digital-brain/content/book/du10_model_contr_vibrat_mechan_system.md

+++ title = "Modeling and control of vibration in mechanical systems" author = ["Thomas Dehaeze"] draft = true +++

Tags

[Stewart Platforms]({{< relref "stewart_platforms" >}}), [Vibration Isolation]({{< relref "vibration_isolation" >}})

Reference

(Du and Xie 2010)

Author(s)

Du, C., & Xie, L.

Year

2010

1. Mechanical Systems and Vibration

1.1 Magnetic recording system

1.2 Stewart platform

1.3 Vibration sources and descriptions

1.4 Types of vibration

1.4.1 Free and forced vibration

1.4.2 Damped and undamped vibration

1.4.3 Linear and nonlinear vibration

1.4.4 Deterministic and random vibration

1.4.5 Periodic and nonperiodic vibration

1.4.6 Broad-band and narrow-band vibration

1.5 Random vibration

1.5.1 Random process

1.5.2 Stationary random process

1.5.3 Gaussian random process

1.6 Vibration analysis

1.6.1 Fourier transform and spectrum analysis

1.6.2 Relationship between the Fourier and Laplace transforms

1.6.3 Spectral analysis

2. Modeling of Disk Drive System and Its Vibration

2.1 Introduction

2.2 System description

2.3 System modeling

2.3.1 Modeling of a VCM actuator

2.3.2 Modeling of friction

2.3.3 Modeling of a PZT microactuator

2.3.4 An example

2.4 Vibration modeling

2.4.1 Spectrum-based vibration modeling

2.4.2 Adaptive modeling of disturbance

2.5 Conclusion

3. Modeling of [Stewart Platforms]({{< relref "stewart_platforms" >}})

3.1 Introduction

3.2 System description and governing equations

3.3 Modeling using adaptive filtering approach

3.3.1 Adaptive filtering theory

3.3.2 Modeling of a Stewart platform

3.4 Conclusion

4. Classical Vibration Control

4.1 Introduction

4.2 Passive control

4.2.1 Isolators

4.2.2 Absorbers

4.2.3 Resonators

4.2.4 Suspension

4.2.5 An application example – Disk vibration reduction via stacked disks

4.3 Self-adapting systems

4.4 Active vibration control

4.4.1 Actuators

4.4.2 Active systems

4.4.3 Control strategy

4.5 Conclusion

5. Introduction to Optimal and Robust Control

5.1 Introduction

5.2 H2 and H∞ norms

5.2.1 H2 norm

5.2.2 H∞ norm

5.3 H2 optimal control

5.3.1 Continuous-time case

5.3.2 Discrete-time case

5.4 H∞ control

5.4.1 Continuous-time case

5.4.2 Discrete-time case

5.5 Robust control

5.6 Controller parametrization

5.7 Performance limitation

5.7.1 Bode integral constraint

5.7.2 Relationship between system gain and phase

5.7.3 Sampling

5.8 Conclusion

6. Mixed H2/H∞ Control Design for Vibration Rejection

6.1 Introduction

6.2 Mixed H2/H∞ control problem

6.3 Method 1: slack variable approach

6.4 Method 2: an improved slack variable approach

6.5 Application in servo loop design for hard disk drives

6.5.1 Problem formulation

6.5.2 Design results

6.6 Conclusion

7. Low-Hump Sensitivity Control Design for Hard Disk Drive Systems

7.1 Introduction

7.2 Problem statement

7.3 Design in continuous-time domain

7.3.1 H∞ loop shaping for low-hump sensitivity functions

7.3.2 Application examples

7.3.3 Implementation on a hard disk drive

7.4 Design in discrete-time domain

7.4.1 Synthesis method for low-hump sensitivity function

7.4.2 An application example

7.4.3 Implementation on a hard disk drive

7.5 Conclusion

8. Generalized KYP Lemma-Based Loop Shaping Control Design

8.1 Introduction

8.2 Problem description

8.3 Generalized KYP lemma-based control design method

8.4 Peak filter

8.4.1 Conventional peak filter

8.4.2 Phase lead peak filter

8.4.3 Group peak filter

8.5 Application in high frequency vibration rejection

8.6 Application in mid-frequency vibration rejection

8.7 Conclusion

9. Combined H2 and KYP Lemma-Based Control Design

9.1 Introduction

9.2 Problem formulation

9.3 Controller design for specific disturbance rejection and overall error minimization

9.3.1 Q parametrization to meet specific specifications

9.3.2 Q parametrization to minimize H2 performance

9.3.3 Design steps

9.4 Simulation and implementation results

9.4.1 System models

9.4.2 Rejection of specific disturbance and H2 performance minimization

9.4.3 Rejection of two disturbances with H[sub(2)] performance minimization

9.5 Conclusion

10. Blending Control for Multi-Frequency Disturbance Rejection

10.1 Introduction

10.2 Control blending

10.2.1 State feedback control blending

10.2.2 Output feedback control blending

10.3 Control blending application in multi-frequency disturbance rejection

10.3.1 Problem formulation

10.3.2 Controller design via the control blending technique

10.4 Simulation and experimental results

10.4.1 Rejecting high-frequency disturbances

10.4.2 Rejecting a combined mid and high frequency disturbance

10.5 Conclusion

11. H∞-Based Design for Disturbance Observer

11.1 Introduction

11.2 Conventional disturbance observer

11.3 A general form of disturbance observer

11.4 Application results

11.5 Conclusion

12. Two-Dimensional H2 Control for Error Minimization

12.1 Introduction

12.2 2-D stabilization control

12.3 2-D H2 control

12.4 SSTW process and modeling

12.4.1 SSTW servo loop

12.4.2 Two-dimensional model

12.5 Feedforward compensation method

12.6 2-D control formulation for SSTW

12.7 2-D stabilization control for error propagation containment

12.7.1 Simulation results

12.8 2-D H2 control for error minimization

12.8.1 Simulation results

12.8.2 Experimental results

12.9 Conclusion

13. Nonlinearity Compensation and Nonlinear Control

13.1 Introduction

13.2 Nonlinearity compensation

13.3 Nonlinear control

13.3.1 Design of a composite control law

13.3.2 Experimental results in hard disk drives

13.4 Conclusion

14. Quantization Effect on Vibration Rejection and Its Compensation

14.1 Introduction

14.2 Description of control system with quantizer

14.3 Quantization effect on error rejection

14.3.1 Quantizer frequency response measurement

14.3.2 Quantization effect on error rejection

14.4 Compensation of quantization effect on error rejection

14.5 Conclusion

15. Adaptive Filtering Algorithms for Active Vibration Control

15.1 Introduction

15.2 Adaptive feedforward algorithm

15.3 Adaptive feedback algorithm

15.4 Comparison between feedforward and feedback controls

15.5 Application in Stewart platform

15.5.1 Multi-channel adaptive feedback AVC system

15.5.2 Multi-channel adaptive feedback algorithm for hexapod platform

15.5.3 Simulation and implementation

15.6 Conclusion

Bibliography

Du, Chunling, and Lihua Xie. 2010. Modeling and Control of Vibration in Mechanical Systems. Automation and Control Engineering. CRC Press. https://doi.org/10.1201/9781439817995.