Control of Axially Moving Systems

✍ Scribed by Keum-Shik Hong, Li-Qun Chen, Phuong-Tung Pham, Xiao-Dong Yang

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 324
• Category: Library

✦ Synopsis

This book provides a comprehensive guideline on dynamic analysis and vibration control of axially moving systems. First, the mathematical models of various axially moving systems describing the string, beam, belt, and plate models are developed. Accordingly, dynamical issues such as the equilibrium configuration, critical velocity, stability, bifurcation, and further chaotic dynamics are analyzed. Second, this book covers the design of the control schemes based on the hitherto control strategies for axially moving systems: feedback control using the transfer function, variable structure control, control by regulating the axial velocity, wave cancellation approach, boundary control using the Lyapunov method, adaptive control, and hybrid control methods. Finally, according to the contents discussed in the book, specific aspects are outlined for initiating future research endeavors to be undertaken concerning axially moving systems. This book is useful to graduate students and researchers in industrial sectors such as continuous manufacturing systems, transport systems, power transmission systems, and lifting systems not to mention in academia. 

✦ Table of Contents

Preface
Contents
Abbreviations
Fundamental Notations
1 Introduction
1.1 Industrial Axially Moving Systems
1.2 Dynamics of Axially Moving Systems
1.3 Control of Axially Moving Systems
References
2 String Model
2.1 Introduction
2.2 Dynamic Models of Axially Moving Strings
2.2.1 Linear Model
2.2.2 Strings with Time-Varying Velocity
2.2.3 Large Amplitude Vibration
2.2.4 Varying-Length Strings
2.2.5 Viscoelastic Strings
2.2.6 Strings with Non-homogenous Boundaries
2.3 Approximate Model
2.4 Dynamic Analysis of String Model
2.4.1 Equilibrium Solution
2.4.2 Stability Analysis
2.4.3 Bifurcation and Chaotic Dynamics
References
3 Beam Model
3.1 Introduction
3.2 Dynamic Models of Axially Moving Beams
3.2.1 Euler–Bernoulli Beam
3.2.2 Varying-Length Beam
3.2.3 Viscoelastic Beams
3.2.4 Rayleigh Beam
3.2.5 Timoshenko Beam
3.2.6 Beams with Nonhomogenous Boundaries
3.2.7 Fluid-Conveying Pipe
3.2.8 Nanoscale Beams
3.2.9 Laminated Composite Beams
3.3 Approximate Model
3.4 Dynamic Analysis of Beam Models
3.4.1 Equilibrium Solutions
3.4.2 Stability Analysis
3.4.3 Bifurcation and Chaotic Dynamics
References
4 Control of Axially Moving Strings and Beams
4.1 Control Based on an ODE Model
4.1.1 Model-Based Feedback Control
4.1.2 Sliding Mode Control
4.1.3 Control Based on Regulating Axial Velocity
4.2 Control Based on a PDE Model
4.2.1 Transfer Function-Based Method
4.2.2 Wave Cancellation Method
4.2.3 Boundary Control Based on the Lyapunov Method
4.2.4 Adaptive Control
4.3 Hybrid Control Methods
4.4 Simulation Examples
References
5 Belt Model
5.1 Introduction
5.2 Dynamic Models of Axially Moving Belts
5.2.1 Belt Model Using a Closed-Form Strain
5.2.2 Belt Model Using Approximate Strains
5.2.3 Viscoelastic Belt
5.2.4 Shear Deformation and Rotary Inertia
5.2.5 Transverse Vibration
5.2.6 Belts with Nonhomogenous Boundaries
5.3 Approximate Model
5.4 Dynamic Analysis of Belt Models
5.4.1 Equilibrium Solutions
5.4.2 Stability Analysis
5.4.3 Bifurcation and Chaotic Dynamics
References
6 Control of Axially Moving Belts
6.1 Boundary Control Based on the Lyapunov Method
References
7 Plate Model
7.1 Introduction
7.2 Dynamic Models of Axially Moving Plates
7.2.1 Elastic Plate
7.2.2 Viscoelastic Plate
7.2.3 Laminated Composite Plate
7.3 Approximate Models
7.4 Dynamic Analysis of Plate Models
7.4.1 Equilibrium Solutions and Stability of an Isotropic Plate
7.4.2 Equilibrium Solutions and Stability of an Orthotropic Plate
References
8 Control of Axially Moving Plates and Membranes
8.1 Control Based on Regulating Axial Velocity
Reference
9 Conclusions and Future Directions
9.1 Concluding Remarks
9.2 Future Directions
Appendix A
Derivation of the Closed-loop Transfer Function of Eq. (4.71)
Appendix B
Criterion 4.1 (Stability for a Linear String)
Appendix C
Proof of Lemmas 4.6 and 4.7
Appendix D
Expansion of (7.13)
Appendix E
Elements of Mass Matrices, Damping Matrices, and Stiffness Matrices in (7.68) and (7.69)
Appendix F
MATLAB Codes
Index