Dynamic Modeling, Simulation, and Control of a Single-link Flexible Manipulator with General Motions

Download Dynamic Modeling, Simulation, and Control of a Single-link Flexible Manipulator with General Motions PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (195 download)

DOWNLOAD NOW!


Book Synopsis Dynamic Modeling, Simulation, and Control of a Single-link Flexible Manipulator with General Motions by : Sumiran V. Neriya

Download or read book Dynamic Modeling, Simulation, and Control of a Single-link Flexible Manipulator with General Motions written by Sumiran V. Neriya and published by . This book was released on 1988 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Flexible Robot Manipulators

Download Flexible Robot Manipulators PDF Online Free

Author :
Publisher : IET
ISBN 13 : 0863414486
Total Pages : 579 pages
Book Rating : 4.8/5 (634 download)

DOWNLOAD NOW!


Book Synopsis Flexible Robot Manipulators by : M. Osman Tokhi

Download or read book Flexible Robot Manipulators written by M. Osman Tokhi and published by IET. This book was released on 2008-05-20 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the latest developmens in modelling, simulation and control of flexible robot manipulators. Coverage includes an overall review of previously developed methodologies, a range of modelling approaches including classical techniques, parametric and neuromodelling approaches and numerical modelling/simulation techniques.

Modelling and Control of Flexible Manipulators in 3D Motion

Download Modelling and Control of Flexible Manipulators in 3D Motion PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (817 download)

DOWNLOAD NOW!


Book Synopsis Modelling and Control of Flexible Manipulators in 3D Motion by : Badrul Aisham Md Zain

Download or read book Modelling and Control of Flexible Manipulators in 3D Motion written by Badrul Aisham Md Zain and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents investigations into modelling and control of flexible manipulators in 3D motion. A finite difference (FD) simulation environment characterising a single-link manipulator in horizontal plane motion and corresponding experimental rig is considered as test bed in this work. The dynamic model of the system is derived using the Lagrange equation and discretised using the FD method. Mathematical models are developed based on physical laws and first principles to represent the dynamics of a physical system well. The simulation algorithm is extended by deriving mathematical model of a single-link flexible manipulator in vertical plane motion with inclusion of gravity. The dynamic behaviour of the system for vertical motion is formulated. The response of the manipulator is assessed in comparison to the corresponding theoretical ones in time and the frequency domains to verify the accuracy of the model in characterizing the behaviour of the flexible manipulator system. However, for systems with complex behaviour and non-linear dynamics, modelling based on first principles is often a formidable and undesirable task, so to solve. these problems, system identification proven as an excellent tool to model such complex systems, is adopted. The objective of system identification is to find exact or approximate model of a dynamic system based on observed system input and output. Linear and non-linear models for the flexible manipulator system are developed using system identification techniques. Linear parametric models, characterising the flexible manipulator system are obtained using the potential of recursive least squares (RLS) estimation, genetic algorithms (GAs) and particle swarm optimisation (PSO) techniques, and combination of estimation and optimisation methods with GARLS. Moreover, the development of PSO with spread factor (PSOSF) and momentum factor (PSOMF) are used to develop suitable model of the flexible manipulator. Furthermore, nonlinear models using multi-layer perceptron (MLP) neural networks (NNs) are developed. These comprise combination GA with inverse NN (GAINN) and PSO with inverse NN (PSOINN). Data from an experimental flexible manipulator system is used to model the system using auto regressive moving average (ARMA) model structure with one-step-ahead prediction.

Modeling and Experimental Validation of a Single-Link Flexible Manipulator

Download Modeling and Experimental Validation of a Single-Link Flexible Manipulator PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 97 pages
Book Rating : 4.:/5 (64 download)

DOWNLOAD NOW!


Book Synopsis Modeling and Experimental Validation of a Single-Link Flexible Manipulator by : Kevin P. Gannon

Download or read book Modeling and Experimental Validation of a Single-Link Flexible Manipulator written by Kevin P. Gannon and published by . This book was released on 1986 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structural flexibility effects on robot mechanisms is a very important consideration in the move toward lighter, faster, and more accurate robot systems. This thesis presents the computer simulation and experimental validation of a dynamic model of an experimental single-link flexible manipulator, using the Equivalent Rigid Link System with an enhanced natural-mode discretization. The experimental arm is driven by a hydraulic actuator and moves in a vertical plane. Hydraulic actuator and moves in a vertical plane. Hydraulic actuator dynamics and the effects of gravity are included in the equations of motion. Computer simulation for the experimental arm is performed by the Dynamic Simulation Language (DSL). The validation of the dynamic model includes the comparison between the actual tip position and the predicted arm tip position.

