ont été développés à l'aide de l'approche des limites mobiles et connectés aux modèles développés de l'éjecteur et des modèles à l'état stationnaire de la pompe et de la vanne un seul modèle dynamique du système. En l’absence de données expérimentales précises sur la dynamique d’un système SRE, le modèle dynamique développé du SRE a été simulé numériquement pour étudier sa réponse temporelle. Enfin, une stratégie de commande extrêmale (ESC) a été élaboré pour régler automatiquement le SRE à ses conditions de fonctionnement optimales, c’est-à-dire pour trouver la vitesse de la pompe qui minimise la pression dans des conditions d'entrée de condenseur fixes. Afin de proposer une ESC implémentable en temps discret sur une installation réelle sujette à un bruit de mesure important et un traitement hors-ligne par trame, une nouvelle commande extrémale basée sur une approche par phaseur avec une procédure de traitement de signal par trame (BPESC) a été développée et simulée avec le modèle numérique. Les résultats de la simulation ont indiqué que le modèle BPESC peut trouver la vitesse optimale de la pompe avec de bonnes performances en termes de précision et de vitesse de convergence

Investigation of Some Self-Optimizing Control Problems for Net-Zero Energy Buildings

Green buildings are sustainable buildings designed to be environmentally responsible and resource efficient. The Net-Zero Energy Building (NZEB) concept is anchored on two pillars: reducing the energy consumption and enhancing the local energy generation. In other words, efficient operation of the existing building equipment and efficient power generation of building integrated renewable energy sources are two important factors of NZEB development. The heating, ventilation and air conditioning (HVAC) systems are an important class of building equipment that is responsible for large portion of building energy usage, while the building integrated photovoltaic (BIPV) system is well received as the key technology for local generation of clean power. Building system operation is a low-investment practice that aims low operation and maintenance cost. However, building HVAC and BIPV are systems subject to complicated intrinsic processes and highly variable environmental conditions and occupant behavior. Control, optimization and monitoring of such systems desire simple and effective approaches that require the least amount of model information and the use of smallest number but most robust sensor measurements. Self-optimizing control strategies promise a competitive platform for control, optimization and control integrated monitoring for building systems, and especially for the development of cost-effective NZEB. This dissertation study endorses this statement with three aspects of work relevant to building HVAC and BIPV, which could contribute several small steps towards the ramification of the self-optimizing control paradigm. This dissertation study applies self-optimizing control techniques to improve the energy efficiency of NZEB from two aspects. First, regarding the building HVAC efficiency, the dither based extremum seeking control (DESC) scheme is proposed for energy efficient operation of the chilled-water system typically used in the commercial building ventilation and air conditioning (VAC) systems. To evaluate the effectiveness of the proposed control strategy, Modelica based dynamic simulation model of chilled water chiller-tower plant is developed, which consists of a screw chiller and a mechanical-draft counter-flow wet cooling tower. The steady-state performance of the cooling tower model is validated with the experimental data in a classic paper and good agreement is observed. The DESC scheme takes the total power consumption of the chiller compressor and the tower fan as feedback, and uses the fan speed setting as the control input. The inner loop controllers for the chiller operation include two proportional-integral (PI) control loops for regulating the evaporator superheat and the chilled water temperature. Simulation was conducted on the whole dynamic simulation model with different environment conditions. The simulation results demonstrated the effectiveness of the proposed ESC strategy under abrupt changes of ambient conditions and load changes. The potential for energy savings of these cases are also evaluated. The back-calculation based anti-windup ESC is also simulated for handling the integral windup problem due to actuator saturation. Second, both maximum power point tracking (MPPT) and control integrated diagnostics are investigated for BIPV with two different extremum seeking control strategies, which both would contribute to the reduction of the cost of energy (COE). In particular, the Adaptive Extremum Seeking Control (AESC) is applied for PV MPPT, which is based on a PV model with known model structure but unknown nonlinear characteristics for the current-voltage relation. The nonlinear uncertainty is approximated by a radial basis function neural network (RBFNN). A Lyapunov based inverse optimal design technique is applied to achieve parameter estimation and gradient based extremum seeking. Simulation study is performed for scenarios of temperature change, irradiance change and combined change of temperature and irradiance. Successful results are observed for all cases. Furthermore, the AESC simulation is compared to the DESC simulation, and AESC demonstrates much faster transient responses under various scenarios of ambient changes. Many of the PV degradation mechanisms are reflected as the change of the internal resistance. A scheme of detecting the change of PV internal shunt resistance is proposed using the available signals in the DESC based MPPT with square-wave dither. The impact of the internal resistance on the transient characteristics of step responses is justified by using the small-signal transfer function analysis. Simulation study is performed for both the single-string and multi-string PV examples, and both cases have demonstrated successful results. Monotonic relationship between integral error indices and the shunt internal resistance is clearly observed. In particular, for the multi-string, the inter-channel coupling is weak, which indicates consistent monitoring for multi-string operation. The proposed scheme provides the online monitoring ability of the internal resistance condition without any additional sensor, which benefits further development of PV degradation detection techniques

Safe Zeroth-Order Optimization Using Quadratic Local Approximations

This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging towards a KKT primal-dual pair. Assuming to have prior knowledge on the smoothness of the unknown objective and constraints, we propose a novel zeroth-order method that iteratively computes quadratic approximations of the constraint functions, constructs local feasible sets and optimizes over them. Under some mild assumptions, we prove that this method returns an $\eta$-KKT pair (a property reflecting how close a primal-dual pair is to the exact KKT condition) within $O({1}/{\eta^{2}})$ iterations. Moreover, we numerically show that our method can achieve faster convergence compared with some state-of-the-art zeroth-order approaches. The effectiveness of the proposed approach is also illustrated by applying it to nonconvex optimization problems in optimal control and power system operation.Comment: arXiv admin note: text overlap with arXiv:2211.0264

