Enhanced matching perturbation attenuation with discrete-time implementations of sliding-mode controllers

International audienceContinuous-time Sliding Mode Control yields when embedded into Filippov's mathematical framework, closed-loop systems with a set-valued controller, represented by differential inclusions. In particular, besides finite-time convergence to the sliding surface and robustness to matched disturbances, such controllers allow an exact compensation of the disturbance on the sliding manifold. In other words, the set-valued input is the exact copy of minus the perturbation. A novel discretization methodology has been recently introduced by the authors, which is based on an implicit discretization of the Filippov's differential inclusion, which in theory totally suppresses the chattering due to the discretization (numerical chattering). In this work we propose an extension of the implicit method, enhancing the perturbation attenuation (in terms of chattering) by using previous values of the set-valued input. This allows to estimate on-line the unknown perturbation, with a time delay due to the sampling. Simulation results illustrate the effectiveness of the method

Analyse et implémentation du contrôle par modes glissants en temps discret

This work is dedicated to the discrete-time version of Sliding Mode Control, a well-known technique in the field of Automatic Control.The main contribution of this research effort is the use of an implicit discretization instead of an explicit one.The main contributions in the three domains of Automatic Control are as follows: analysis of the implicitly discretized sliding mode controllers (many properties of the continuous-time version are preserved, or have very similar counterparts). Simulations were run using a new Control toolbox in Siconos, a platform dedicated to the simulation of non-smmooth dynamical system. Finally, experiments confirm the superiority of the implicit discrete-time sliding mode controllers.Cette thèse concerne la commande par modes glissants en temps discret. L'axe principal de ce travail fut l'utilisation d'une méthode de discrétisation implicite et non explicite pour la partir discontinue de la commande. Les contributions majeures sont : l'analyse de la commande par mode glissant discrétisée implicitement (stabilité, rejet de perturbations, ...). Des simulations, réalisées à l'aide d'un nouveau module "Control" dans la plateforme Siconos, illustrent certains résultats théoriques. Enfin des essais expérimentaux confirment la supériorité de la discrétisation implicite sur celle de l'explicite

Vibration attenuation by mass redistribution

A nontraditional approach for active structural vibration attenuation was proposed using mass redistribution. The focus was on pendulum structures where the objective was to examine the effectiveness of mass reconfiguration along or within a structure to attenuate its vibrational energy. The mechanics associated with a translating mass along a rotating structure give rise to a Coriolis inertia force which either opposes or increases angular oscillations, thereby producing positive or negative damping, respectively. A strategy of cycling the mass to maximize attenuation and minimize amplification required the mass be moved at twice the frequency of the structural vibrations and be properly coordinated with the angular oscillations. The desired coordination involved moving the mass away from the pivot as the pendulum nears its vertical position and moving the mass towards the pivot when the pendulum nears its maximum angular excursion. System mass reconfiguration was analyzed by studying various mass displacement profiles including sinusoidal, piece-wise constant velocity and modified proportional and derivative action patterns. These strategies were optimized for various time intervals to maximize the rate of energy attenuation or minimize the final energy state. For small amplitude oscillations with sinusoidal mass motion, the dynamic behavior was modeled by Mathieu-Hill equations to explain the beating phenomenon that occurred when the frequency of the mass motion remained constant. Several control systems were designed to generate aforementioned mass reconfiguration profiles. The methodologies included human operator, modified proportional and derivative action, knowledge or rule based and artificial neural network controllers. The human operator system improved with experience and was the most effective. Other systems depended on the chosen parameterization or the implementation of self-adjusting parameters. Several unique tools were developed during the course of this research, as referenced herein

Investigations of Model-Free Sliding Mode Control Algorithms including Application to Autonomous Quadrotor Flight

