Finite settling time stabilization for linear multivariable time-invariant discrete-time systems: An algebraic approach

The problem of Total Finite Settling Time Stabilization of linear time-invariant discrete-time systems is investigated in this thesis. This problem falls within the same area of the well-known deadbeat (time-optimal) control and in particular, constitutes a generalization of this problem. That is, instead of seeking time-optimum performance, it is required that all internal and external variables (signals) of the closed-loop system settle to a new steady state after a finite time from the application of a step change to any of its inputs and for every initial condition. The state/output deadbeat control is a special case of the Total FSTS problem. Using a mathematical and system theory framework based on sequences and the polynomial equation (algebraic) approach, we are able to tackle the FSTS problem in a unifying manner. The one-parameter (unity) feedback configuration is mainly used for the solution of the FSTS problem and FSTS related control strategies. The whole problem is reduced to the solution of a polynomial matrix Diophantine equation which guarantees not only internal stability but also internal FSTS and is further reduced to the solution of a linear algebra problem over R. This approach enables the parametrizat ion of the family of all FSTS controllers, as well as those which are causal, in a Youla-Bongiorno-Kucera type parametrization. The minimal McMillan degree FSTS problem is completely solved for vector plants and a parametrization of the FSTS controllers according to their McMillan degree is obtained. In the MIMO case bounds of the minimum McMillan degree controllers are derived and families of FSTS controllers with given lower/upper McMillan degree bounds are provided in parametric form. Having parametrized the family of all FSTS controllers, the state deadbeat regulation is treated as a special case of FSTS and complete parametrization of all the deadbeat regulators is presented. In addition, further performance criteria, or design constraints are imposed such as, FSTS tracking and/or disturbance rejection, partial assignment of controller dynamics, l1-, l∞-optimization and robustness to plant parameter variations. Finally, the Simultaneous-FSTS problem is formulated, and necessary as well as sufficient conditions for its solution are derived. Also, a two-parameter control scheme is introduced to alleviate some of the drawbacks of the one-parameter control. A parametrization of the family of FSTS controllers as well as the FSTS controllers for tracking and/or disturbance rejection is given as an illustration of the particular advantages of the two-parameter FSTS controllers

Direct Torque Control for Silicon Carbide Motor Drives

Direct torque control (DTC) is an extensively used control method for motor drives due to its unique advantages, e.g., the fast dynamic response and the robustness against motor parameters variations, uncertainties, and external disturbances. Using higher switching frequency is generally required by DTC to reduce the torque ripples and decrease stator current total harmonic distortion (THD), which however can lower the drive efficiency. Through the use of the emerging silicon carbide (SiC) devices, which have lower switching losses compared to their silicon counterparts, it is feasible to achieve high efficiency and low torque ripple simultaneously for DTC drives. To overcome the above challenges, a SiC T-type neutral point clamped (NPC) inverter is studied in this work to significantly reduce the torque and flux ripples which also effectively reduce the stator current ripples, while retaining the fast-dynamic response as the conventional DTC. The unbalanced DC-link is an intrinsic issue of the T-type inverter, which may also lead to higher torque ripple. To address this issue, a novel DTC algorithm, which only utilizes the real voltage space vectors and the virtual space vectors (VSVs) that do not contribute to the neutral point current, is proposed to achieve inherent dc-link capacitor voltage balancing without using any DC-link voltage controls or additional DC-link capacitor voltages and/or neutral point current sensors. Both dynamic performance and efficiency are critical for the interior permanent-magnet (IPM) motor drives for transportation applications. It is critical to determine the optimal reference stator flux linkage to improve the efficiency further of DTC drives and maintain the stability of the drive system, which usually obtained by tuning offline and storing in a look-up table or calculated online using machine models and parameters. In this work, the relationship between the stator flux linkage and the magnitude of stator current is analyzed mathematically. Then, based on this relationship, a perturb and observe (P&O) method is proposed to determine the optimal flux for the motor which does not need any prior knowledge of the machine parameters and offline tuning. However, due to the fixed amplitude of the injected signal the P&O algorithm suffers from large oscillations at the steady state conditions. To mitigate the drawback of the P&O method, an adaptive high frequency signal injection based extremum seeking control (ESC) algorithm is proposed to determine the optimal reference flux in real-time, leading to a maximum torque per ampere (MTPA) like approach for DTC drives. The stability analysis and key parameters selection for the proposed ESC algorithm are studied. The proposed method can effectively reduce the motor copper loss and at the same time eliminate the time consuming offline tuning effort. Furthermore, since the ESC is a model-free approach, it is robust against motor parameters variations, which is desirable for IPM motors

