Vehicle Dynamics, Stability, and Control, Second Edition

Author: Dean Karnopp

Publisher: CRC Press

ISBN: 146656086X

Category: Technology & Engineering

Page: 326

View: 1041

Anyone who has experience with a car, bicycle, motorcycle, or train knows that the dynamic behavior of different types of vehicles and even different vehicles of the same class varies significantly. For example, stability (or instability) is one of the most intriguing and mysterious aspects of vehicle dynamics. Why do some motorcycles sometimes exhibit a wobble of the front wheel when ridden "no hands" or a dangerous weaving motion at high speed? Why does a trailer suddenly begin to oscillate over several traffic lanes just because its load distribution is different from the usual? Other questions also arise: How do humans control an inherently unstable vehicle such as a bicycle and how could a vehicle be designed or modified with an automatic control system to improve its dynamic properties? Using mainly linear vehicle dynamic models as well as discussion of nonlinear limiting effects, Vehicle Dynamics, Stability, and Control, Second Edition answers these questions and more. It illustrates the application of techniques from kinematics, rigid body dynamics, system dynamics, automatic control, stability theory, and aerodynamics to the study of the dynamic behavior of a number of vehicle types. In addition, it presents specialized topics dealing specifically with vehicle dynamics such as the force generation by pneumatic tires, railway wheels, and wings. The idea that vehicles can exhibit dangerous behavior for no obvious reason is in itself fascinating. Particularly obvious in racing situations or in speed record attempts, dynamic problems are also ubiquitous in everyday life and are often the cause of serious accidents. Using relatively simple mathematical models, the book offers a satisfying introduction to the dynamics, stability, and control of vehicles.

Vehicle Dynamics and Control

Author: Rajesh Rajamani

Publisher: Springer Science & Business Media

ISBN: 1461414334

Category: Technology & Engineering

Page: 498

View: 826

Vehicle Dynamics and Control provides a comprehensive coverage of vehicle control systems and the dynamic models used in the development of these control systems. The control system applications covered in the book include cruise control, adaptive cruise control, ABS, automated lane keeping, automated highway systems, yaw stability control, engine control, passive, active and semi-active suspensions, tire-road friction coefficient estimation, rollover prevention, and hybrid electric vehicles. In developing the dynamic model for each application, an effort is made to both keep the model simple enough for control system design but at the same time rich enough to capture the essential features of the dynamics. A special effort has been made to explain the several different tire models commonly used in literature and to interpret them physically. In the second edition of the book, chapters on roll dynamics, rollover prevention and hybrid electric vehicles have been added, and the chapter on electronic stability control has been enhanced. The use of feedback control systems on automobiles is growing rapidly. This book is intended to serve as a useful resource to researchers who work on the development of such control systems, both in the automotive industry and at universities. The book can also serve as a textbook for a graduate level course on Vehicle Dynamics and Control.

Vehicle Stability

Author: Dean Karnopp

Publisher: CRC Press

ISBN: 9780203913567

Category: Technology & Engineering

Page: 344

View: 6089

This reference offers a systematic approach to the dynamics and stability of vehicles such as cars, bicycles, trailers, motorcycles, and trains and shows how mathematical models of varying degrees of complexity can be used to suggest design guidelines for assurance of vehicle stability. Based on more than 30 years of teaching experience from a renowned authority in mechanical systems modeling, this volume illustrates the derivations of equations of motion using Newton's laws, Lagrange's equations, and bond graphs through a series of examples dispersed throughout the text and describes the similarities and differences in the stability properties of various vehicle types.

