Design of an adaptive state feedback controller for a magnetic levitation system

This paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controller in terms of the operating point. The results of the simulation show that the operating point has significant effect on the performance of nonadaptive SFC, and this performance may degrade as the operating point deviates from the equilibrium point, while the ASFC achieves the required design specification for any operating point and outperforms the state feedback controller from this point of view

Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop

The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach.This work was partially supported by the following grants under the Slovak Grant Agency, the Slovak Research and Development Agency: VEGA 1/0552/14, VEGA 1/0729/12, VEGA 1/0497/11, VEGA 1/2578/12, and APVV-0482-11, and the European Union through the European Regional Development Fund, and the Estonian Doctoral School in Information and Communication Technology through the interdisciplinary project FOMCON

Design of PID Controller for Magnetic Levitation System using Harris Hawks Optimization

In most real-time industrial systems, optimal controller implementation is very essential to maintain the output based on the reference input. The controller design problem becomes a complex task when the real-time system model becomes greatly non-linear and unstable. The proposed research aims to design the finest PID controller for the unstable Magnetic Levitation System (MLS) using the Harris Hawks Optimization (HHO) algorithm. The MLS is a highly unstable electro-mechanical system and hence the design of the controller is a complex task. The proposed work implements one Degree of Freedom (1DOF) and 2DOF PID for the system. In this work, the essential controller is designed with a two-step process; (i) Initial optimization search to find the P-controller (Kp) gain to stabilize the system and (ii) Tuning the integral (Ki) and derivative (Kd) gains to reduce the deviation between the reference input and MLS output. The performance of the proposed controller is validated with the servo and regulatory operations and the result of this study confirms that the proposed method helps to get better error value and time domain specifications compared to other available methods

Adaptif STR-PID Untuk Pengendalian Posisi Pada Magnetic Levitation Ball

Magnetic Levitation Ball merupakan suatu sistem yang terdiri atas bola baja bersifat ferromagnetik  yaitu benda yang memiliki sifat kemagnetan yang kuat,  dimana benda tersebut akan melayang diatas permukaan suatu medium udara atau di bawah sebuah elektromagnet. Permasalahan utama Magnetic Levitation Ball terletak pada sistemnya yang nonlinier, dimana perubahan setpoint tidak sebanding dengan perubahan keluaran.  Oleh karena itu diperlukan suatu kendali untuk mengendalikan posisi Magnetic Levitation Ball  agar benda itu melayang sesuai dengan setpoint dan karakteristik sistem yang diinginkan, dalam hal ini kendali yang digunakan adalah Adaptif STR-PID, dimana Adaptif STR (Self Tuning Regulator) mampu melakukan adaptasi nilai parameter PID sesuai dengan setiap keadaan yang terjadi pada sistem tersebut, seperti mampu mengikuti perubahan setpoint dan mengatasi adanya gangguan.  Dari hasil penelitian ini, telihat STR-PID mampu mencapai setpoint yang diinginkan, dengan error steady state= 0 m, overshoot= 0%, dan mampu mengatasi gangguan yang terjadi

Disturbance rejection FOPID controller design in v-domain

Due to the adverse effects of unpredictable environmental disturbances on real control systems, robustness of control performance becomes a substantial asset for control system design. This study introduces a v-domain optimal design scheme for Fractional Order Proportional-Integral-Derivative (FOPID) controllers with adoption of Genetic Algorithm (GA) optimization. The proposed design scheme performs placement of system pole with minimum angle to the first Riemann sheet in order to obtain improved disturbance rejection control performance. In this manner, optimal placement of the minimum angle system pole is conducted by fulfilling a predefined reference to disturbance rate (RDR) design specification. For a computer-aided solution of this optimal design problem, a multi-objective controller design strategy is presented by adopting GA. Illustrative design examples are demonstrated to evaluate performance of designed FOPID controllers. © 2020COST ActionEuropean Cooperation in Science and Technology (COST) [CA15225]; COST (European Cooperation in Science and Technology)European Cooperation in Science and Technology (COST

Adaptive Control

Adaptive control has been a remarkable field for industrial and academic research since 1950s. Since more and more adaptive algorithms are applied in various control applications, it is becoming very important for practical implementation. As it can be confirmed from the increasing number of conferences and journals on adaptive control topics, it is certain that the adaptive control is a significant guidance for technology development.The authors the chapters in this book are professionals in their areas and their recent research results are presented in this book which will also provide new ideas for improved performance of various control application problems

Optimisation of time domain controllers for supply ships using genetic algorithms and genetic programming

The use of genetic methods for the optimisation of propulsion and heading controllers for marine vessels is presented in this thesis. The first part of this work is a study of the optimisation, using Genetic Algorithms, of controller designs based on a number of different time-domain control methodologies such as PID, Sliding Mode, H8, and Pole Placement. These control methodologies are used to provide the structure for propulsion and navigation controllers for a ship. Given the variety in the number of parameters to optimise and the controller structures, the Genetic Algorithm is tested in different control optimisation problems with different search spaces. This study presents how the Genetic Algorithm solves this minimisation problem by evolving controller parameters solutions that satisfactorily perform control duties while keeping actuator usage to a minimum. A variety of genetic operators are introduced and a comparison study is conducted to find the Genetic Algorithm scheme best suited to the parameter controller optimisation problem. The performance of the four control methodologies is also compared. A variation of Genetic Algorithms, the Structured Genetic Algorithm, is also used for the optimisation of the H8 controller. The H8 controller optimisation presents the difficulty that the optimisation focus is not on parameters but on transfer functions. Structured Genetic Algorithm incorporates hierarchy in the representation of solutions making it very suitable for structural optimisation. The H8 optimisation problem has been found to be very appropriate for comparing the performance of Genetic Algorithms versus Structured Genetic Algorithm. During the second part of this work, the use of Genetic Programming to optimise the controller structure is assessed. Genetic Programming is used to evolve control strategies that, given as inputs the current and desired state of the propulsion and heading dynamics, generate the commanded forces required to manoeuvre the ship. Two Genetic Programming algorithms are implemented. The only difference between them is how they generate the numerical constants needed for the solution of the problem. The first approach uses a random generation of constants while the second approach uses a combination of Genetic Programming with Genetic Algorithms. Finally, the controllers optimised using genetic methods are evaluated through computer simulations and real manoeuvrability tests in a laboratory water basin facility

