Sliding mode differentiator via improved adaptive notch filter

summary:To tackle the difficulty in tuning the parameters of sliding mode differentiator (SMD), an improved adaptive notch filter based real-time parameter tuning scheme (denoted as ANF-SMD) is presented. Specifically, the integral feedback of the system output errors is introduced in constructing the cost function for the adaptive notch filter so as to estimate the real-time amplitude and frequency of given inputs. Then, upon the deterministic formula between the parameters of the SMD and the input signals, the parameters of the SMD can be adjusted adaptively as inputs vary. Simulation results show that the proposed ANF-SMD scheme performs well in signal filtering and differentiation estimation. The effectiveness of the proposed ANF-SMD is further experimentally verified on the pressure signal processing for the altitude ground test facility

Smooth non linear high gain observers for a class of dynamical systems

High-gain observers are powerful tools for estimating the state of nonlinear systems. However, their design poses several challenges due to the need of dealing with phenomena such as peaking and chattering. To address these issues, we propose a differentiator operator design based on a non linear second order high-gain observer, which is suited to a class of dynamical systems. Our method includes a procedure to determine high gains in order to avoid chattering in the case of noise-free models, and cut-off frequency based gain design in the case of noisy measurements. Complementary, we suggest performing observability analyses to ensure a priori the feasibility of the estimation. The main strengths of our approach are its simplicity and robustness. We demonstrate the performance of the proposed method by applying it to two processes (chemical and biological).Xunta de Galicia | Ref. ED431F 2021/003MCIN/AEI/10.13039/501100011033 | Ref. RYC-2019-027537-

Signal corrector and decoupling estimations for UAV control

For a class of uncertain systems with large-error sensing, the low-order stable signal corrector and observer are presented for signal correction and uncertainty estimation according to completely decoupling estimation. The model-free signal corrector can reject the bounded stochastic disturbance/error in global position sensing, and system uncertainty can be estimated by the observer, even the existence of large disturbance in position sensing. Furthermore, a general form of signal corrector is given. The describing function method is used to analyse the robustness of the corrector in frequency domain, and the parameter selection rules are presented. The merits of the signal corrector includes its model free, gain-bounded stable structure, sufficient rejection of bounded stochastic disturbance/error in sensing and ease of parameters’ regulation. The corrector and observer are applied to a UAV navigation and control for large disturbance/error corrections in position/attitude angle and the uncertainties estimation in the UAV flight dynamics. The control laws are designed according to the correction-estimation results. Finally, experiments demonstrate the effectiveness of the proposed method

Design and analysis of stable differentiator-predictor

In this paper, the phase lead by the general phase-lead compensator is analysed, and a criterion of its parameters selection is proposed. In order to get the relatively large time-interval prediction for stochastic signal, two types of differentiator-predictors are presented to estimate future signal and its derivatives: linear high-gain differentiator-predictor and nonlinear differentiator-predictor. Furthermore, a nonlinear extended differentiator-predictor is designed for future estimation and chattering rejection. The stability analysis of differentiator-predictors is described in time domain. The iterative transfer function method is proposed to analyse the robustness in frequency domain, and the rules of differentiator-predictor parameters selection are presented. The analysis shows that the nonlinear differentiator-predictor has stronger adaptability and robustness than the linear high-gain differentiator-predictor. Simulations demonstrate the effectiveness of the proposed methods

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

Feasible, Robust and Reliable Automation and Control for Autonomous Systems

The Special Issue book focuses on highlighting current research and developments in the automation and control field for autonomous systems as well as showcasing state-of-the-art control strategy approaches for autonomous platforms. The book is co-edited by distinguished international control system experts currently based in Sweden, the United States of America, and the United Kingdom, with contributions from reputable researchers from China, Austria, France, the United States of America, Poland, and Hungary, among many others. The editors believe the ten articles published within this Special Issue will be highly appealing to control-systems-related researchers in applications typified in the fields of ground, aerial, maritime vehicles, and robotics as well as industrial audiences