Schienenfahrzeugdynamik

Author: Klaus Knothe,Sebastian Stichel

Publisher: Springer-Verlag

ISBN: 364255766X

Category: Mathematics

Page: 341

View: 5531

Mit der Renaissance des Schienenverkehrs hat das Spezialgebiet "Schienenfahrzeugdynamik" an Bedeutung gewonnen. Auf entsprechendes Interesse wird das erste Buch im deutschsprachigen Raum stoßen, das hier seinen Schwerpunkt hat. Obwohl es auf der Vorlesung "Schienenfahrzeugdynamik" an der TU Berlin basiert und Vorkenntnisse bezüglich Mechanik, Schwingungslehre und angewandter Mathematik voraussetzt, spricht es auch den Praktiker an. Das Buch behandelt die Vertikaldynamik bis hin zu Komfortbetrachtungen und die Lateraldynamik so weit, daß dem Leser ein Verständnis der Stabilität von Schienenfahrzeugen möglich ist. Den Vorgängen im Kontakt Rad/Schiene wird besondere Aufmerksamkeit gewidmet. Es enthält die jüngsten Erkenntnisse aus Forschung und Bahnpraxis. Die Autoren gehen detailliert auf die spezielle Terminologie der Schienenfahrzeugdynamik und benachbarter Fachgebiete ein.

Heat Exchanger Design Handbook, Second Edition

Author: Kuppan Thulukkanam

Publisher: CRC Press

ISBN: 1439842124

Category: Technology & Engineering

Page: 1260

View: 4683

Completely revised and updated to reflect current advances in heat exchanger technology, Heat Exchanger Design Handbook, Second Edition includes enhanced figures and thermal effectiveness charts, tables, new chapter, and additional topics––all while keeping the qualities that made the first edition a centerpiece of information for practicing engineers, research, engineers, academicians, designers, and manufacturers involved in heat exchange between two or more fluids. See What’s New in the Second Edition: Updated information on pressure vessel codes, manufacturer’s association standards A new chapter on heat exchanger installation, operation, and maintenance practices Classification chapter now includes coverage of scrapped surface-, graphite-, coil wound-, microscale-, and printed circuit heat exchangers Thorough revision of fabrication of shell and tube heat exchangers, heat transfer augmentation methods, fouling control concepts and inclusion of recent advances in PHEs New topics like EMbaffle®, Helixchanger®, and Twistedtube® heat exchanger, feedwater heater, steam surface condenser, rotary regenerators for HVAC applications, CAB brazing and cupro-braze radiators Without proper heat exchanger design, efficiency of cooling/heating system of plants and machineries, industrial processes and energy system can be compromised, and energy wasted. This thoroughly revised handbook offers comprehensive coverage of single-phase heat exchangers—selection, thermal design, mechanical design, corrosion and fouling, FIV, material selection and their fabrication issues, fabrication of heat exchangers, operation, and maintenance of heat exchangers —all in one volume.

Vehicle Dynamics

Author: Martin Meywerk

Publisher: John Wiley & Sons

ISBN: 1118971353

Category: Technology & Engineering

Page: 360

View: 4497

Vehicle Dynamics comprehensively covers the fundamentals of vehicle dynamics with application to automotive mechatronics. It is divided into the three parts covering longitudinal, vertical and lateral dynamics and considers the application of these to modern mechatronic systems including the anti-lock braking system and dynamic stability control. It also covers driving resistances, powertrain with IC engines and converters, hybrid powertrains and wheel loads and braking process. The conflict Between safety and comfort is discussed, and dynamic behaviour, the suspension system and the electronic stability program are also all considered. Vehicle Dynamics includes exercise problems, MATLAB® codes and is accompanied by a website hosting animations.

