Adaptive neural control of nonlinear systems with hysteresis

Ph.DDOCTOR OF PHILOSOPH

Nanopositionnement 3D à base de mesure à courant tunnel et piezo-actionnement

The objective of this thesis was to elaborate high performance control strategies and their real-time validation on a tunneling current-based 3D nanopositioning system developed in GIPSA-lab. The thesis lies in the domain of micro-/nano mechatronic systems (MEMS) focused on applications of fast and precise positioning and scanning tunneling microscopy (STM). More precisely, the aim is to position the metallic tunneling tip (like in STM) over the metallic surface using piezoelectric actuators in X, Y and Z directions and actuated micro-cantilever (like in Atomic Force Microscope AFM), electrostatically driven in Z direction, with high precision, over possibly high bandwidth. However, the presence of different adverse effects appearing at such small scale (e.g. measurement noise, nonlinearities of different nature, cross-couplings, vibrations) strongly affect the overall performance of the 3D system. Therefore a high performance control is needed. To that end, a novel 3D model of the system has been developed and appropriate control methods for such a system have been elaborated. First the focus is on horizontal X and Y directions. The nonlinear hysteresis and creep effects exhibited by piezoelectric actuators have been compensated and a comparison between different compensation methods is provided. Modern SISO and MIMO robust control methods are next used to reduce high frequency effects of piezo vibration and cross-couplings between X and Y axes. Next, the horizontal motion is combined with the vertical one (Z axis) with tunneling current and micro-cantilever control. Illustrative experimental results for 3D nanopositioning of tunneling tip, as well as simulation results for surface topography reconstruction and multi-mode cantilever positioning, are finally given.L'objectif de la thèse est l'élaboration de lois de commande de haute performance et leur validation en temps réel sur une plateforme expérimentale 3D de nano-positionnement à base de courant à effet tunnel, développée au laboratoire GIPSA-lab. Elle s'inscrit donc dans le cadre des systèmes micro-/nano-mécatronique (MEMS), et de la commande. Plus précisément, le principal enjeu considéré est de positionner la pointe métallique à effet tunnel (comme en microscopie à effet tunnel STM) contre la surface métallique en utilisant des actionneurs piézoélectriques en X, Y et Z et un micro-levier (comme en microscopie à force atomique AFM) actionné électrostatiquement en Z avec une grande précision et une bande passante élevée. Cependant, la présence de différents effets indésirables apparaissant à cette petite échelle (comme le bruit de mesure, des non-linéarités de natures différentes, les couplages, les vibrations) affectent fortement la performance globale du système 3D. En conséquence, une commande de haute performance est nécessaire. Pour cela, un nouveau modèle 3D du système a été développé et des méthodes de contrôle appropriées pour un tel système ont été élaborées. Tout d'abord l'accent est mis sur de positionnement selon les axes X et Y. Les effets d'hystérésis et de fluage non linéaires présents dans les actionneurs piézoélectriques ont été compensés et une comparaison entre les différentes méthodes de compensation est effectuée. Des techniques modernes de commande robuste SISO et MIMO sont ensuite utilisées pour réduire les effets des vibrations piézoélectriques et des couplages entre les axes X et Y. Le mouvement horizontal est alors combiné avec le mouvement vertical (Axe Z) et une commande du courant tunnel et du micro-levier. Des résultats expérimentaux illustrent le nano positionnement 3D de la pointe, et des résultats de simulation pour la reconstruction de la topographie de la surface ainsi que le positionnement du micro-levier à base d'un modèle multi-modes

