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Spline adaptive inverse control scheme with filtered error feedback

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Abstract

This paper presents a new scheme for the control of unknown block-oriented nonlinear systems using spline adaptive filter (SAF). The principle of adaptive inverse control (AIC) is utilized as the control structure in this scheme. First, the mathematical model of the unknown controlled plant was established through SAF, which consists of a linear FIR filter and a nonlinear spline interpolation function. The controller is obtained by adaptively establishing the inverse model of linear FIR filter and nonlinear spline function, respectively. In this process, a shift form DCT-LMS with variable learning rate (VL-DCTS-LMS) algorithm is proposed in order to adapt the inverse of FIR filter, and a modified Newton–Raphson method is used for directly calculating the inverse of spline interpolation function. Considering the steady-state error resulted by the plant modeling inaccuracy, filtered error feedback is introduced into the plant input in order to eliminate the control error. The effectiveness of the proposed control scheme is verified by several numerical examples, including some additional discussions and a comparison with other control methods.

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Data Availability Statement

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Nos. 51705396, 51835009, 51911530774).

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710054, China

    Liangdong Yang, Jinxin Liu, Qian Zhang, Ruqiang Yan & Xuefeng Chen

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  1. Liangdong Yang
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  2. Jinxin Liu
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  3. Qian Zhang
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  4. Ruqiang Yan
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  5. Xuefeng Chen
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Correspondence to Jinxin Liu.

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Yang, L., Liu, J., Zhang, Q. et al. Spline adaptive inverse control scheme with filtered error feedback. Nonlinear Dyn 106, 2309–2328 (2021). https://doi.org/10.1007/s11071-021-06882-6

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