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## Repetitive control

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Repetitive control uses a time delay element in a feedback loop to reduce tracking error for systems with periodic reference or disturbance inputs of known period. The SISO continuous-time and discrete-time repetitive control architectures and design methods based on minimising mixed sensitivity at the fundamental periodic frequency and its harmonics are introduced in this chapter. The chapter also has COMES toolbox design examples. The first example is on an AFM application while the second example is on a Quanser QUBE™ servo system application.

Chapter Contents:

• 6.1 Introduction to repetitive control
• 6.2 Stability analysis of repetitive control system
• 6.2.1 Regeneration spectrum analysis
• 6.2.2 Regeneration spectrum analysis applied to repetitive control
• 6.3 Repetitive controller basics
• 6.3.1 Internal model principle
• 6.3.2 Periodic signal generator
• 6.3.4 Low-pass filter q(s) and dynamic compensator b(s)
• 6.4 Parameter space approach to repetitive control
• 6.4.1 Mapping robust performance frequency domain specifications into controller parameter space
• 6.5 Case study: high-speed atomic force microscope scanner position control
• 6.6 Case study: Quanser QUBE™ Servo system
• 6.7 COMES toolbox: repetitive control system design
• 6.8 Discrete-time repetitive control
• 6.8.1 Basic elements of discrete-time repetitive control
• 6.8.2 Discrete-time repetitive control design procedure based on the parameter space approach
• 6.9 Case study: high-speed atomic force microscope scanner position control
• 6.10 Chapter summary and concluding remarks
• References

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