Dynamic modeling and control strategies of organic Rankine cycle systems: Methods and challenges

Organic Rankine cycle systems are suitable technologies for utilization of low/medium-temperature heat sources, especially for small-scale systems. Waste heat from engines in the transportation sector, solar energy, and intermittent industrial waste heat are by nature transient heat sources, making it a challenging task to design and operate the organic Rankine cycle system safely and efficiently for these heat sources. Therefore, it is of crucial importance to investigate the dynamic behavior of the organic Rankine cycle system and develop suitable control strategies. This paper provides a comprehensive review of the previous studies in the area of dynamic modeling and control of the organic Rankine cycle system. The most common dynamic modeling approaches, typical issues during dynamic simulations, and different control strategies are discussed in detail. The most suitable dynamic modeling approaches of each component, solutions to common problems, and optimal control approaches are identified. Directions for future research are provided. The review indicates that the dynamics of the organic Rankine cycle system is mainly governed by the heat exchangers. Depending on the level of accuracy and computational effort, a moving boundary approach, a finite volume method or a two-volume simplification can be used for the modeling of the heat exchangers. From the control perspective, the model predictive controllers, especially improved model predictive controllers (e.g. the multiple model predictive control, switching model predictive control, and non-linear model predictive control approach), provide excellent control performance compared to conventional control strategies (e.g. proportional–integral controller, proportional–derivative controller, and proportional–integral–derivative controllers). We recommend that future research focuses on the integrated design and optimization, especially considering the design of the heat exchangers, the dynamic response of the system and its controllability

Fuel Cell Renewable Hybrid Power Systems

Climate change is becoming visible today, and so this book—through including innovative solutions and experimental research as well as state-of-the-art studies in challenging areas related to sustainable energy development based on hybrid energy systems that combine renewable energy systems with fuel cells—represents a useful resource for researchers in these fields. In this context, hydrogen fuel cell technology is one of the alternative solutions for the development of future clean energy systems. As this book presents the latest solutions, readers working in research areas related to the above are invited to read it

Zwei-Freiheitsgrade-Struktur zur robusten Radschlupfregelung für Antiblockiersysteme

Die Regelung des gebremsten Rades eines gummibereiften Fahrzeugs stellt seit vier Jahrzehnten Generationen von Ingenieuren vor schwierige Herausforderungen und es wurden bereits zahlreiche Ansätze dazu erdacht und implementiert. Eine wesentliche Herausforderung der Regelstrecke ist die mit der Fahrzeuggeschwindigkeit skalierte Dynamik, wenn der Radschlupf als relative Geschwindigkeitsdifferenz zwischen Fahrzeug und Radaufstandspunkt geregelt werden soll, sowie die hohe Nichtlinearität der Reifenkraftschlusskennlinie in Abhängigkeit des Schlupfes. In der tatsächlichen Implementierung kommt darüber hinaus noch der Abtastcharakter der Regelung auf einem digitalen Mikrocontroller hinzu, der im Rahmen dieser Arbeit systematisch in den Entwurf mit einbezogen werden soll. Dazu wird zuerst ein physikalisches Modell des Fahrzeugs einschließlich der Bremsenaktorik aufgestellt und dieses anschließend mittels Strukturmaßen untersucht sowie Schlüsse für die notwendige Reglerstruktur aus dieser Untersuchung abgeleitet. In dieser Arbeit wird ein modellbasierter Ansatz zur Regelung des Radschlupfes vorgeschlagen, der aus einer Zwei-Freiheitsgrade-Struktur mit nichtlinearer modellbasierter Vorsteuerung und einer robust entworfenen Rückführung mittels Gain-Scheduling besteht. Für die Vorsteuerung wird ein Ansatz über die exakte Eingangs-/Ausgangslinearisierung gewählt, mit dem sich das nichtlineare System bezogen auf das Ein-/Ausgangsverhalten wie ein lineares System regeln lässt. Für die Rückführung wird ein Gain-Scheduling über die Schedulingparameter Fahrzeuggeschwindigkeit und Radschlupf durchgeführt, um den durch die hohe Parameterunsicherheit in der Reifenkennline und die reziproke Abhängigkeit der Systemdynamik von der Geschwindigkeit variablen Parameterbereich in kleinere Unsicherheitsbereiche zu unterteilen, für die anschließend ein linearer Regler mit fester Struktur über die Methode der robusten Polbereichsvorgabe entworfen wird. Basierend auf diesem Schlupfregler wird in einem zweiten Schritt ein Algorithmus verwendet, der in der Lage ist, das Maximum der Reibwertkennlinie einzuregeln, um den verfügbaren Kraftschluss bestmöglich auszunutzen, das sog. Extremum Seeking. Der gesamte Reglerentwurf erfolgt dabei rein zeitdiskret, um die charakteristischen Effekte der Diskretisierung bei einer digitalen Regelung behandeln zu können. Die vorgeschlagene Reglerstruktur wird dabei in Simulationen für unterschiedliche Reibwerte der modellbasierten Vorsteuerung und der realen Strecke untersucht und dabei gezeigt, dass die Regelung mit Extremwertsuche auch in der Lage ist, das Maximum zu finden, wenn die Reibwertkurve ihr Maximum verändert