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## Input shaping control

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This chapter is on input shaping, also known as preview control. This is a feedforward control approach that can be applied to reference and disturbance inputs that are known in advance. A discrete-time closed-loop controlled system is considered and its approximate inverse filter that is not causal is designed to achieve desirable inputto-output behaviour. The external input is assumed to be known in advance. Thus, the approximate inverse filter also known as the preview filter as it is not causal. It is applied to the known input offline, resulting in a new input which is applied online to the closed-loop system (hence the name input shaping). This chapter starts with a characterisation of non-minimum phase zeros and approximate inversion methods used to treat them as they cannot be inverted directly. The ZP, ZPG, ZPGE and ZPGO and TSA methods are presented in this chapter as different possible approximate inverse filters for feedforward control.

Chapter Contents:

• 4.1 Introduction to input shaping control
• 4.2 Discrete-time NMP zeros
• 4.3 Different feed forward controller designs
• 4.4 Zero phase compensation
• 4.5 Zero phase gain compensation
• 4.6 Characterisation of complex non-minimum phase zeros
• 4.7 Zero phase extended gain compensation
• 4.8 Zero phase optimal gain compensation
• 4.9 Truncated series approximation compensation
• 4.10 Case study: electrohydraulic testing system
• 4.11 Robustness analysis
• 4.12 Chapter summary and concluding remarks
• References

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