Design and analysis of continuous hybrid differentiator

In this paper, a continuous hybrid differentiator is presented based on a strong Lyapunov function. The differentiator design can not only reduce sufficiently chattering phenomenon of derivative estimation by introducing a perturbation parameter, but also the dynamical performances are improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating sliding mode items and the linear filter. Frequency analysis is applied to compare the hybrid continuous differentiator with sliding mode differentiator. The merits of the continuous hybrid differentiator include the excellent dynamical performances, restraining noises sufficiently, and avoiding the chattering phenomenon

Rapid-convergent nonlinear differentiator

A nonlinear differentiator being fit for rapid convergence is presented, which is based on singular perturbation technique. The differentiator design can not only sufficiently reduce the chattering phenomenon of derivative estimation by introducing a continuous power function, but the dynamical performances are also improved by adding linear correction terms to the nonlinear ones. Moreover, strong robustness ability is obtained by integrating nonlinear items and the linear filter. The merits of the rapid-convergent differentiator include the excellent dynamical performances, restraining noises sufficiently, avoiding the chattering phenomenon and being not based on system model. The theoretical results are confirmed by computer simulations and an experiment.Comment: 26 pages, 15 figure

On Convergence of Tracking Differentiator with Multiple Stochastic Disturbances

In this paper, the convergence and noise-tolerant performance of a tracking differentiator in the presence of multiple stochastic disturbances are investigated for the first time. We consider a quite general case where the input signal is corrupted by additive colored noise, and the tracking differentiator itself is disturbed by additive colored noise and white noise. It is shown that the tracking differentiator tracks the input signal and its generalized derivatives in mean square and even in almost sure sense when the stochastic noise affecting the input signal is vanishing. Some numerical simulations are performed to validate the theoretical results

HOSM State Estimation and Robust PID Control of a Chemical Process

This paper presents some results of the authors’ studies on robust estimation and control for chemical processes. Here, an observer-based controller is designed for a chemical process. A High Order Sliding Mode Observer (HOSMO) for state and parameter estimation is synthesized and, a Multi-Variable PID (MV-PID) controller is calculated using the estimated variables. The HOSMO presents insensitivity and robustness against a class of uncertainties in the system, and the MV-PID allows the tracking of slow-varying and piecewise constant references, which are often proposed to drive chemical processes. Numerical simulations show that the observer-based controller presents a good performance in presence of parametric variations, which often are presented in chemical processes; the proposed structure is compared with a First Order Sliding Mode Observer (FOSMO) coupled with a MV-PID.CinvestavUniversidad Nacional de Colombi

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Observability studies for spacecraft attitude determination based on temperature data