Computer Simulation and Experimental Validation of a Dynamic Model (Equivalent Rigid Link System) on a Single-Link Flexible Manipulator

Download Computer Simulation and Experimental Validation of a Dynamic Model (Equivalent Rigid Link System) on a Single-Link Flexible Manipulator PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (641 download)

DOWNLOAD NOW!


Book Synopsis Computer Simulation and Experimental Validation of a Dynamic Model (Equivalent Rigid Link System) on a Single-Link Flexible Manipulator by : Robert P. Petroka

Download or read book Computer Simulation and Experimental Validation of a Dynamic Model (Equivalent Rigid Link System) on a Single-Link Flexible Manipulator written by Robert P. Petroka and published by . This book was released on 1986 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flexibility effects on robot manipulator design and control are typically ignored which is justified when large, bulky robotic mechanisms are moved at slow speeds. However, when increased speed and improved accuracy is desired in robot system performance it is necessary to consider flexible manipulators. This project simulates the motion of a single-link, flexible manipulator using the Equivalent Rigid Link System dynamic model and experimentally validates the computer simulation results. validation of the flexible manipulator dynamic model is necessary to ensure confidence of the model for use in future design and control applications of flexible manipulators.

Advanced Studies of Flexible Robotic Manipulators

Download Advanced Studies of Flexible Robotic Manipulators PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9789812796721
Total Pages : 464 pages
Book Rating : 4.7/5 (967 download)

DOWNLOAD NOW!


Book Synopsis Advanced Studies of Flexible Robotic Manipulators by : Fei-Yue Wang

Download or read book Advanced Studies of Flexible Robotic Manipulators written by Fei-Yue Wang and published by World Scientific. This book was released on 2003 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flexible robotic manipulators pose various challenges in research as compared to rigid robotic manipulators, ranging from system design, structural optimization, and construction to modeling, sensing, and control. Although significant progress has been made in many aspects over the last one-and-a-half decades, many issues are not resolved yet, and simple, effective, and reliable controls of flexible manipulators still remain an open quest. Clearly, further efforts and results in this area will contribute significantly to robotics (particularly automation) as well as its application and education in general control engineering. To accelerate this process, the leading experts in this important area present in this book the state of the art in advanced studies of the design, modeling, control and applications of flexible manipulators. Sample Chapter(s). Chapter 1: Flexible-link Manipulators: Modeling, Nonlinear Control and Observer (235 KB). Contents: Flexible-Link Manipulators: Modeling, Nonlinear Control and Observer (M A Arteaga & B Siciliano); Energy-Based Control of Flexible Link Robots (S S Ge); Trajectory Planning and Compliant Control for Two Manipulators to Deform Flexible Materials (O Al-Jarrah et al.); Force Control of Flexible Manipulators (F Matsuno); Experimental Study on the Control of Flexible Link Robots (D Wang); Sensor Output Feedback Control of Flexible Robot Arms (Z-H Luo); On GA Based Robust Control of Flexible Manipulators (Z-Q Xiao & L-L Cui); Analysis of Poles and Zeros for Tapered Link Designs (D L Girvin & W J Book); Optimum Shape Design of Flexible Manipulators with Tip Loads (J L Russell & Y-Q Gao); Mechatronic Design of Flexible Manipulators (P-X Zhou & Z-Q Xiao); A Comprehensive Study of Dynamic Behaviors of Flexible Robotic Links: Modeling and Analysis (Y-Q Gao & F-Y Wang). Readership: Researchers, lecturers and graduate students in robotics & automated systems, electrical & electronic engineering, and industrial engineering

Fundamentals in Modeling and Control of Mobile Manipulators

Download Fundamentals in Modeling and Control of Mobile Manipulators PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1466580429
Total Pages : 292 pages
Book Rating : 4.4/5 (665 download)

DOWNLOAD NOW!


Book Synopsis Fundamentals in Modeling and Control of Mobile Manipulators by : Zhijun Li

Download or read book Fundamentals in Modeling and Control of Mobile Manipulators written by Zhijun Li and published by CRC Press. This book was released on 2016-04-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mobile manipulators combine the advantages of mobile platforms and robotic arms, extending their operational range and functionality to large spaces and remote, demanding, and/or dangerous environments. They also bring complexity and difficulty in dynamic modeling and control system design.

