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E-raamat: Mechanical Systems: A Unified Approach to Vibrations and Controls

  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Sep-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319083711
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Mechanical Systems: A Unified Approach to Vibrations and ControlsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Sep-2014
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319083711
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This essential textbook concerns analysis and control of engineering mechanisms, which includes almost any apparatus with moving parts used in daily life, from musical instruments to robots. A particular characteristic of this book is that it presents with considerable breadth and rigor both vibrations and controls. Many contemporary texts combine both of these topics in a single, one term course. This text supports the more favorable circumstance where the material is covered in a one year sequence contains enough material for a two semester sequence, but it can also be used in a single semester course combining two topics. Mechanical Systems: A Unified Approach to Vibrations and Controls presents a common notation and approach to these closely related areas. Examples from the both vibrations and controls components are integrated throughout this text.

Overview with Some Definitions and Mathematics.- One Degree of Freedom Systems.- More Than One Degree of Freedom Systems and the Euler-Lagrange Process.- Modal Analysis.- Vibration Measurement.- State Space, Equilibrium, Linearization, and Stability.- Classical Control.- The Basics of State Space Control.- Observers.- Tracking Control.- Introduction to Nonlinear Control.
1 Overview with Some Definitions and Mathematics
1(20)
1.1 General Introduction
1(4)
1.2 Vibrations
5(1)
1.3 Control
6(2)
1.4 Energy
8(1)
1.5 Scaling: Nondimensional Equations of Motion
9(2)
1.6 Complex Numbers and Trigonometric Functions
11(10)
1.6.1 Harmonic Functions and Periodicity
15(2)
Exercises
17(3)
References
20(1)
2 One Degree of Freedom Systems
21(58)
2.1 Development
21(5)
2.1.1 An Aside About Friction
21(3)
2.1.2 The One Degree of Freedom Equation of Motion
24(2)
2.2 Mathematical Analysis of the One Degree of Freedom Systems
26(20)
2.2.1 Undamped Free Oscillations
26(7)
2.2.2 Damped Unforced Systems
33(5)
2.2.3 Forced Motion
38(3)
2.2.4 The Particular Solution for a Harmonically Forced Damped System
41(5)
2.3 Special Topics
46(12)
2.3.1 Natural Frequencies Using Energy
46(4)
2.3.2 A General Particular Solution to Eq. (2.4)
50(2)
2.3.3 Combining Springs and Dampers
52(2)
2.3.4 Measuring the Damping Ratio
54(2)
2.3.5 Support Motion
56(2)
2.4 Applications
58(11)
2.4.1 Unbalanced Rotating Machinery
58(4)
2.4.2 Simple Air Bag Sensor
62(3)
2.4.3 Seismometers and Accelerometers
65(4)
2.5 Preview of Things to Come
69(10)
2.5.1 Introduction to Block Diagrams
69(3)
2.5.2 Introduction to Simulation: The Simple Pendulum
72(3)
Exercises
75(3)
References
78(1)
3 More Than One Degree of Freedom Systems and the Euler-Lagrange Process
79(50)
3.1 Introduction: Degrees of Freedom
79(5)
3.2 The Euler-Lagrange Equations
84(12)
3.2.1 The Basic Undamped, Force-Free Euler-Lagrange Equations
85(8)
3.2.2 External Forces (and Torques)
93(2)
3.2.3 Dissipation and the Rayleigh Dissipation Function
95(1)
3.3 Linearization and Stability I
96(9)
3.4 Some Two Degree of Freedom Systems
105(9)
3.4.1 A Double Pendulum
105(3)
3.4.2 The Pendulum on a Disk
108(2)
3.4.3 Vibration Absorption
110(4)
3.5 Electromechanical Systems
114(12)
3.5.1 Simple Motors
114(9)
3.5.2 Magnetic Suspension
123(3)
3.6 Summary
