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Gradient-Descent-Based Velocity Observer with a Residual Displacement Term for ILSMC in Contour Following Applications

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Abstract

Industrial applications such as pick-and-place tasks and CNC machining often involve repetitive motions that may contain periodic disturbances. Due to the periodic nature of these applications, the idea of iterative learning control can be exploited to cope with external periodic disturbances so as to improve system performance. In addition, in order to ensure satisfactory motion accuracy for operation scenarios that may encounter significant disturbance, (e.g., machining and polishing), a robust controller is essential. In particular, iterative learning sliding mode control (ILSMC) is shown to be suitable for control applications that encounter periodic disturbances. However, when the disturbance contains high frequency components, ILSMC may become less effective in compensating for external disturbances if its velocity estimation is not accurate enough. In order to cope with the aforementioned problem, this paper develops a gradient-descent-based velocity observer with a residual displacement compensation term to provide accurate velocity feedback to be used in ILSMC. Both theoretical analysis and experimental results are provided to verify the effectiveness of the proposed approach.

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Abbreviations

x(t):

State vector

\(d_{T} (t)\) :

Periodic disturbance

\(d_{N} (t)\) :

Non-periodic disturbance

L(i):

Learning function for the ith iteration

T(t):

Total accumulated time duration without any measured encoder pulse

Ω :

Magnitude of switching force

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Acknowledgements

This work was supported in part by the Ministry of Science and Technology of the Republic of China, Taiwan, under Grant NSC 102-2221-E-006-204 and MOST 103-2221-E-006-185-MY2.

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  1. Department of Electrical Engineering, National Cheng Kung University, Tainan, 701, Taiwan

    Feng-Ta Chang & Ming-Yang Cheng

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  1. Feng-Ta Chang
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Correspondence to Ming-Yang Cheng.

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Chang, FT., Cheng, MY. Gradient-Descent-Based Velocity Observer with a Residual Displacement Term for ILSMC in Contour Following Applications. Int. J. Precis. Eng. Manuf. 20, 1691–1703 (2019). https://doi.org/10.1007/s12541-019-00181-2

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