Flexible Robot Manipulators

Download Flexible Robot Manipulators PDF Online Free

Author :
Publisher : IET
ISBN 13 : 1849195838
Total Pages : 532 pages
Book Rating : 4.8/5 (491 download)

DOWNLOAD NOW!


Book Synopsis Flexible Robot Manipulators by : M.O. Tokhi

Download or read book Flexible Robot Manipulators written by M.O. Tokhi and published by IET. This book was released on 2017-06-28 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Industrial automation is driving the development of robot manipulators in various applications, with much of the research effort focussed on flexible manipulators and their advantages compared to their rigid counterparts. This book reports recent advances and new developments in the analysis and control of these robot manipulators.

Dynamic Analysis and Position Control of a Single Flexible-link Flexible-joint Robot Manipulator Using Time Delay

Download Dynamic Analysis and Position Control of a Single Flexible-link Flexible-joint Robot Manipulator Using Time Delay PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 306 pages
Book Rating : 4.:/5 (156 download)

DOWNLOAD NOW!


Book Synopsis Dynamic Analysis and Position Control of a Single Flexible-link Flexible-joint Robot Manipulator Using Time Delay by : Yuan Dong

Download or read book Dynamic Analysis and Position Control of a Single Flexible-link Flexible-joint Robot Manipulator Using Time Delay written by Yuan Dong and published by . This book was released on 2006 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamics and Control of Light Weight Flexible Manipulators

Download Dynamics and Control of Light Weight Flexible Manipulators PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

DOWNLOAD NOW!


Book Synopsis Dynamics and Control of Light Weight Flexible Manipulators by : Amor Jnifene

Download or read book Dynamics and Control of Light Weight Flexible Manipulators written by Amor Jnifene and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current robot manipulators are controlled using methods that do not take into account the links and joints flexibility. Consequently, tasks are usually carried in a slow fashion. The objective of this research is to improve the performance of light weight flexible manipulators by developing dynamic models and control strategies that include the effects of the links flexibility. Toward achieving this objective, the dynamic model of a single link flexible manipulator has been developed. Two hermit cubic functions are used in conjunction with the deflection and the slope at the tip of the link in order to express the deflection at any point along the link. The model is used to simulate the response of the single link manipulator and its ability to follow various trajectories under collocated control. Even though collocated control such as the computed torque method leads to asymptotic stability in the case of rigid link manipulators, the end point of the single link flexible manipulator has shown sustained oscillations under this type of control. In order to improve the performance of the single link and reduce the tip deflection, dynamic stiffening has been added to the link by using the angular position of a point along the link as the controlled variable. This control method is referred to as the non collocated control. Simulations of the robot motion under non collocated control has shown a significant reduction in the position error of the end point. In order to increase the damping of the flexible link, a new approach referred to as the Computed Torque/Delayed Deflection (CTDD) has been used. The CTDD approach combines the non collocated control with a delayed deflection at the point being used for non collocation feedback. The fastest decay in the end point vibrations was obtained when the delay time is selected to be half the period of the lowest frequency in the system. The CTDD has been extended to the case of a two link flexible manipulator. Simulations results for the tracking performance of the two link flexible manipulator have been carried out using two paths: A straight line path and a four points path. The advantages of using the CTDD approach are outlined by comparing its performance to those of a collocated control (computed torque method) and the non collocated control.

Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller

Download Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (654 download)

DOWNLOAD NOW!


Book Synopsis Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller by :