Sliding mode control is a robust nonlinear control algorithm that has been used to implement tracking controllers for unmanned aircraft systems that are robust to modeling uncertainty and exogenous disturbances, thereby providing excellent performance for autonomous operation. A significant advance in the application of sliding mode control for unmanned aircraft systems would be adaptation of a model-free sliding mode control algorithm, since the most complex and time-consuming aspect of implementation of sliding mode control is the derivation of the control law with incorporation of the system model, a process required to be performed for each individual application of sliding mode control. The performance of four different model-free sliding mode control algorithms was compared in simulation using a variety of aerial system models and real-world disturbances (e.g. the effects of discretization and state estimation). The two best performing algorithms were shown to exhibit very similar behavior. These two algorithms were implemented on a quadrotor (both in simulation and using real-world hardware) and the performance was compared to a traditional PID-based controller using the same state estimation algorithm and control setup. Simulation results show the model-free sliding mode control algorithms exhibit similar performance to PID controllers without the tedious tuning process. Comparison between the two model-free sliding mode control algorithms showed very similar performance as measured by the quadratic means of tracking errors. Flight testing showed that while a model-free sliding mode control algorithm is capable of controlling realworld hardware, further characterization and significant improvements are required before it is a viable alternative to conventional control algorithms. Large tracking errors were observed for both the model-free sliding mode control and PID based flight controllers and the performance was characterized as unacceptable for most applications. The poor performance of both controllers suggests tracking errors could be attributed to errors in state estimation, which effectively introduce unknown dynamics into the feedback loop. Further testing with improved state estimation would allow for more conclusions to be drawn about the performance characteristics of the model-free sliding mode control algorithms

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Indirect adaptive higher-order sliding-mode control using the certainty-equivalence principle

Seit den 50er Jahren werden große Anstrengungen unternommen, Algorithmen zu entwickeln, welche in der Lage sind Unsicherheiten und Störungen in Regelkreisen zu kompensieren. Früh wurden hierzu adaptive Verfahren, die eine kontinuierliche Anpassung der Reglerparameter vornehmen, genutzt, um die Stabilisierung zu ermöglichen. Die fortlaufende Modifikation der Parameter sorgt dabei dafür, dass strukturelle Änderungen im Systemmodell sich nicht auf die Regelgüte auswirken. Eine deutlich andere Herangehensweise wird durch strukturvariable Systeme, insbesondere die sogenannte Sliding-Mode Regelung, verfolgt. Hierbei wird ein sehr schnell schaltendes Stellsignal für die Kompensation auftretender Störungen und Modellunsicherheiten so genutzt, dass bereits ohne besonderes Vorwissen über die Störeinflüsse eine beachtliche Regelgüte erreicht werden kann. Die vorliegende Arbeit befasst sich mit dem Thema, diese beiden sehr unterschiedlichen Strategien miteinander zu verbinden und dabei die Vorteile der ursprünglichen Umsetzung zu erhalten. So benötigen Sliding-Mode Verfahren generell nur wenige Informationen über die Störung, zeigen jedoch Defizite bei Unsicherheiten, die vom Systemzustand abhängen. Auf der anderen Seite können adaptive Regelungen sehr gut parametrische Unsicherheiten kompensieren, wohingegen unmodellierte Störungen zu einer verschlechterten Regelgüte führen. Ziel dieser Arbeit ist es daher, eine kombinierte Entwurfsmethodik zu entwickeln, welche die verfügbaren Informationen über die Störeinflüsse bestmöglich ausnutzt. Hierbei wird insbesondere Wert auf einen theoretisch fundierten Stabilitätsnachweis gelegt, welcher erst durch Erkenntnisse der letzten Jahre im Bereich der Lyapunov-Theorie im Zusammenhang mit Sliding-Mode ermöglicht wurde. Anhand der gestellten Anforderungen werden Regelalgorithmen entworfen, die eine Kombination von Sliding-Mode Reglern höherer Ordnung und adaptiven Verfahren darstellen. Neben den theoretischen Betrachtungen werden die Vorteile des Verfahrens auch anhand von Simulationsbeispielen und eines Laborversuchs nachgewiesen. Es zeigt sich hierbei, dass die vorgeschlagenen Algorithmen eine Verbesserung hinsichtlich der Regelgüte als auch der Robustheit gegenüber den konventionellen Verfahren erzielen.Since the late 50s, huge efforts have been made to improve the control algorithms that are capable of compensating for uncertainties and disturbances. Adaptive controllers that adjust their parameters continuously have been used from the beginning to solve this task. This adaptation of the controller allows to maintain a constant performance even under changing conditions. A different idea is proposed by variable structure systems, in particular by the so-called sliding-mode control. The idea is to employ a very fast switching signal to compensate for disturbances or uncertainties. This thesis deals with a combination of these two rather different approaches while preserving the advantages of each method. The design of a sliding-mode controller normally does not demand sophisticated knowledge about the disturbance, while the controller's robustness against state-dependent uncertainties might be poor. On the other hand, adaptive controllers are well suited to compensate for parametric uncertainties while unstructured influence may result in a degraded performance. Hence, the objective of this work is to design sliding-mode controllers that use as much information about the uncertainty as possible and exploit this knowledge in the design. An important point is that the design procedure is based on a rigorous proof of the stability of the combined approach. Only recent results on Lyapunov theory in the field of sliding-mode made this analysis possible. It is shown that the Lyapunov function of the nominal sliding-mode controller has a direct impact on the adaptation law. Therefore, this Lyapunov function has to meet certain conditions in order to allow a proper implementation of the proposed algorithms. The main contributions of this thesis are sliding-mode controllers, extended by an adaptive part using the certainty-equivalence principle. It is shown that the combination of both approaches results in a novel controller design that is able to solve a control task even in the presence of different classes of uncertainties. In addition to the theoretical analysis, the advantages of the proposed method are demonstrated in a selection of simulation examples and on a laboratory test-bench. The experiments show that the proposed control algorithm delivers better performance in regard to chattering and robustness compared to classical sliding-mode controllers

