15 KiB
15 KiB
+++ title = "Modeling and control of vibration in mechanical systems" author = ["Dehaeze Thomas"] draft = true +++
- Tags
- [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
- 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.md" >}})
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. doi:10.1201/9781439817995.