Download or read book Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of lightweight, thin flexible structures creates a dilemma in the aerospace and robotic industries. While increased operating efficiency and mobility can be achieved by employing such structures, these benefits are compromised by significant structural vibrations due to the increased flexibility. To address this problem, extensive research in the area of vibration control of flexible structures has been performed over the last two decades. The majority of the research has been based on the use of discrete piezoceramic actuators (PZTs) as active dampers, as they are commercial availability and have high force and bandwidth capabilities. Many different active vibration control strategies have previously been proposed, in order to effectively suppress vibrations. The synthesized vibration controllers will be less effective or even make the system to become unstable if the actuator locations and control gains are not chosen properly. However, there is currently no quantitative procedure that deals with these procedures simultaneously. This thesis presents a theoretical and numerical study of vibration control of a singlelink flexible manipulator attached to a rotating hub, with PZTs bonded to the surface of the link. A commercially available fibre optic sensor called ShapeTapeTM is introduced as a new feedback sensing technique, which is complemented by a quantitative and definitive model based procedure for selecting the individual PZT locations and gains. Based on Euler-Bernoulli beam theory, discrete finite element equations are obtained using Lagrange's equations for a PZT-mounted beam element. Slewing of the flexible link by a rotating hub induces vibrations in the link that persist long after the hub stops rotating. These vibrations are suppressed through a combined scheme of PD-based hub motion control and proposed PZT actuator control, which is a composite linear (L-type) and angular (A-type) velocity feedback controller. A Lyapunov approach was used to.

Flexible Manipulators

Download Flexible Manipulators PDF Online Free

Author :
Publisher : Academic Press
ISBN 13 : 0123970369
Total Pages : 269 pages
Book Rating : 4.1/5 (239 download)

DOWNLOAD NOW!


Book Synopsis Flexible Manipulators by : Yanqing Gao

Download or read book Flexible Manipulators written by Yanqing Gao and published by Academic Press. This book was released on 2012-04-12 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Intelligent Systems Series comprises titles that present state-of-the-art knowledge and the latest advances in intelligent systems. Its scope includes theoretical studies, design methods, and real-world implementations and applications. Flexible manipulators play a critical role in applications in a diverse range of fields, such as construction automation, environmental applications, and space engineering. Due to the complexity of the link deformation and dynamics, the research effort on accurate modeling and high performance control of flexible manipulators has increased dramatically in recent years. This book presents analysis, data and insights that will of particular use for researchers and engineers working on the optimization and control of robotic manipulators and automation systems. Government and industry groups have specifically stressed the importance of innovation in robotics, manufacturing automation, and control systems for maintaining innovation and high-value-added manufacturing Discusses the latest research on the quantitative effects of size, shape, mass distribution, tip load, on the dynamics and operational performance of flexible manipulators Presents unique analyses critical to the effective modeling and optimization of manipulators: hard to find data unavailable elsewhere

Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller

Download Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (858 download)

DOWNLOAD NOW!


Book Synopsis Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller by : Kerem Gurses

Download or read book Dynamic Modeling and Vibration Control of a Single-link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller written by Kerem Gurses and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of lightweight, thin flexible structures creates a dilemma in the aerospace androbotic industries. While increased operating efficiency and mobility can be achieved byemploying such structures, these benefits are compromised by significant structuralvibrations due to the increased flexibility. To address this problem, extensive research inthe area of vibration control of flexible structures has been performed over the last twodecades. The majority of the research has been based on the use of discrete piezoceramicactuators (PZTs) as active dampers, as they are commercial availability and have highforce and bandwidth capabilities. Many different active vibration control strategies havepreviously been proposed, in order to effectively suppress vibrations. The synthesizedvibration controllers will be less effective or even make the system to become unstable ifthe actuator locations and control gains are not chosen properly. However, there iscurrently no quantitative procedure that deals with these procedures simultaneously. This thesis presents a theoretical and numerical study of vibration control of a singlelinkflexible manipulator attached to a rotating hub, with PZTs bonded to the surface ofthe link. A commercially available fibre optic sensor called ShapeTapeTM is introduced asa new feedback sensing technique, which is complemented by a quantitative anddefinitive model based procedure for selecting the individual PZT locations and gains. Based on Euler-Bernoulli beam theory, discrete finite element equations are obtainedusing Lagrange's equations for a PZT-mounted beam element. Slewing of the flexiblelink by a rotating hub induces vibrations in the link that persist long after the hub stopsrotating. These vibrations are suppressed through a combined scheme of PD-based hubmotion control and proposed PZT actuator control, which is a composite linear (L-type)and angular (A-type) velocity feedback controller. A Lyapunov approach was used tosynthesize the PZT controller. The feedback sensing of linear and angular velocities isrealized by using the ShapeTapeTM, which measures the bend and twist of the flexiblelink's centerline. Both simulation and experimental results show that tip vibrations aremost effectively suppressed using the proposed composite controller. Its performanceadvantage over the individual linear or angular velocity feedback controllers confirmstheoretical predictions made based on a non-proportional damping model of the PZTeffects. Furthermore, it is demonstrated that the non-proportional nature of the PZTdamping effect must be considered in order to bound the range of allowable controllergain values.