Design and Control of Power Converters 2019

In this book, 20 papers focused on different fields of power electronics are gathered. Approximately half of the papers are focused on different control issues and techniques, ranging from the computer-aided design of digital compensators to more specific approaches such as fuzzy or sliding control techniques. The rest of the papers are focused on the design of novel topologies. The fields in which these controls and topologies are applied are varied: MMCs, photovoltaic systems, supercapacitors and traction systems, LEDs, wireless power transfer, etc

Lead pursuit control of multiphase drives

Los accionamientos multifásicos, compuestos por una máquina eléctrica de más de tres fases alimentada por un convertidor de potencia, han atraído recientemente un importante interés en la comunidad investigadora debido a las ventajas que presentan frente a las máquinas trifásicas convencionales. Este es el caso de la mejor distribución de potencia por fase, la menor producción de armónicos en el convertidor de potencia y, la más importante, la tolerancia a fallos, lo cual significa que la máquina multifásica puede seguir funcionando cuando una o varias fases se pierden, siempre que el número restante de fases sea igual o mayor que tres. Debido a esta alta fiabilidad, los accionamientos multifásicos son especialmente adecuados para aplicaciones relacionadas con los vehículos eléctricos (terrestres, marítimos y aéreos) y las energías renovables por razones de seguridad y/o económicas. El uso de controladores avanzados y de alto rendimiento en accionamientos multifásicos es particularmente relevante, ya que las estrategias de control convencionalmente aplicadas a los accionamientos trifásicos no terminan de alcanzar un estándar en su extensión al caso multifásico. La razón es la mayor complejidad y número de variables a controlar. En este contexto, los controladores predictivos han encontrado un interesante nicho de aplicación en convertidores de potencia y accionamientos multifásicos debido a su formulación intuitiva y flexible: un modelo del sistema es usado para calcular las predicciones de las variables controladas, que luego se comparan con las referencias impuestas dentro de una función de coste. Esta estrategia permite incorporar varios objetivos de control y restricciones en el proceso de control a través de la función de coste. Sin embargo, es bien sabido que este tipo de controlador sufre de un alto coste computacional y contenido armónico de corriente que limita su aplicación en los accionamientos multifásicos. La investigación desarrollada en esta Tesis se centra en la mitigación de las limitaciones citadas siguiendo dos objetivos principales: • La incorporación de observadores de corrientes rotóricas en el controlador predictivo para mejorar así la precisión del modelo predictivo y, consecuentemente, el rendimiento del sistema de control, principalmente en términos de contenido armónico y pérdidas por conmutación en el convertidor de potencia. Un observador de Luenberger es construido para este propósito utilizando una estrategia innovadora de posicionamiento de polos en su diseño. • La introducción de un grado de libertad adicional en el controlador predictivo basado en tiempos de muestreo variables e implementado usando el concepto de lead pursuit. El resultado es un controlador novedoso que conduce a una resolución en los tiempos de conmutación más fina en comparación con las técnicas predictivas más convencionales, lo que proporciona una reducción importante en el contenido armónico. Las estrategias de control propuestas son validadas mediante simulación y experimentación utilizando un accionamiento compuesto por una máquina de inducción de cinco fases como caso de ejemplo. Los resultados y conclusiones derivadas de esta investigación han sido presentados en cinco trabajos principales publicados en revistas internacionales de alto impacto, los cuales constituyen las contribuciones de esta Tesis por compendio de artículos. Sin embargo, otros trabajos relacionados con la línea de investigación han sido también publicados en artículos de revista y conferencia y en un capítulo de libro.Multiphase drives, constituted by an electric machine with more than three phases fed by a power converter, have recently attracted an important interest in the research community due to the advantages that they present over the conventional three-phase ones. This is the case of the better power distribution per phase, the lower harmonic production in the power converter, and the most important one, the fault-tolerant capability, which means that the multiphase machine can still be operated when one or several phases are missing, provided that the number of remaining phases is equal or greater than three. Due to this high reliability, multiphase drives are specially well suited for applications related to electric vehicles (terrestrial, maritime and aerial) and renewable energies for safety and/or economical reasons. The use of advanced and high-performance controllers in multiphase drives is particularly relevant, since the control strategies conventionally applied to three-phase drives do not reach a standard in their extension to the multiphase case. The reason is the greater complexity and number of variables that must be controlled. In this context, predictive controllers have found an interesting niche of application in power converters and multiphase drives due to their intuitive and flexible formulation: a model of the system is used to compute predictions of the controlled variables, which are later compared with the imposed references in a cost function. This strategy permits incorporating several control objectives and constraints in the control process through the cost function. However, it is well known that this type of controller suffers from a high computational cost and current harmonic content that limit its application in multiphase drives. The research developed in this Thesis work is focused on the mitigation of the cited limitations following two main goals: • The incorporation of rotor current observers in the predictive controller in order to improve the accuracy of the predictive model and, consequently, the control system performance, principally in terms of harmonic content and commutation losses in the power converter. A Luenberger observer is constructed for that purpose using an innovative pole-placement strategy in its design. • The introduction of an additional degree of freedom in the predictive controller based on variable sampling times and implemented using the lead-pursuit concept. The result is a novel controller that leads to a finer resolution in the commuting times in comparison with more conventional predictive techniques, which provides an important reduction in the harmonic content. The proposed control strategies are validated by simulation and experimentation using a five-phase induction machine drive as case example. The results and conclusions derived from this research have been presented in five main works published in high-impact international journals, which constitute the contributions of this article compendium Thesis. Nevertheless, other related works have also been published in journal and conference papers and a book chapter