Steam Generators and Waste Heat Boilers

For Process and Plant Engineers

Author: V. Ganapathy

Publisher: CRC Press

ISBN: 1482247127

Category: Science

Page: 539

View: 8594

Incorporates Worked-Out Real-World Problems Steam Generators and Waste Heat Boilers: For Process and Plant Engineers focuses on the thermal design and performance aspects of steam generators, HRSGs and fire tube, water tube waste heat boilers including air heaters, and condensing economizers. Over 120 real-life problems are fully worked out which will help plant engineers in evaluating new boilers or making modifications to existing boiler components without assistance from boiler suppliers. The book examines recent trends and developments in boiler design and technology and presents novel ideas for improving boiler efficiency and lowering gas pressure drop. It helps plant engineers understand and evaluate the performance of steam generators and waste heat boilers at any load. Learn How to Independently Evaluate the Thermal Performance of Boilers and Their Components This book begins with basic combustion and boiler efficiency calculations. It then moves on to estimation of furnace exit gas temperature (FEGT), furnace duty, view factors, heat flux, and boiler circulation calculations. It also describes trends in large steam generator designs such as multiple-module; elevated drum design types of boilers such as D, O, and A; and forced circulation steam generators. It illustrates various options to improve boiler efficiency and lower operating costs. The author addresses the importance of flue gas analysis, fire tube versus water tube boilers used in chemical plants, and refineries. In addition, he describes cogeneration systems; heat recovery in sulfur plants, hydrogen plants, and cement plants; and the effect of fouling factor on performance. The book also explains HRSG simulation process and illustrates calculations for complete performance evaluation of boilers and their components. Helps plant engineers make independent evaluations of thermal performance of boilers before purchasing them Provides numerous examples on boiler thermal performance calculations that help plant engineers develop programming codes with ease Follows the metric and SI system, and British units are shown in parentheses wherever possible Includes calculation procedures for the basic sizing and performance evaluation of a complete steam generator or waste heat boiler system and their components with appendices outlining simplified procedures for estimation of heat transfer coefficients Steam Generators and Waste Heat Boilers: For Process and Plant Engineers serves as a source book for plant engineers, consultants, and boiler designers.

Integrated Vehicle Dynamics and Control

Author: Wuwei Chen,Hansong Xiao,Qidong Wang,Linfeng Zhao,Maofei Zhu

Publisher: John Wiley & Sons

ISBN: 1118379993

Category: Technology & Engineering

Page: 400

View: 3196

A comprehensive overview of integrated vehicle system dynamics exploring the fundamentals and new and emerging developments This book provides a comprehensive coverage of vehicle system dynamics and control, particularly in the area of integrated vehicle dynamics control. The book consists of two parts, (1) development of individual vehicle system dynamic model and control methodology; and (2) development of integrated vehicle dynamic model and control methodology. The first part focuses on investigating vehicle system dynamics and control according to the three directions of vehicle motions, including longitudinal, vertical, and lateral. Corresponding individual control systems, e.g. Anti-lock Brake System (ABS), Active Suspension, Electric Power Steering System (EPS), are introduced and developed respectively. Particular attention is paid in the second part of the book to develop integrated vehicle dynamic control system. Integrated vehicle dynamics control system is an advanced system that coordinates all the chassis control systems and components to improve the overall vehicle performance including safety, comfort, and economy. Integrated vehicle dynamics control has been an important research topic in the area of vehicle dynamics and control over the past two decades. The research topic on integrated vehicle dynamics control is investigated comprehensively and intensively in the book through both theoretical analysis and experimental study. In this part, two types of control architectures, i.e. centralized and multi-layer, have been developed and compared to demonstrate their advantages and disadvantages. Integrated vehicle dynamics control is a hot topic in automotive research; this is one of the few books to address both theory and practice of integrated systems Comprehensively explores the research area of integrated vehicle dynamics and control through both theoretical analysis and experimental study Addresses a full range of vehicle system topics including tyre dynamics, chassis systems, control architecture, 4 wheel steering system and design of control systems using Linear Matrix Inequality (LMI) Method

Dynamic Modeling and Control of Engineering Systems

Author: Bohdan T. Kulakowski,John F. Gardner,J. Lowen Shearer

Publisher: Cambridge University Press

ISBN: 113946423X

Category: Technology & Engineering

Page: N.A

View: 5060

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 30% more examples.

Vehicle Dynamics of Modern Passenger Cars

Author: Peter Lugner

Publisher: Springer

ISBN: 3319790080

Category: Technology & Engineering

Page: 375

View: 6213

The book provides the essential features necessary to understand and apply the mathematical-mechanical characteristics and tools for vehicle dynamics including control mechanism. An introduction to passenger car modeling of different complexities provides the basics for the dynamical behavior and presents vehicle models later used for the application of control strategies. The presented modeling of the tire behavior, also for transient changes of the contact patch properties, shows the necessary mathematical descriptions used for the simulation of the vehicle dynamics. The introduction to control for cars and its extension to complex applications using e.g. observers and state estimators is a main part of the book. Finally the formulation of proper multibody codes for the simulation leads to the integration of all parts. Examples of simulations and corresponding test verifications show the profit of such a theoretical support for the investigation of the dynamics of passenger cars.