Discrete Modeling and Sliding Mode Control of Piezoelectric Actuators

With the ability to generate fine displacements with a resolution down to sub-nanometers, piezoelectric actuators (PEAs) have found wide applications in various nano-positioning systems. However, existence of various effects in PEAs, such as hysteresis and creep, as well as dynamics can seriously degrade the PEA performance or even lead to instability. This raises a great need to model and control PEAs for improved performance, which have drawn remarkable attention in the literature. Sliding mode control (SMC) shows its potential to the control of PEA, by which the hysteresis and other nonlinear effects can be regard as disturbance to the dynamic model and thus rejected or compensated by its switching control. To implement SMC in digital computers, this research is aimed at developing novel discrete models and discrete SMC (DSMC)-based control schemes for PEAs, along with their experimental validation. The first part of this thesis concerns with the modeling and control of one-degree of freedom (DOF) PEA, which can be treated as a single-input-single-output (SISO) system. Specifically, a novel discrete model based on the concept of auto-regressive moving average (ARMA) was developed for the PEA hysteresis; and to compensate for the PEA hysteresis and improve its dynamics, an output tracking integrated discrete proportional-integral-derivative-based SMC (PID-SMC) was developed. On this basis, by making use of the availability of PEA hysteresis models, two control schemes, named “the discrete inversion feedforward based PID-SMC” and “the discrete disturbance observer (DOB)-based PID-SMC”, were further developed. To illustrate the effectiveness of the developed models and control schemes, experiments were designed and conducted on a commercially available one-DOF PEA, as compared with the existing ones. The second part of the thesis presents the extension of the developed modeling and control methods to multi-DOF PEAs. Given the fact that details with regard to the PEA internal configurations is not typically provided by the manufacturer, a state space model based on the black box system identification was developed for the three-DOF PEA. The developed model was then integrated in the output tracking based discrete PID-SMC, with its effectiveness verified through the experiments on a commercially available three-DOF PEA. The superiority of the proposed control method over the conventional PID controller was also experimentally investigated and demonstrated. Finally, by integrating with a DOB in the discrete PID-based SMC, a novel control scheme is resulted to compensate for the nonlinearities of the three-DOF PEA. To verify its effectiveness, the discrete DOB based PID-SMC was applied in the control experiments and compared with the existing SMC. The significance of this research lies in the development of the discrete models and PID-based SMC for PEAs, which is of great help to improve their performance. The successful application of the proposed method in the control of multi-DOF PEA allows the application of SMC to the control of complicated multi-inputs-multi-outputs (MIMO) systems without details regarding the internal configuration. Also, integration of the inversion based feedforward control and the DOB in the SMC design has been proven effective for the tracking control of PEAs

Robust control of systems with output hysteresis and input saturation using a finite time stability approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a robust control approach for a class of nonlinear dynamic systems consisting of a linear plant connected in series with a hysteresis operator, and affected by control input saturation. Such a class of systems commonly appears in applications concerning smart materials, in particular thermal shape memory alloys wire actuators. The goal of this paper is to design a robust controller, in the form of an output PI law, which ensures set-point regulation with a desired decay rate and, at the same time, accounts for the effects of both hysteresis and input saturation. The resulting controller appears as attractive on the implementation stand-point, since no accurate hysteresis compensator is required. In order to deal with the proposed problem, the hysteretic plant is first reformulated as a linear parameter-varying system. Subsequently, a finite time stability approach is used to impose constraints on the control input. A new set of bilinear matrix inequalities is developed, in order to perform the design with reduced conservatism by properly exploiting some structural properties of the model. The effectiveness of the method is finally validated by means of a numerical case of study. © 2018 IEEE.Peer ReviewedPostprint (author's final draft