DIRECT AND INDIRECT TORQUE CONTROL OF UNBALANCED PERMANENT MAGNET SYNCHRONOUS MACHINES

Electrical machines may exhibit various types of imbalances and undesirable harmonic distortions. These may increase the torque and flux ripples, acoustic noise, unbalanced three-phase currents, while also reducing efficiency. These types of imbalances and undesirable harmonic distortions cannot be controlled by using the conventional indirect torque control (ITC) and direct torque control (DTC) strategies. For some high-performance motion control, such as precision machine tools, robotics, and servo drives, low torque ripples are, however, obligatory. Nowadays, more studies have been conducted on the ITC strategy to control undesired current harmonics, such as double synchronic reference frames (DSRF), resonant controller, second order generalized integration, and reference current generation. Such strategies, however, can rarely be applied to DTC strategy. In this research, the influence of asymmetric winding impedances, unbalanced back-EMF, and inverter nonlinearity in three-phase surface-mounted PMSMs has been systematically investigated by employing space vector modulations (SVM) based ITC and DTC strategies. This thesis firstly presents a modified ITC strategy by extracting the positive and negative sequence components in the stationary abc frame, and then a coordination transformation is used to control the machine in DSRF. This strategy provides faster dynamic response when compared with the conventional DSRF strategy, since the filters and the decoupling network are not required. Due to the lack of research regarding the DTC strategy under unbalanced conditions, this research investigates and proposes modified cascaded and parallel DTC-SVM strategies. The conventional cascaded DTC strategy is investigated under balanced and unbalanced conditions. Then, a modified control strategy is introduced by adding two compensators (the conventional PI-controller with a resonant controller, and the use of the negative- and positive-sequence voltage vectors) to suppress the 2nd harmonic components in the torque and stator flux linkage. Furthermore, for parallel DTC-SVM, the compensation of the 2nd and 6th harmonic components is investigated by means of either a resonant controller or an adaptive filter. In addition to the simplicity of the proposed strategies, these may also be able to significantly reduce the torque and flux ripples, while maintaining the merit of the fast dynamic response of the conventional DTC strategy even under variable fundamental frequency. Moreover, it has been proven that the compensation from using a resonant controller or an adaptive filter is parameter independent. Thus, regardless of unbalanced conditions, an effective torque ripple minimisation can still be achieved by properly selecting the dominant harmonic compensation