Applied Dynamics

Author: Haim Baruh

Publisher: CRC Press

ISBN: 1482250799

Category: Science

Page: 872

View: 7423

Gain a Greater Understanding of How Key Components Work Using realistic examples from everyday life, including sports (motion of balls in air or during impact) and vehicle motions, Applied Dynamics emphasizes the applications of dynamics in engineering without sacrificing the fundamentals or rigor. The text provides a detailed analysis of the principles of dynamics and vehicle motions analysis. An example included in the topic of collisions is the famous "Immaculate Reception," whose 40th anniversary was recently celebrated by the Pittsburgh Steelers. Covers Stability and Response Analysis in Depth The book addresses two- and three-dimensional Newtonian mechanics, it covers analytical mechanics, and describes Lagrange’s and Kane’s equations. It also examines stability and response analysis, and vibrations of dynamical systems. In addition, the text highlights a developing interest in the industry—the dynamics and stability of land vehicles. Contains Lots of Illustrative Examples In addition to the detailed coverage of dynamics applications, over 180 examples and nearly 600 problems richly illustrate the concepts developed in the text. Topics covered include: General kinematics and kinetics Expanded study of two- and three-dimensional motion, as well as of impact dynamics Analytical mechanics, including Lagrange’s and Kane’s equations The stability and response of dynamical systems, including vibration analysis Dynamics and stability of ground vehicles Designed for classroom instruction appealing to undergraduate and graduate students taking intermediate and advanced dynamics courses, as well as vibration study and analysis of land vehicles, Applied Dynamics can also be used as an up-to-date reference in engineering dynamics for researchers and professional engineers.

Dynamical Analysis of Vehicle Systems

Theoretical Foundations and Advanced Applications

Author: W. Schiehlen

Publisher: Springer Science & Business Media

ISBN: 3211766669

Category: Technology & Engineering

Page: 304

View: 2767

This volume presents an integrated approach of the common fundamentals of rail and road vehicles based on multibody system dynamics, rolling wheel contact and control system design. The methods presented allow an efficient and reliable analysis of the resulting state equations. The book provides also a better understanding of the basic physical phenomena of vehicle dynamics. Particular attention is paid to developments of future rail and road vehicles including motorcycles.

Dynamic Modeling and Control of Engineering Systems

Author: J. Lowen Shearer

Publisher: N.A

ISBN: 9780133564037

Category: Technology & Engineering

Page: 375

View: 4169

This book presents a comprehensive treatment of the analysis of lumped parameter physical systems. The first portion of the book deals with the fundamentals of dynamics system modeling including a discussion of mechanical systems (translational and rotational), analytical solutions of ordinary differential equations and a discussion of state space theory. This book includes treatment of both input/output and state space models, analogies between physical domains (mechanical, electrical, fluid, and thermal) with an emphasis on the appropriate physical laws, an in-depth discussion of mixed (multi-domain) systems, and a discussion of nonlinearities and linearization methods. Contains chapters on Discrete- Time systems and digital control. It also presents a discussion of transfer functions, stability, and feedback control. It provides specific examples and problems geared toward MATLAB and SIMULINK as well as example files and supplementary files to run with MATLAB and SIMULINK. A valuable reference book for engineering and computer professionals responsible for systems modeling.

Off-road Vehicle Dynamics

Analysis, Modelling and Optimization

Author: Hamid Taghavifar,Aref Mardani

Publisher: Springer

ISBN: 331942520X

Category: Technology & Engineering

Page: 183

View: 2516

This book deals with the analysis of off-road vehicle dynamics from kinetics and kinematics perspectives and the performance of vehicle traversing over rough and irregular terrain. The authors consider the wheel performance, soil-tire interactions and their interface, tractive performance of the vehicle, ride comfort, stability over maneuvering, transient and steady state conditions of the vehicle traversing, modeling the aforementioned aspects and optimization from energetic and vehicle mobility perspectives. This book brings novel figures for the transient dynamics and original wheel terrain dynamics at on-the-go condition.