126(3)
Exercises
127(1)
References
128(1)
4 Modal Analysis
129(44)
4.1 Discrete Systems
129(29)
4.1.1 Undamped Systems
129(8)
4.1.2 Forced Motion
137(5)
4.1.3 Damping
142(16)
4.2 Continuous Elastic Systems
158(15)
4.2.1 Introduction
158(2)
4.2.2 The Vibrating String
160(3)
4.2.3 Longitudinal Vibrations of a Slender Beam
163(2)
4.2.4 Transverse Vibrations of a Slender Beam
165(3)
Exercises
168(3)
References
171(2)
5 Vibration Measurement
173(28)
5.1 Vibration Measurement
173(8)
5.2 Fourier Series and Transforms and Power Spectra
181(20)
5.2.1 Fourier Series
182(9)
5.2.2 Power Spectra
191(3)
5.2.3 The Nyquist Phenomenon
194(4)
Exercises
198(1)
References
199(2)
6 State Space, Equilibrium, Linearization, and Stability
201(56)
6.1 State Space
201(10)
6.1.1 Some Comments on Eigenvalues and Eigenvectors
205(6)
6.2 Solving the General Inhomogeneous System of Linear Equations
211(11)
6.2.1 The State Transition Matrix
211(4)
6.2.2 Diagonalization
215(6)
6.2.3 Companion Form
221(1)
6.3 Equilibrium, Linearization, and Stability
222(7)
6.3.1 Equilibrium
222(1)
6.3.2 Linearization in State Space
223(4)
6.3.3 Stability
227(2)
6.4 Putting It All Together
229(15)
6.4.1 The Overhead Crane
232(12)
6.5 The Phase Plane
244(7)
6.5.1 The Simple Pendulum
245(4)
6.5.2 The van der Pol Oscillator
249(2)
6.6 Summary
251(6)
6.6.1 Four Linear Electromechanical Systems for Future Reference
251(3)
Exercises
254(2)
References
256(1)
7 Classical Control
257(32)
7.1 Introduction
257(14)
7.1.1 What Do We Mean by Control?
257(2)
7.1.2 PID Control of a Single-Input--Single-Output System
259(12)
7.2 The Laplace Transform
271(6)
7.2.1 The Transform
271(2)
7.2.2 Solving Single Linear Ordinary Differential Equations of Any Order
273(3)
7.2.3 Solving Systems of Linear Differential Equations
276(1)
7.3 Control in the Frequency Domain
277(8)
7.4 The Connection Between Transfer Functions and State Space
285(4)
Exercises
286(2)
References
288(1)
8 The Basics of State Space Control
289(44)
8.1 Introduction
289(6)
8.1.1 Review of the Process: A Meta-algorithm
290(2)
8.1.2 Transfer Function vs. State Space
292(3)
8.2 Controllability
295(5)
8.2.1 The Controllability Theorem
295(3)
8.2.2 Companion Form
298(2)
8.3 Using the Companion Form to Control a System
300(8)
8.3.1 Application to the Simple (4D) Overhead Crane
303(5)
8.4 Three More Examples
308(19)
8.4.1 More on Pole Placement
316(6)
8.4.2 Disturbances
322(5)
8.5 Summary
327(6)
Exercises
329(2)
Reference
331(2)
9 Observers
333(28)
9.1 Introduction
333(1)
9.2 General Analysis
334(16)
9.2.1 Linear Systems
334(10)
9.2.2 Nonlinear Systems
344(6)
9.3 The High-Inductance Overhead Crane
350(7)
9.3.1 The Gains
351(2)
9.3.2 The Observer Gains
353(4)
9.4 Summary
357(4)
Exercises
358(1)
Reference
359(2)
10 Tracking Control
361(34)
10.1 Introduction
361(1)
10.2 Tracking with Full State Feedback
362(11)
10.2.1 Reference Dynamics
363(3)
10.2.2 The Reference State and the Matrix Ar
366(7)
10.3 The Overhead Crane as an Extended Example of Tracking Control
373(14)
10.3.1 General Comments
373(1)
10.3.2 Tracking a Sinusoidal Path
373(10)
10.3.3 Tracking a More Useful Position
383(4)
10.4 Tracking with an Observer
387(3)
10.5 Summary of Linear Control
390(5)
Exercises
391(4)
11 Introduction to Nonlinear Control
395(36)
11.1 Feedback Linearization
395(14)
11.1.1 A Symbolic Third-Order System
397(12)
11.2 Nonlinear Control of a Kinematic Chain
409(6)
11.3 Elementary Robotics
415(16)
11.3.1 Some Comments on Three-Dimensional Motion
417(6)
11.3.2 Path Following
423(6)
Exercises
429(2)
References 431(2)
Index 433
Dr. Roger Gans is Professor Emeritus of Mechanical Engineering at the University of Rochester
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