Advanced Mathematics and Computational Applications in Control Systems Engineering

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an essential and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have increased, and real systems have become more complex. In control engineering and all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in the problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related to numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system. This book is a comprehensive set of articles reflecting recent advances in developing and applying advanced mathematics and computational applications in control system engineering

Intelligent model-based control of complex three-link mechanisms

The aim of this study is to understand the complexity and control challenges of the locomotion of a three-link mechanism of a robot system. In order to do this a three-link robot gymnast (Robogymnast) has been built in Cardiff University. The Robogymnast is composed of three links (one arm, one torso, one leg) and is powered by two geared DC motors. Currently the robot has three potentiometers to measure the relative angles between adjacent links and only one tachometer to measure the relative angular position of the first link. A mathematical model for the robot is derived using Lagrange equations. Since the model is inherently nonlinear and multivariate, it presents more challenges when modelling the Robogymnast and dealing with control motion problems. The proposed approach for dealing with the design of the control system is based on a discrete-time linear model around the upright position of the Robogymnast. To study the swinging motion of the Robogymnast, a new technique is proposed to manipulate the frequency and the amplitude of the sinusoidal signals as a means of controlling the motors. Due to the many combinations of the frequency and amplitude, an optimisation method is required to find the optimal set. The Bees Algorithm (BA), a novel swarm-based optimisation technique, is used to enhance the performance of the swinging motion through optimisation of the manipulated parameters of the control actions. The time taken to reach the upright position at its best is 128 seconds. Two different control methods are adopted to study the balancing/stablising of the Robogymnast in both the downward and upright configurations. The first is the optimal control algorithm using the Linear Quadratic Regulator (LQR) technique with integrators to help achieve and maintain the set of reference trajectories. The second is a combination of Local Control (LC) and LQR. Each controller is implemented via reduced order state observer to estimate the unmeasured states in terms of their relative angular velocities. From the identified data in the relative angular positions of the upright balancing control, it is reported that the maximum amplitude of the deviation in the relative angles on average are approximately 7.5° for the first link and 18° for the second link. It is noted that the third link deviated approximately by 2.5° using only the LQR controller, and no significant deviation when using the LQR with LC. To explore the combination between swinging and balancing motions, a switching mechanism between swinging and balancing algorithm is proposed. This is achieved by dividing the controller into three stages. The first stage is the swinging control, the next stage is the transition control which is accomplished using the Independent Joint Control (IJC) technique and finally balancing control is achieved by the LQR. The duration time of the transition controller to track the reference trajectory of the Robogymnast at its best is found to be within 0.4 seconds. An external disturbance is applied to each link of the Robogymnast separately in order to study the controller's ability to overcome the disturbance and to study the controller response. The simulation of the Robogymnast and experimental realization of the controllers are implemented using MATLAB® software and the C++ program environment respectively

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Applicable Solutions in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered 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 great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. 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 event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Engineering Dynamics and Life Sciences

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”

Navigational Strategies for Control of Underwater Robot using AI based Algorithms

Autonomous underwater robots have become indispensable marine tools to perform various tedious and risky oceanic tasks of military, scientific, civil as well as commercial purposes. To execute hazardous naval tasks successfully, underwater robot needs an intelligent controller to manoeuver from one point to another within unknown or partially known three-dimensional environment. This dissertation has proposed and implemented various AI based control strategies for underwater robot navigation. Adaptive versions of neuro-fuzzy network and several stochastic evolutionary algorithms have been employed here to avoid obstacles or to escape from dead end situations while tracing near optimal path from initial point to destination of an impulsive underwater scenario. A proper balance between path optimization and collision avoidance has been considered as major aspects for evaluating performances of proposed navigational strategies of underwater robot. Online sensory information about position and orientation of both target and nearest obstacles with respect to the robot’s current position have been considered as inputs for path planners. To validate the feasibility of proposed control algorithms, numerous simulations have been executed within MATLAB based simulation environment where obstacles of different shapes and sizes are distributed in a chaotic manner. Simulation results have been verified by performing real time experiments of robot in underwater environment. Comparisons with other available underwater navigation approaches have also been accomplished for authentication purpose. Extensive simulation and experimental studies have ensured the obstacle avoidance and path optimization abilities of proposed AI based navigational strategies during motion of underwater robot. Moreover, a comparative study has been performed on navigational performances of proposed path planning approaches regarding path length and travel time to find out most efficient technique for navigation within an impulsive underwater environment

Fractional Calculus and the Future of Science

Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

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