Vehicle Dynamics

Author: Rao V. Dukkipati

Publisher: Alpha Science International, Limited

ISBN: 9781842650141

Category: Technology & Engineering

Page: 591

View: 772

This monograph consolidates information in the guided ground transportation area from a wide spectrum of sources. Various aspects of vehicle system classification; analytical techniques and direct numerical integration methods for determining vibration response of linear dynamics systems; wheel-rail contact mechanics; various aspects of rail vehicle dynamics; lading dynamics; air-cushion vehicle system performance: resistance, stability and control; and magnetically levitated vehicles, which depend on the action of magnetic forces for levitation, propulsion and guidance are presented.

Applications of Model Predictive Control to Vehicle Dynamics for Active Safety and Stability

Author: N.A

Publisher: Stanford University

ISBN: N.A

Category:

Page: N.A

View: 769

Each year in the United States, thousands of lives are lost as a result of loss of control crashes. Production driver assistance systems such as electronic stability control (ESC) have been shown to be highly effective in preventing many of these automotive crashes, yet these systems rely on a sensor suite that yields limited information about the road conditions and vehicle motion. Furthermore, ESC systems rely on gains and thresholds that are tuned to yield good performance without feeling overly restrictive to the driver. This dissertation presents an alternative approach to providing stabilization assistance to the driver which leverages additional information about the vehicle and road that may be obtained with advanced estimation techniques. This new approach is based on well-known and robust vehicle models and utilizes phase plane analysis techniques to describe the limits of stable vehicle handling, alleviating the need for hand tuning of gains and thresholds. The resulting state space within the computed handling boundaries is referred to as a safe handling envelope. In addition to the boundaries being straightforward to calculate, this approach has the benefit of offering a way for the designer of the system to directly adjust the controller to accomodate the preferences of different drivers. A model predictive control structure capable of keeping the vehicle within the safe handling boundaries is the final component of the envelope control system. This dissertation presents the design of a controller that is capable of smoothly and progressively augmenting the driver steering input to enforce the boundaries of the envelope. The model predictive control formulation provides a method for making trade-offs between enforcing the boundaries of the envelope, minimizing disruptive interventions, and tracking the driver's intended trajectory. Experiments with a steer-by-wire test vehicle demonstrate that the model predictive envelope control system is capable of operating in conjunction with a human driver to prevent loss of control of the vehicle while yielding a predictable vehicle trajectory. These experiments considered both the ideal case of state information from a GPS/INS system and an a priori friction estimate as well as a real-world implementation estimating the vehicle states and friction coefficient from steering effort and inertial sensors. Results from the experiments demonstrated a controller that is tolerant of vehicle and tire parameterization errors and works well over a wide range of conditions. When real time sensing of the states and friction properties is enabled, the results show that coupling of the controller and estimator is possible and the model predictive control structure provides a mechanism for minimizing undesirable coupled dynamics through tuning of intuitive controller parameters. The model predictive control structure presented in this dissertation may also be considered as a general framework for vehicle control in conjunction with a human driver. The structure utilized for envelope control may also be used to restrict other vehicle states for safety and stability. Results are presented in this dissertation to show that a model predictive controller can coordinate a secondary actuator to alter the planar states and reduce the energy transferred into the roll modes of the vehicle. The systematic approach to vehicle stabilization presented in this dissertation has the potential to improve the design methodology for future systems and form the basis for the inclusion of more advanced functions as sensing and computing capabilities improve. The envelope control system presented here offers the opportunity to advance the state of the art in stabilization assistance and provides a way to help drivers of all skill levels maintain control of their vehicle.