Adaptive control and neural network control of nonlinear discrete-time systems

Ph.DDOCTOR OF PHILOSOPH

Output feedback control and robustness in the gap metric

Zusammenfassung Mueller, Markus: Output feedback control and robustness in the gap metric Ilmenau : Univ.-Verl. Ilmenau, 2009. - 254 S. ISBN 978-3-939473-60-2 Die vorgelegte Arbeit behandelt den Entwurf und die Robustheit von drei verschiedenen Regelstrategien für lineare Differentialgleichungssysteme mit mehrdimensionalen Ein- und Ausgangssignalen (MIMO): Stabilisierung durch Ausgangs-Ableitungs-Rückführung, Lambda-tracking und Funnel-Regelung. Damit diese Regler bei der Anwendung auf ein lineares System die gewünschten Stabilisierung/Regelung erbringen, ist eine explizite Kenntnis der Systemmatrizen nicht notwendig. Es müssen nur strukturelle Eigenschaften des Systems bekannt sein: der Relativgrad, dass das System minimalphasig ist, und dass die sogenannte "high-frequency gain" Matrix positiv definit ist. Diese stukturellen Eigenschaften werden für MIMO-Systeme in den ersten Kapiteln der Arbeit ausführlich behandelt. Für MIMO-Systeme mit nicht striktem Relativgrad wird eine Normalform hergeleitet, die die gleichen Eigenschaften wie die bekannte Normalform für SISO-Systeme oder MIMO-Systeme mit striktem Relativgrad aufweist. Die Normalform sowie Minimalphasigkeit und Positivität der "high-frequency gain" Matrix bilden die Grundlage dafür, dass die oben genannten Regelstrategien Systeme mit diesen Eigenschaften im jeweiligen Sinn stabilisieren. Robustheit bzw. robuste Stabilisierung beschreibt folgendes Prinzip: falls ein geschlossener Kreis aus einem linearen System und einem Regler in gewissem Sinne stabil ist und die Gap-Metrik (der Abstand) zwischen dem im geschlossenen Kreis betrachteten System und einem anderen "neuen" System hinreichend klein ist, so ist der geschlossene Kreis aus dem "neuen" System und dem gleichen Regler wieder stabil. Die gleiche Aussage stimmt auch für den Fall, dass man den Regler und nicht das System austauscht. Für Ausgangs-Ableitungs-Rückführung wird gezeigt, dass, falls diese ein System stabilisiert, die auftretenden Ableitungen des Ausgangs durch Euler-Approximationen der Ableitungen ersetzt werden können, falls diese hinreichend genau sind. Für Lambda-tracking und Funnel-Regelung wird gezeigt, dass beide Regler auch für die Stabilisierung linearer Systeme verwendet werden können, die einen geringen Abstand zu einem System haben, dass die o.g. Voraussetzungen erfüllt, selbst diese Voraussetzungen aber nicht erfüllen.Abstract: This dissertation considers the design and robustness analysis of three different control strategies for linear systems of differential equations with multidimensional input and output signals (MIMO): high-gain output derivative feedback control, lambda-tracking and funnel control. To apply these control strategies to linear systems and achieve the desired control objectives (stabilization or tracking), the explicit system's data needs not to be known, but certain structural properties of the systems are required. The system's relative degree must be known, the system must be minimum phase and the so-called "high-frequency gain" matrix must be positive definite. These properties are considered in detail for linear MIMO-systems with non-strict relative degree. A normal form is developed which has the same properties as the well-known normal form for SISO-systems or MIMO-systems with strict relative degree. Normal form, minimum phase property and positivity of the high-frequency gain matrix are the crucial assumptions for the application of the control strategies mentioned above. It is shown that each controller achieves certain control objectives when applied to any system which satisfies these assumptions. The result on robustness and robust stability are as follows: if a closed-loop system represented by the application of a controller to a linear plant is stable (in some sense), and the gap metric (i.e. the distance) between the stabilised system and a different "new" system is sufficiently small, then the closed-loop system represented by the application of the controller to the "new" system is again stable. This conclusion holds also true when changing the roles of system and controller. For high-gain output derivative feedback control it is shown that the controller still stabilizes a system when the derivatives of the output are replaced by Euler approximations of the derivatives, provided the approximation is sufficiently precise. For lambda-tracking and funnel control it is shown that both controllers may be applied to systems which are "close" (in terms of a small gap) to any system from the class of minimum phase systems, with relative degree one and positive definite high-frequency gain matrix, but not necessarily satisfy any of these assumptions

A single-step identification strategy for the coupled TITO process using fractional calculus

The reliable performance of a complete control system depends on accurate model information being used to represent each subsystem. The identification and modelling of multivariable systems are complex and challenging due to cross-coupling. Such a system may require multiple steps and decentralized testing to obtain full system models effectively. In this paper, a direct identification strategy is proposed for the coupled two-input two-output (TITO) system with measurable input–output signals. A well-known closed-loop relay test is utilized to generate a set of inputs–outputs data from a single run. Based on the collected data, four individual fractional-order transfer functions, two for main paths and two for cross-paths, are estimated from single-run test signals. The orthogonal series-based algebraic approach is adopted, namely the Haar wavelet operational matrix, to handle the fractional derivatives of the signal in a simple manner. A single-step strategy yields faster identification with accurate estimation. The simulation and experimental studies depict the efficiency and applicability of the proposed identification technique. The demonstrated results on the twin rotor multiple-input multiple- output (MIMO) system (TRMS) clearly reveal that the presented idea works well with the highly coupled system even in the presence of measurement noise

Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

Open Access via the Wiley Agreement ACKNOWLEDGEMENTS This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.Peer reviewedPublisher PD