Modeling of a One Flexible Link Manipulator

Download Modeling of a One Flexible Link Manipulator PDF Online Free

Author :
Publisher :
ISBN 13 : 9789533070735
Total Pages : pages
Book Rating : 4.0/5 (77 download)

DOWNLOAD NOW!


Book Synopsis Modeling of a One Flexible Link Manipulator by : Mohamad Saad

Download or read book Modeling of a One Flexible Link Manipulator written by Mohamad Saad and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamic Modeling and Payload-adaptation Control of a Flexible One-link Manipulator

Download Dynamic Modeling and Payload-adaptation Control of a Flexible One-link Manipulator PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (219 download)

DOWNLOAD NOW!


Book Synopsis Dynamic Modeling and Payload-adaptation Control of a Flexible One-link Manipulator by : Jian-Shiang Chen

Download or read book Dynamic Modeling and Payload-adaptation Control of a Flexible One-link Manipulator written by Jian-Shiang Chen and published by . This book was released on 1989 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Vibration Control of Single Link Flexible Manipulator by Using Neural Network

Download Vibration Control of Single Link Flexible Manipulator by Using Neural Network PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 71 pages
Book Rating : 4.:/5 (953 download)

DOWNLOAD NOW!


Book Synopsis Vibration Control of Single Link Flexible Manipulator by Using Neural Network by : Muhammad Zulhilmi Zakaria

Download or read book Vibration Control of Single Link Flexible Manipulator by Using Neural Network written by Muhammad Zulhilmi Zakaria and published by . This book was released on 2013 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: This project presents simulation on minimizing vibration error in single link flexible manipulator system by using neural network system. Flexible manipulator system has a flexible link, an actuator-gear mechanism to rotate the link, an optical encoder to measure joint rotation, accelerometers and strain gauges to sense flexible motion, an optical arrangement to measure the endpoint position and an occasional force sensor attached to the end-point. The overall aim of this project is to develop a dynamic modeling and controller for single link flexible manipulator. In spite of it, we need to minimize the vibration using neural network controller in single link flexible manipulator. The vibration error that occurs in the flexible manipulator is needed to be study and try to reduce it by using the controller (neural network). Towards this thesis, the single link flexible manipulator system being minimize the error by using intelligent neural network controller, and be compared with system existing controller (PID) and the system without controller so that we can see the clearly error percentage reduced. In order to achieve the objective for this project, mathematical model will develop based on system identification using different method such as Lagrage method, Euler-Beurnoulli and System Identification Toolbox in MATLAB and implement it in Mathlab simulink. The results that we achieved is the neural network give the best in order to minimize the vibration error compared to the system without controller about 60% reduction of error and 10% of reduction of error when compared with system with PID controller. Conclusively, the intelligent neural network give us the better results and followed the characteristic of single link flexible manipulator as we desired.

Modelling and Control of Robot Manipulators

Download Modelling and Control of Robot Manipulators PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1447104498
Total Pages : 391 pages
Book Rating : 4.4/5 (471 download)

DOWNLOAD NOW!


Book Synopsis Modelling and Control of Robot Manipulators by : Lorenzo Sciavicco

Download or read book Modelling and Control of Robot Manipulators written by Lorenzo Sciavicco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamental and technological topics are blended uniquely and developed clearly in nine chapters with a gradually increasing level of complexity. A wide variety of relevant problems is raised throughout, and the proper tools to find engineering-oriented solutions are introduced and explained, step by step. Fundamental coverage includes: Kinematics; Statics and dynamics of manipulators; Trajectory planning and motion control in free space. Technological aspects include: Actuators; Sensors; Hardware/software control architectures; Industrial robot-control algorithms. Furthermore, established research results involving description of end-effector orientation, closed kinematic chains, kinematic redundancy and singularities, dynamic parameter identification, robust and adaptive control and force/motion control are provided. To provide readers with a homogeneous background, three appendices are included on: Linear algebra; Rigid-body mechanics; Feedback control. To acquire practical skill, more than 50 examples and case studies are carefully worked out and interwoven through the text, with frequent resort to simulation. In addition, more than 80 end-of-chapter exercises are proposed, and the book is accompanied by a solutions manual containing the MATLAB code for computer problems; this is available from the publisher free of charge to those adopting this work as a textbook for courses.