Homogeneous finite-gain Lp-stability analysis on homogeneous systems

In dieser Arbeit wird gezeigt, dass die klassische Lp-Stabilität und Lp-Verstärkung für beliebige stetige, gewichtete homogene Systeme nicht wohldefiniert ist. Indem die klassische Lp-Norm von Signalen zu einer homogenen Lp-Norm so angepasst wird, dass diese bezüglich der Gewichtsvektoren homogen ist, ist es möglich zu zeigen, dass jedes intern stabile homogene System für hinreichend große p eine global definierte endliche homogene Lp-Verstärkung besitzt. Mit Hilfe einer homogenen Lyapunov-Funktion kann die homogene Lp-Stabilität durch eine homogene partielle Differentialungleichung charakterisiert werden, die sich im eingangsaffinen Fall in eine homogene Hamilton-Jacobi-Ungleichung transformieren lässt. Des Weiteren werden in dieser Arbeit detaillierte Methoden zur Abschätzung von oberen Schranken für homogene Lp-Verstärkungen aus diesen Ungleichungen abgeleitet. Dies schließt die homogene L∞-Verstärkung und die homogene Eingangs-Zustands-Verstärkung ebenfalls ein. Bei rückgekoppelten homogenen Systemen, bei denen die Gewichtsvektoren zwischen den Systemen zueinander passend sind, erlaubt die additive Ungleichung für die homogene Lp-Norm die Einführung des homogenen Small-Gain Theorems für beliebige p, wodurch eine Stabilitätsanalyse des geschlossenen Regelkreises ermöglicht wird. Weiterhin können homogene H∞-Regler entworfen werden, wenn das System eingangsaffin ist. Da die konventionellen Werkzeuge der linearen Systemtheorie nicht zur Verfügung stehen, können solche homogenen H∞-Regler nur garantieren, dass der geschlossene Regelkreis eine homogene Lp-Verstärkung hat, die kleiner als ein bestimmbarer Wert ist. Ihre Optimalität kann hingegen nicht garantiert werden. In jedem Kapitel werden mehrere kurze Beispiele vorgestellt, um zu veranschaulichen, wie eine solche homogene Lp-Verstärkung berechnet werden kann. Insbesondere ist eine detaillierte Analyse des “Continuous Super-Twisting Like Algorithm" mit tieferen Einblicken für interessierte Leser enthalten.In this thesis, it is shown that the classical Lp-stability and Lp-gain is not well-defined for arbitrary continuous weighted homogeneous systems. By modifying the classical Lp-norm of signals to be homogeneous w.r.t. some weight vectors, which is called homogeneous Lp-norm, it is possible to show that every internally stable homogeneous system has a globally defined finite homogeneous Lp-gain, for p sufficiently large. With the help of a homogeneous Lyapunov function, homogeneous Lp-stability can be characterized by a homogeneous partial differential inequality, which in the input affine case can be transformed to a homogeneous Hamilton-Jacobi inequality. Furthermore, in this thesis some detailed methods to calculate upper estimates for the homogeneous Lp-gain are provided from theses inequalities. This also includes the homogeneous L∞-gain and homogeneous Input-to-State gain. For feedback interconnected systems, if the weight vectors between plants are matched, the additive inequality for homogeneous Lp-norm allows the introduction of the homogeneous small gain theorem for each p, enabling stability analysis on the closed loop system. Finally, some homogeneous H∞-controllers can be designed, if the system is affine in the control input. Without the convenient tools for the linear systems, such homogeneous H∞-controllers can only guarantee that the closed loop system has homogeneous Lp-gain less than some derivable numbers, its optimality can not be guaranteed. Several short examples are presented within each chapter to illustrate how such homogeneous Lp-gain can be calculated. In particular a detailed analysis on the Continuous Super-Twisting Like Algorithm is included with deeper insight for interested readers

Adaptive and Supertwisting Adaptive Spacecraft Orbit Control Around Asteroids

This paper addresses the development of control systems for the orbit control of spacecraft around irregularly shaped rotating asteroids with uncertain parameters. The objective is to steer the spacecraft along prescribed orbits. First, a nonlinear adaptive law for orbit control was designed. This was followed by the design of a supertwisting adaptive (STWA) control system. In the closed-loop system, which includes the adaptive law or the STWA law, all the signals remain bounded, and the trajectory tracking error asymptotically converges to zero for any initial condition. Finally, under the assumption of boundedness of the derivative of the uncertain functions of the model in a region of the state space, a supertwisting control (STW) law for finite-time convergence of the trajectory was obtained. Based on the Lyapunov theory, stability properties of the closed-loop systems were analyzed. Simulation results for 433 Eros and Ida asteroids were presented for illustration. The results showed that control of spacecraft along closed orbits or to a fixed point is accomplished using each of these controllers, despite uncertainties in the parameters of the asteroid models

