Milling of flexible and thin workpieces is widely used in the industry, but traditional tool control is ineffective. The innovation of this paper is in realistic theoretical methods and explores chatter suppression in the milling of a large, low-frequency workpiece through the application of piezoelectric patches and a reinforcement learning-based controller, which has not been employed before. Due to uncertainties and nonlinearities in the milling process, two model-independent controllers are presented: one based on deep reinforcement learning (DRL), employing the soft-actor-critic (SAC) algorithm, which is compared with an optimized type-2 fuzzy controller to analyze the effectiveness of the new SAC method. Initially, a developed nonlinear model based on experimental data for milling cutting forces is presented to serve as an accurate model for agent training. Nonlinear equations for a cantilever plate with attached piezoelectric patches and accelerometers are derived using von Karman strains, Hamilton’s principle, and the constitutive equations of piezoelectric patches. The coupled nonlinear delayed differential equations (NDDEs) are obtained through the Galerkin and mode summation method. Furthermore, tool wear and process damping (PD) effects are included in these equations. A type-2 fuzzy controller is designed, and its parameters are optimized with a genetic algorithm. Subsequently, an agent is trained using the SAC algorithm of the deep reinforcement learning method for chatter suppression. Eventually, the performance of these two methods is compared in several factors, including the stability lobes, vibration and power spectrum responses, control voltages, and efficiency after the occurrence of chatter, considering the voltage saturation and sampling time. The SAC-based controller outperforms the optimized type-2 fuzzy controller, demonstrating superior material removal rate (MRR), robustness, and optimal responses under varying conditions, proving its effectiveness in machining vibration control.

中文翻译：

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带有压电致动器的柔性板工件非线性铣削中的振振抑制：基于软演员批评家的控制器与优化的 2 型模糊控制器的比较


柔性和薄工件的铣削在工业中应用广泛，但传统的刀具控制效率低下。本文的创新在于现实理论方法，通过应用压电贴片和基于强化学习的控制器来探索大型低频工件铣削中的颤振抑制，这在以前从未使用过。由于铣削过程中的不确定性和非线性，提出了两个独立于模型的控制器：一个基于深度强化学习 （DRL），采用软行为者批评者 （SAC） 算法，与优化的 2 类模糊控制器进行比较，以分析新 SAC 方法的有效性。最初，提出了一个基于铣削切削力实验数据开发的非线性模型，作为代理训练的准确模型。带有压电贴片和加速度计的悬臂板的非线性方程是使用 von Karman 应变、汉密尔顿原理和压电贴片的本构方程推导的。耦合非线性延迟微分方程 （NDDE） 是通过 Galerkin 和模态求和方法获得的。此外，这些方程还包括刀具磨损和工艺阻尼 （PD） 效应。设计了一种 2 型模糊控制器，并采用遗传算法对其参数进行优化。随后，使用深度强化学习方法的 SAC 算法训练代理，以抑制颤振。最后，在考虑电压饱和和采样时间的情况下，从几个因素上比较了这两种方法的性能，包括稳定性波瓣、振动和功率谱响应、控制电压以及发生颤振后的效率。 基于 SAC 的控制器优于优化的 2 型模糊控制器，在不同条件下表现出卓越的材料去除率 （MRR）、稳健性和最佳响应，证明了其在加工振动控制方面的有效性。