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Fraktionale Flussschätzung in aktiven Magnetlagern

Seit jeher sind Wirbelströme ein fester Bestandteil der Leistungsbilanz und Verlustberechnung in zahlreichen elektromagnetischen Energiewandlern. In aktiven Magnetlagern und Aktoren haben sie jedoch häufig einen zusätzlichen Einfluss auf die Kraftdynamik, da die einhergehende Feldverdrängung parasitäre Magnetisierungsströme hervorbringt, welche die meist strombasierten Kraftregler beeinträchtigen. Besonders betroffen sind die in dieser Dissertation beispielhaft betrachteten magnetischen Axiallager mit ihrer dreidimensionalen Flussführung, für welche die sonst übliche und effektive Blechung des Kerns unwirksam wird. Aus diesen Gründen werden regelungsbasierte Lösungen angestrebt. Bekannte fortschrittliche Topologien nutzen mitunter aufwendige Regler und Beobachter, wobei der direkte physikalische Bezug zu den mechanischen Parametern Steifigkeit und Dämpfung meist verloren geht. Diese Analogie zu mechanischen Lagern ist jedoch essentiell für eine einfache Inbetriebnahme des Magnetlagers, ein Grund, weshalb sich viele alternative Topologien nicht nachhaltig durchsetzen konnten und die dezentrale kaskadierte Lageregelung mit unterlagerter Stromregelung noch immer als weit verbreiteter Industriestandard gilt. Die in Axiallagern eingeschränkte Stabilität, Dynamik und Bandbreite aufgrund der Wirbelstromeffekte wird dabei zu Gunsten der einfacheren Anwendbarkeit toleriert. Diese Arbeit stellt ein fraktionales Kompensationsglied in Gestalt eines Flussschätzers vor, welches im Rückführungszweig der unterlagerten Regelung die Folgen der Wirbelströme dort herausrechnet, wo sie physikalisch wirken. Die resultierende modellbasierte Flussregelung erhält somit sämtliche physikalische Bezüge und die gute Anwendbarkeit, bei gleichzeitig verbesserten Regelungseigenschaften, sodass diesbezüglich keine Kompromisse notwendig sind. Das zugrundeliegende Modell leitet sich aus der Lösung der Diffusionsgleichung für den massiven Kern ab und stellt zunächst ein transzendentes fraktionales System dar, welches nicht direkt in einer Regelung anwendbar ist. Über Kettenbruchentwicklungen und Frequenzganganalysen ist es jedoch möglich, eine rationale Systembeschreibung zu ermitteln, die in Form einer digitalen Biquad-Filter-Kaskade auch in bestehende Mikroprozessor-Regelungen echtzeitfähig implementierbar ist. Die Arbeit dokumentiert das Vorgehen für eine Vielzahl von Randbedingungen und berücksichtigt verschiedene denkbare Einschränkungen, die in praktischen Anwendungen erwartbar sind. Der messtechnische Funktionsnachweis zeigt eine nahezu vollständige Kompensation der Wirbelstromeffekte in der unterlagerten Regelung, während sich die Bandbreite der Lageregelung nachweislich mindestens vervierfacht bei einem um bis zu 90 % Überschwingen gegenüber dem Industriestandard.Eddy currents have always been part of loss calculations and power balances in numerous electromagnetic energy converters. In active magnetic bearings and actuators they additionally have a great influence on the force dynamic, as the concomitant magnetic skin effect provokes parasitic magnetizing currents that impair the usually current-based force controllers. Thrust bearings with their three-dimensional flux propagation, which serve as example in this thesis, are especially affected, due to the ineffectiveness of the commonly applied lamination of the iron core. For these reasons, control-based solutions are desired. Known advanced control topologies employ possibly intricating controllers and observers, which hardly preserve the direct physical reference to mechanical parameters like stiffness and damping. However, this analogy to mechanical bearings is essential for a simple bearing operation. That is one reason why many alternative topologies could not been established sustainably and the decentralized cascaded position control with subordinated current control is considered as the indisputable industry standard. Its limitation of stability, dynamic and bandwidth, caused by the eddy current effects in thrust bearings, is only tolerated, in favor of a superior applicability. This thesis introduces a fractional-order compensation element in the form of a flux estimator that compensates the eddy currents effects, where they physically occur, to wit, within the feedback path of the subordinated control. Hence, the resulting flux control maintains all physical references and the simple applicability, but does not compromise on the control characteristic in this regard. The underlying model is derived from the solution of the diffusing equation that describes the nonlaminated core. It firstly constitutes a transcendental fractional-order system, which cannot be directly applied to a bearing control. However, by the use of continued fraction expansions and frequency analysis, a rational system description is determinable, which can be implemented as biquad filter cascade for real-time application even in existing microprocessor controls. This work documents the procedure for a variety of boundary conditions while considering various possible restrictions, which are to be expected in practical applications. The experimental proof of concept reveals a nearly complete compensation of the eddy current effects in the subordinated control. The bandwidth of the outer position control is at least quadrupled, while the overshoot can be reduced by up to 90 % compared to the industry standard