Control of Axially Moving Systems

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