Abstract
The weighted function windows are used in many areas as signal analysis and application systems. In addition, the weighted functions are broad uses in filter design where different windows allow to choose different filter characteristics. The most common individual window types are rectangular, Hanning, Flat Top, and Keiser-Bessel. This paper presents the Flat-Top Windows (FTW) applied to control systems where the FTW are used as activation functions on a radial basis neural network (RBF). Contrary to the "traditional" FT weighted function windows, where time windows limit the information, this paper proposes new ones that, including new parameters, allow translation and dilation of the window. Additionally, these new parameters are updated using a gradient descent algorithm. The new FTW is applied to the Quanser helicopter control where the RBF neural network is used for: a) the input-output identification of the system and b) auto-tuning PID controllers. Numerical simulation results are presented to show the system’s performance under different conditions.
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Notes
- 1.
Let the vectors \(a,b,c\in \mathbb {R}^{n\times 1}\) where \(c_x = a_x\cdot b_x\) with \(x\in \lbrace 1,2,...,n\rbrace \) [13].
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Castro, O.F.G. et al. (2022). RBF Neural Network Based on FT-Windows for Auto-Tunning PID Controller. In: Pichardo Lagunas, O., Martínez-Miranda, J., Martínez Seis, B. (eds) Advances in Computational Intelligence. MICAI 2022. Lecture Notes in Computer Science(), vol 13612. Springer, Cham. https://doi.org/10.1007/978-3-031-19493-1_11
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