Theory of Ground Vehicles

Author: J. Y. Wong

Publisher: John Wiley & Sons

ISBN: 9780471354611

Category: Technology & Engineering

Page: 528

View: 2826

An updated edition of the classic reference on the dynamics of road and off–road vehicles As we enter a new millennium, the vehicle industry faces greater challenges than ever before as it strives to meet the increasing demand for safer, environmentally friendlier, more energy efficient, and lower emissions products. Theory of Ground Vehicles, Third Edition gives aspiring and practicing engineers a fundamental understanding of the critical factors affecting the performance, handling, and ride essential to the development and design of ground vehicles that meet these requirements. As in previous editions, this book focuses on applying engineering principles to the analysis of vehicle behavior. A large number of practical examples and problems are included throughout to help readers bridge the gap between theory and practice. Covering a wide range of topics concerning the dynamics of road and off–road vehicles, this Third Edition is filled with up–to–date information, including: ∗ The Magic Formula for characterizing pneumatic tire behavior from test data for vehicle handling simulations ∗ Computer–aided methods for performance and design evaluation of off–road vehicles, based on the author′s own research ∗ Updated data on road vehicle transmissions and operating fuel economy ∗ Fundamentals of road vehicle stability control ∗ Optimization of the performance of four–wheel–drive off–road vehicles and experimental substantiation, based on the author′s own investigations ∗ A new theory on skid–steering of tracked vehicles, developed by the author.

Dynamic Stability of Hydraulic Gates and Engineering for Flood Prevention

Author: Ishii, Noriaki,Anami, Keiko,Knisely, Charles W.

Publisher: IGI Global

ISBN: 1522530800

Category: Technology & Engineering

Page: 660

View: 3606

Hydraulic gates are utilized in multiple capacities in modern society. As such, the failure of these gates can have disastrous consequences, and it is imperative to develop new methods to avoid these occurrences. Dynamic Stability of Hydraulic Gates and Engineering for Flood Prevention is a critical reference source containing scholarly research on engineering techniques and mechanisms to decrease the failure rate of hydraulic gates. Including a range of perspectives on topics such as fluid dynamics, vibration mechanisms, and flow stability, this book is ideally designed for researchers, academics, engineers, graduate students, and practitioners interested in the study of hydraulic gate structure.

Fundamentals of Helicopter Dynamics

Author: C. Venkatesan

Publisher: CRC Press

ISBN: 1466566353

Category: Technology & Engineering

Page: 338

View: 7548

Helicopter Dynamics Introduced in an Organized and Systematic Manner A result of lecture notes for a graduate-level introductory course as well as the culmination of a series of lectures given to designers, engineers, operators, users, and researchers, Fundamentals of Helicopter Dynamics provides a fundamental understanding and a thorough overview of helicopter dynamics and aerodynamics. Written at a basic level, this text starts from first principles and moves fluidly onward from simple to more complex systems. Gain Valuable Insight on Helicopter Theory Divided into 11 chapters, this text covers historical development, hovering and vertical flight, simplified rotor blade model in flap mode, and forward flight. It devotes two chapters to the aeroelastic response and stability analysis of isolated rotor blade in uncoupled and coupled modes. Three chapters address the modeling of coupled rotor–fuselage dynamics and the associated flight dynamic stability, and provide a simplified analysis of the ground resonance aeromechanical stability of a helicopter. Explains equations derived from first principles and approximations Contains a complete set of equations which can be used for preliminary studies Requires a basic first–level course in dynamics, as well as a basic first–level course in aerodynamics Useful for any student who wants to learn the complexities of dynamics in a flying vehicle, Fundamentals of Helicopter Dynamics is an ideal resource for aerospace/aeronautical, helicopter, and mechanical/control engineers, as well as air force schools and helicopter/rotorcraft manufacturers.

Computation and Asymptotics

Author: Rudrapatna V. Ramnath

Publisher: Springer Science & Business Media

ISBN: 3642257488

Category: Mathematics

Page: 120

View: 9768

This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of different scales in a dynamic phenomenon enable us to make judicious use of them in developing computational approaches which are highly efficient. Many such applications have been developed in such areas as astrodynamics, fluid mechanics and so on. This book presents a novel approach to make use of the different time constants inherent in the system to develop rapid computational methods. First, the fundamental notions of asymptotic analysis are presented with classical examples. Next, the novel systematic and rigorous approaches of system decomposition and reduced order models are presented. Next, the technique of multiple scales is discussed. Finally application to rapid computation of several aerospace systems is discussed, demonstrating the high efficiency of such methods.