Control of power converter in modern power systems

A la portada consta el nom del programa interuniversitari: Joint Doctoral Programme in Electric Energy Systems [by the] Universidad de Málaga, Universidad de Sevilla, Universidad del País Vasco/Euskal Erriko Unibertsitatea i Universitat Politècnica de CatalunyaPower system is undergoing an unpreceded paradigm shift: from centralized to distributed generation. As the renewable-based generations and battery storage systems are increasingly displacing conventional generations, it becomes more and. more difficult to maintain the stability and reliability of the grid by using only conventional generations. The main reason for the degradation of grid stability is the rapid penetration of nonconventional sources. These new generations interface with the grids through power electronics converters which are conventionally designed to maximize conversion efficiency and resource utilization. Indeed, these power converters only focus on their internal operation despite the grid conditions, which often worsens the grid operation. To overcome such a drawback, the grid-forming concept has been proposed for power converters, aiming to redesign the control of the power converters to enforce more grid-friendly behaviours such as inertia response and power oscillation damping to name a few. Despite the rich literature, actual adaptation of grid-forming controller in real-world applications is still rare because incentives for renewable power plants to provide services based on such advanced grid-forming functions were at best scarce. In the last years, however, several system operators have imposed new requirements and markets for grid-supporting services. In addition, the existing grid-forming controllers require modification to low-level control firmware of a power converter, which is often unrealistic due to the control hardware limitations as well as necessary testing and certifications. To ensure a stable operation of a grid-forming converter under adverse operating conditions, a robust voltage sensorless current controller is developed in this PhD thesis. The proposed controller is able to handle most of the possible abnormal conditions of the grid such as impedance variations, unbalanced voltage; harmonics distortion. These abnormalities of the grid are mathematically represented using equivalent linear models such that they can be used for calculating the controller gains. Linear matrix inequality techniques are also used to facilitate parameter tuning. In fact, the performance and stability of the current control loop can be determined through only two tuning parameters instead of eight parameters for a controller of a similar structure. The existing grid-forming implementations are designed considering that the control firmware of the power converter can be upgraded at will. However, modifications of the control firmware are not straightforward and cost-effective at mass scale. To overcome such a limitation, an external synchronous controller is presented in this PhD thesis. The external synchronous controller uses measurements, which are either provided by the power converter or a dedicated measurement unit, to calculate the actual active and reactive power that should be injected by the power converters in a way that the power plant acts as an aggregated grid­forming converter. As a result, any conventional power converters can be utilized for providing grid-supporting services with minimal modification to the existing infrastructure. Power converters can provide even better performance than a synchronous generator if a proper control scheme is used. In this regard, the final chapter of this PhD thesis presents the multi-rotor virtual machine implementation for grid-forming converter to boost their damping performance to power oscillations. The multi-rotor virtual machine-controller implements several virtual rotors instead of only one rotor as in typical grid-forming strategies. Since each of the virtual rotors is tuned to target a specific critical mode, the damping participation to such a mode can be increased and adjusted individually. The controllers presented in this PhD thesis are