Die Schätzung und Steuerung der Fluglage ist elementar für jede Raumfahrzeugmission. Die erforderliche Genauigkeit hängt von der jeweiligen Mission und ihren Nutzlasten ab. Ein funktionierendes Lageregelungssystem ist jedoch immer unverzichtbar, um die Zielgenauigkeit und Stabilität der Nutzlasten zu gewährleisten, die für den Erfolg der Mission entscheidend sind. Daher ist es sinnvoll, redundante Methoden zur Schätzung und Regelung der aktuellen Fluglage einzusetzen. Diese Arbeit fokussiert sich primär auf die Lageschätzung. Hierbei wird untersucht ob und wie Temperaturmessungen für die Lagebestimmung genutzt werden können. Diese Untersuchung wird durchgeführt, indem die zugrundeliegenden mathematischen Beschreibungen der Fluglage sowie der Temperaturdynamik betrachtet werden. Auf deren Grundlage wird dann ein Beobachter zur Lageschätzung entwickelt, der sich hauptsächlich auf die Temperaturdaten von zwei verschiedenen Sensorkonfigurationen stützt. In der ersten Konfiguration wird nur ein einziger Temperatursensor verwendet, dessen Informationen mit Gyroskopmessungen fusioniert werden, um die Lage zu bestimmen. Dies wird durch eine Transformation in Normalform und eine neuartige Lagebeschreibung erreicht. Auftretende Mehrdeutigkeiten bei der Lagebestimmung sowie alternative Beobachterdesigns werden vorgestellt. Die Analyse zeigt, dass mit dem vorgeschlagenen Beobachter lokale Aussagen zur Lageschätzung getroffen werden können - vorausgesetzt, die verwendeten Modelle und Messungen sind ausreichend genau und es steht genügend Rechenleistung zur Verfügung. In der zweiten Konfiguration werden sechs Paare von Temperatursensoren betrachtet. Jedes Paar besteht aus zwei Sensoren mit unterschiedlichen physikalischen Eigenschaften und zeigt in Richtung einer anderen Raumfahrzeugachse. Diese Sensorsignale enthalten genügend Informationen, um die Fluglage zu rekonstruieren, ohne dass die Verwendung von Ableitungen höherer Ordnung erforderlich ist. Es wird ein Algorithmus vorgeschlagen, der die Position der Sonne und der Erde schätzt und diese zur Bestimmung der Lage verwendet. Die Beobachter für beide Konfigurationen verwenden eine Transformation in eine kanonische Form, um ihre Schätzungen zu erhalten. Die resultierenden Beobachter sind daher sowohl in den transformierten als auch in den ursprünglichen Koordinaten formuliert. Während diese Beobachter unter Annahmen die häufig in der Literatur verwendeten werden äquivalent sind, kann es, sobald diese Annahmen fallengelassen werden, zu einer Reihe interessanter Phänomene wie Mehrdeutigkeit der Lösungen und sogar Instabilität kommen. Diese Phänomene werden an unserem vorgestellten System veranschaulicht und es werden Methoden vorgeschlagen, um sie zu bewältigen. Die für die zweite Konfiguration entworfenen Beobachter werden auf die von der Raumsondenmission GRACE erhaltenen Daten angewandt. Dabei hat sich gezeigt, dass die vorgeschlagenen Modelle für die Temperaturschätzung mit einem R2-Wert zwischen 78,8 % und 99,9 % gut geeignet sind. Die vorgeschlagenen Algorithmen erlauben eine Genauigkeit mit einem mittleren Fehler über eine Umlaufbahn von weniger als fünf Grad und lassen sich nachweislich leicht durch zusätzliche Messungen ergänzen.Attitude estimation and control is fundamental for every spacecraft mission. Accuracy requirements are strongly dependant on mission level goals and the respective payloads and experiments. However, it is always essential for the mission success to have a functioning attitude control system to allow a high pointing accuracy and stability of the payloads. Therefore, it is useful to employ redundant means to estimate and control the current attitude. The estimation of the attitude is the main topic of this work in which the information contained in temperature measurements for attitude estimation is investigated. This investigation is carried out by providing the underlying mathematical descriptions of the attitude as well as temperature dynamics. Different observer designs are considered based on these models to estimate the attitude relying mostly on the temperature data obtained from two different sensor configurations. In the first configuration, only a single temperature sensor is employed and the information is fused with gyroscope measurements to determine the attitude. This is achieved based on a transformation into normal form and a novel attitude description. Arising ambiguities in the attitude estimation, as well as alternative observer designs are presented. The analysis shows that with the proposed observer, it is possible to estimate the attitude provided that the employed models and measurements are sufficiently accurate and that enough computational power is available. The second configuration considers six pairs of temperature sensors. Each pair consists of two sensors with different physical properties and every pair points into a different body axis. These sensor signals contain enough information to reconstruct the attitude without requiring the usage of higher-order derivatives. An algorithm is proposed that estimates the position of the Sun and Earth and uses these to estimate the attitude. The observers for both configurations use a transformation of the system dynamics into canonical form to obtain a formulation of the problem that allows for estimation. The resulting observers are therefore formulated in transformed and original coordinates. While these observers are equivalent under assumptions widely used in literature, the moment these assumptions are dropped, a number of interesting phenomena such as ambiguity of the solutions and even instability can occur. These phenomena are illustrated by the system of interest and methods are proposed to deal with them. The designed observers for the second configuration are applied to the data obtained from the spacecraft mission GRACE. The results indicate that the proposed models are well suited for the temperature estimation with a R2 value between 78.8% and 99.9%. The proposed algorithms admit an accuracy with a mean error over an orbit of less than five degrees and are shown to be easily augmented with additional measurements

Theory of nonlinear feedback under uncertainty

AbstractOur main purpose here is to demonstrate the potential of a new approach which is an important expansion of the feedback concept: we have chosen what seemed a natural way of tackling some traditional problems of the control theory and of comparing the results against those offered by conventional methods.The main problem considered is the output stabilization for uncertain plants. Using structural transformations, uncertain systems can change to the form convenient for output feedback design. Synthesis of observer-based control for asymptotical stabilization or uniform ultimate boundedness of the closed-loop system is provided.We consider the notions of asymptotic and exponential invariance of a control system implies its suboptimality.A method is described for stabilization of uncertain discrete-time plants of which only compact sets are known to which plants parameters and exogenous signals belong. New approaches for solving some central problems of mathematical control theory are considered for nonlinear dynamical systems. New criterious of local and global controllability and stabilizability are indicated and some synthesis procedures are suggested