Discrete-time differentiators: design and comparative analysis

This work deals with the problem of online differentiation of noisy signals. In this context, several types of differentiators including linear, sliding-mode based, adaptive, Kalman, and ALIEN differentiators are studied through mathematical analysis and numerical experiments. To resolve the drawbacks of the exact differentiators, new implicit and semi-implicit discretization schemes are proposed in this work to suppress the digital chattering caused by the wrong time-discretization of set-valued functions as well as providing some useful properties, e.g., finite-time convergence, invariant sliding-surface, exactness. A complete comparative analysis is presented in the manuscript to investigate the behavior of the discrete-time differentiators in the presence of several types of noises, including white noise, sinusoidal noise, and bell-shaped noise. Many details such as quantization effect and realistic sampling times are taken into account to provide useful information based on practical conditions. Many comments are provided to help the engineers to tune the parameters of the differentiators

Finite-time sliding mode control strategies and their applications

In many engineering applications, faster convergence is always sought, such as manufacturing plants, defence sectors, mechatronic systems. Nowadays, most of the physical systems are operated in a closed-loop environment in conjunction with a controller. Therefore, the controller plays a critical role in determining the speed of the convergence of the entire closed-loop system. Linear controllers are quite popular for their simple design. However, linear controllers provide asymptotic convergence speed, i.e., the actual convergence is obtained when the time reaches an infinitely large amount. Furthermore, linear controllers are not entirely robust in the presence of non-vanishing types of disturbances. It is always important to design robust controllers because of the presence of model imperfections and unknown disturbances in almost all kinds of systems. Therefore, it is necessary to design controllers that are not only robust, but will also provide faster convergence speed. Out of many robust non-linear control strategies, a further development in sliding mode control (SMC) strategy is considered in this thesis because of its simplicity and robustness. There have been many contributions in the SMC field in the last decade. Many existingmethods are available for the SMC design for second-order systems. However, the SMC design becomes extremely complex if the system order increases. Therefore, the first part of this thesis focuses on developing arbitrary-order SMC strategies with a relatively simpler design while providing finite-time convergence. Novel methods are developed with both continuous and discontinuous control structures. The second part of this thesis focuses on developing algorithms to provide even faster convergence speed than that of finite-time convergent algorithms. Some practical applications need strict constraints on time response due to security reasons or to ameliorate the productiveness. For example, a missile or any aerial launch vehicle can be hugely affected by a strong wind gust deviating it from the desired trajectory, thus yielding a significant degree of initial tracking error. It is worth mentioning that the state convergence achieved in SMC during sliding can be either asymptotic or in finite-time, depending on the selection of the surface. Furthermore, it primarily depends on the initial conditions of the states. This provides a motivation to focus on developing SMC controllers where the convergence time does not depend on initial conditions, and a well-defined theoretical analysis is provided in the thesis regarding arbitrary-order fixed-time convergent SMC design. Subsequently, a predefined-time convergent second-order differentiator and observer are proposed. The main advantage of the proposed differentiator is to calculate the derivative of a given signal in fixed-time while the least upper bound of the fixed stabilisation time is equal to a tunable parameter. Similarly, the proposed predefined-time observer is robust with respect to bounded uncertainties and can also be used to estimate the uncertainties. The final part of the thesis is focused on the applications of the proposed algorithms. First of all, a novel third-order SMC is designed for a piezoelectric-driven motion systems achieving better accuracy and control performance. Later on, an experimental validation of the proposed controller is conducted on an induction motor setup. Later, a fixed-time convergent algorithm is proposed for an automatic generation control (AGC) of a multi-area interconnected power system while considering the non-linearities in the dynamic system. The final part is focused on developing fixed-time convergent algorithms in a co-operative environment. The reason for selecting such a system is the presence of the highest degree of uncertainties. To this end, a novel distributed algorithm is developed for achieving second-order consensus in the multiagent systems by designing a full-order fixed-time convergent sliding surface

Sliding-Mode-Based Differentiation and Filtering

The proposed kth-order filter is based on sliding modes (SMs). It exactly estimates k input derivatives in the absence of noises, and is robust to noises of small magnitudes or having small average values. Estimation accuracy asymptotics are calculated. The filter is applied to the real-time accurate estimation of the equivalent control in SM control systems