validated through simulators and experiments in the framework of the H2020 FlexiTranstore project. The results are throughout analysed to assess the control performance as well as to highlight possible implications.A medida que las generaciones basadas en energías renovables y los sistemas de almacenamiento de baterías desplazan la generación convencional, se vuelve cada vez más difícil mantener la estabilidad y confiabilidad de la red. Estas nuevas generaciones interactúan con las redes a través de convertidores de electrónica de potencia que están diseñados tradicionalmente para maximizar la eficiencia de conversión y la utilización de recursos. Estos convertidores centran su funcionamiento interno independientemente de las condiciones de la red, lo que a menudo empeora el funcionamiento de la red. Para esto, se ha propuesto el concepto de convertidores de potencia formadores de red (grid-forming), con el objetivo de rediseñar el control de los convertidores de potencia para imponer comportamientos más favorables a la red, por ejemplo, la respuesta inercial y la amortiguación de oscilaciones de potencia. No en tanto, la adaptación real del controlador grid-forming en aplicaciones del mundo real todavía es escasa debido a los pocos incentivos para que las plantas de energía renovable proporcionen servicios basados en funciones de formación de red tan avanzadas. Aunque en los últimos años, operadores de sistemas han impuesto nuevos requisitos y mercados para servicios auxiliares, los controladores grid-forming existentes requieren cambios en el firmware de control de bajo nivel de un convertidor de potencia, algo poco realista debido a las limitaciones del hardware de control, así como a las pruebas y certificaciones necesarias. En esta tesis se desarrolla un controlador de corriente robusto, sin sensor de tensión, para garantizar el funcionamiento estable de un convertidor grid-forming en condiciones de operación adversas. Este controlador es capaz de manejar la mayoría de las condiciones anormales de red, como variaciones de impedancia, tensión desequilibrada y distorsión de armónicos. Estas anomalías de la red se representan matemáticamente mediante modelos lineales equivalentes, utilizados para calcular las ganancias del controlador. También, usando técnicas de desigualdad matricial lineal para facilitar el ajuste de parámetros. De hecho, el rendimiento y la estabilidad del bucle de control de la corriente pueden determinarse mediante sólo dos parámetros de sintonización. Las implementaciones de formación de red existentes están diseñadas considerando que el firmware de control del convertidor de potencia puede actualizarse a voluntad. Sin embargo, las modificaciones del firmware de control no son sencillas ni rentables a gran escala. Por tanto, esta tesis presenta un controlador síncrono externo que utiliza las mediciones proporcionadas por el convertidor de potencia o por una unidad de medición dedicada para calcular la potencia activa y reactiva real que deben inyectar los convertidores de potencia, de forma que la central eléctrica actúe como un convertidor grid-forming agregado. Como resultado, cualquier convertidor de potencia convencional puede utilizarse para proporcionar servicios de apoyo a la red con una modificación mínima de la infraestructura existente. Los convertidores de potencia pueden ofrecer mejor rendimiento que un generador síncrono utilizando un esquema de control adecuado. El último capítulo de esta tesis presenta la implementación de una máquina virtual multirrotor para que los convertidores de red aumenten su rendimiento de amortiguación de las oscilaciones de potencia. El controlador de la máquina virtual multirrotor implementa varios rotores virtuales en lugar de un solo rotor como en las estrategias típicas de grid-forming. Dado que cada uno de los rotores virtuales está sintonizado para dirigirse a un modo crítico específico, la participación de la amortiguación a dicho modo puede aumentarse y ajustarse individualmente. Los controladores presentados en esta tesis doctoral han sido validados mediante simulaciones y experimentos en el marco del proyecto H2020 FlexiTranstore.Postprint (published version