Line-of-sight-stabilization and tracking control for inertial platforms

Nowadays, line of sight stabilization and tracking using inertially stabilized platforms (ISPs) are still challenging engineering problems. With a growing demand for high-precision applications, more involved control techniques are necessary to achieve better performance. In this work, kinematic and dynamic models for a three degrees-of-freedom ISP are presented. These models are based in the vehicle-manipulator system (VMS) framework for modeling of robot manipulators operating in a mobile base (vehicles). The dynamic model follows the Euler-Lagrange formulation and is implemented by numeric simulations using the iterative Newton-Euler method. Two distinct control strategies for both stabilization and tracking are proposed: (i) computed torque control and (ii) sliding mode control using the recent SuperTwisting Algorithm (STA) combined with a High-Order Sliding Mode Observer (HOSMO). Simulations using data from a simulated vessel allow us to compare the performance of the computed torque controllers with respect to the commonly used P-PI controller. Besides, the results obtained for the sliding mode controllers indicate that the Super-Twisting algorithm offers ideal robustness to the vehicle motion disturbances and also to parametric uncertainties, resulting in a stabilization precision of approximately 0,8 mrad.Hoje em dia, a estabilização e o rastreamento da linha de visada utilizando plataformas inerciais continuam a constituir desafiadores problemas de engenharia. Com a crescente demanda por aplicações de alta precisão, técnicas de controle complexas são necessárias para atingir melhor desempenho. Neste trabalho, modelos cinemáticos e dinâmicos para uma plataforma mecânica de estabilização inercial são apresentados. Tais modelos se baseiam no formalismo para sistemas veículo-manipulator para a modelagem de manipuladores robóticos operando em uma base móvel (veículo). O modelo dinâmico apresentado segue a formulação analítica de Euler-Lagrange e é implementado em simulações numéricas através do método iterativo de Newton-Euler. Duas estratégias de controle distintas para estabilização e rastreamento são propostas: (i) controle por torque-computado e (ii) controle por modos deslizantes utilizando o recente algoritmo Super-Twisting combinado com um observador baseado em modos deslizantes de alta ordem. Simulações utilizando dados de movimentação de um navio simulado permitem comparar o desempenho dos controladores por torque computado em relação a um tipo comum de controlador linear utilizado na literatura: o P-PI. Além disso, os resultados obtidos para o controle por modos deslizantes permitem concluir que o algoritmo Super-Twisting apresenta rejeição ideal a perturbações provenientes do movimento do veículo e também a incertezas paramétricas, resultando em precisão de estabilização de aproximadamente 0,8 mrad

Flexible joint robotic manipulator: Modeling and design of robust control law

This paper presents modeling and sophisticated control of a single Degree Of Freedom (DOF) flexible robotic arm. The derived model is based on Euler-Lagrange approach while the first and second order (super twisting) Sliding Mode Control (SMC) is proposed as a non-linear control strategy. The control laws are subjected to various test inputs including step and sinusoids to demonstrate their tracking efficiency by observing transient and steady state behaviours. Both orders of SMC are then compared to characterize the control performance in terms of robustness, handling external disturbances and chattering. Results dictate that the super twisting SMC is more accurate and robust against the external noise and chattering phenomena compared to the first order SMC

New Hybrid Sensorless Speed of a Non-Salient Pole PMSG Coupled to Wind turbine Using a Modified Switching Algorithm

©2019 ISA. Published by Elsevier Ltd. All rights reserved. his manuscript is made available under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence (CC BY-NC-ND 4.0). For further details please see: https://creativecommons.org/licenses/by-nc-nd/4.0/The paper focuses on the design of position and speed observers for the rotor of a non-salient pole permanent magnet synchronous generator (NSPPMSG) coupled to a wind turbine. With the random nature of wind speed this observer is required to provide a position and speed estimates over a wide speed range. The proposed hybrid structure combines two observers and a switching algorithm to select the appropriate observer based on a modified weighting coefficients method. The first observer is a higher-order sliding mode observer (HOSMO) based on modified super twisting algorithm (STA) with correction term and operates in the medium and nominal wind speed ranges. The second observer is used in the low speed range and is based on the rotor flux estimation and the control by injecting a direct reference current different to zero. The stability of each observer has been successfully assessed using an appropriate Lyapunov function. The simulation results obtained show the effectiveness and performance of the proposed observer and control scheme.Peer reviewe

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Diseño de controladores continuos convergentes por un tiempo fijo para sistemas dinámicos con incertidumbre

Este documento presenta controladores no lineales que proveen convergencia en tiempo fijo al origen (o a una vecindad del origen) para sistemas dinámicos de alto orden sujetos a incertidumbres (disturbios deterministicos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo). Dos de los tres controladores diseñados incluyen un diferenciador convergente en tiempo fijo, un observador de disturbios convergente en tiempo fijo, y un regulador convergente en tiempo fijo. El diferenciador se da en el caso que el ´único estado medible del sistema dinámico es el de mayor grado relativo. El observador de disturbios convergente en tiempo fijo se emplea para estimar variaciones de disturbios no desvanecentes y no acotados. En caso de que las cotas para los disturbios sean desconocidas se incluye un observador adaptable convergente en tiempo fijo caracterizado por no incrementar de manera excesiva las ganancias del controlador. En cuanto a la presencia simultanea de disturbios determinísticos no desvanescentes y disturbios estocásticos desvanescentes dependientes de los estados y el tiempo, se presenta un algoritmo Super-twisting estocástico convergente en tiempo fijo. El problema de estimación del tiempo de convergencia de los controladores se resuelve calculando una cota superior uniforme del tiempo fijo de convergencia. Finalmente, los algoritmos diseñados se verifican en dos casos de estudio: Un motor DC con armadura y un problema de gestión de stocks. Resultados de las simulaciones confirman convergencia en tiempo fijo y robustez de los controladores diseñados