A Stable Autoregressive Moving Average Hysteresis Model in Flexure Fast Tool Servo Control
A Stable Autoregressive Moving Average Hysteresis Model in Flexure Fast Tool Servo Control
复制标题
柔性快刀伺服控制中稳定的自回归移动平均磁滞模型
DOI：
10.1109/tase.2019.2899342
复制
发表时间：
2019-07-01
影响因子：
5.6
通讯作者：
He, Yunbo
中科院分区：
文献类型：
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作者：
Li, Jiedong;Tang, Hui;He, Yunbo
压电驱动的快速刀具伺服系统具有高速、高精度的优点，对微结构阵列的高质量加工具有很大的吸引力。但在高速运行时，其复杂的磁滞非线性将极大地影响FTS系统的精度和稳定性。因此，本文提出了一种稳定的自回归移动平均（SARMA）模型，旨在准确地描述动态滞后非线性。首先，采用长自回归模型残差计算方法确定模型的阶数，检验模型的适用性；然后，根据Lyapunov稳定性理论，从理论上对自回归移动平均（ARMA）模型进行了严格的稳定性分析。通过引入松弛因子对稳定性条件进行变换，采用拉格朗日乘子和最佳平方逼近方法提高了传统ARMA模型的性能。针对FTS闭环控制系统中位移传感器集成困难的问题，设计了一种基于SARMA模型的滞回补偿直接前馈控制策略。最后，与传统的Prandtl-Ishlinskii （PI）模型和SARMA模型进行了一系列高频轨迹跟踪和对比实验，验证了该方法的有效性和优越性。结果一致表明，SARMA模型在控制精度和线性度方面比传统PI模型提高了近20倍，而FTS动态跟踪控制的平均线性度保持在0.43% （265 nm）以内，行程为280 $\mu \text{m}$，定位带宽达到200 Hz。从业人员注意：为了有效提高压电驱动快速刀具伺服机构的定位精度，需要建立具有准确描述性能的滞回模型，以便进一步进行运动控制。因此，本文提出了一种稳定的自回归移动平均模型。利用李雅普诺夫稳定性理论对自回归移动平均（ARMA）模型进行了严格的稳定性分析。引入松弛因子对稳定性条件进行变换，采用最佳平方逼近法提高传统ARMA模型的性能。结合所建立的滞后模型，成功地进行了一系列跟踪控制试验。与传统的Prandtl-Ishlinskii模型相比，FTS的运动精度提高了20倍。快速刀具伺服系统能够实现毫米行程和纳米级精度，并且可以通过使用其他更大行程和更高分辨率的执行器和传感器进一步提高其性能。综上所述，它的潜在应用前景广阔。
Due to the excellent advantages of high speed and high precision, fast tool servo (FTS) system driven by piezoelectric actuators has great attraction for high-quality machining of microstructural array. However, its complex hysteresis nonlinearity at high speed will greatly affect the accuracy and stability of FTS system. Therefore, a stable autoregressive moving average (SARMA) model is proposed in this paper, which aims to describe the dynamic hysteresis nonlinearity accurately. First, a long autoregressive model residual calculation method is used to determine the order of the model and test the applicability of the model. Then, according to the Lyapunov stability theory, the strict stability analysis of the autoregressive moving average (ARMA) model is carried out in theory. By introducing the relaxation factor to transform the stability condition, the Lagrange multiplier and best square approximation method are applied to enhance the performance of the traditional ARMA model. Aiming at the difficulty of displacement sensor integration in FTS closed-loop controlling system, a hysteresis-compensated direct feedforward control strategy based on the proposed SARMA model is designed. Finally, a series of high-frequency trajectory tracking and comparing experiments has been carried out successfully with the traditional Prandtl–Ishlinskii (PI) and SARMA models to verify the effectiveness and superiority of the method. All results uniformly indicate that the SARMA model is nearly 20 times higher than the traditional PI model in terms of control accuracy and linearity, while the average linearity of FTS’s dynamic tracking control is kept within 0.43% (265 nm), the stroke is 280 $\mu \text{m}$ , and the positioning bandwidth is achieved up to 200 Hz. Note to Practitioners—With the purpose to effectively improve the positioning accuracy for the piezoelectric-actuated fast tool servo mechanism, a hysteresis model with accurate description performance should be established for the further motion control. Therefore, a stable autoregressive moving average model is proposed in this paper. The strict stability analysis of the autoregressive moving average (ARMA) model is carried out using the Lyapunov stability theory. A relaxation factor is introduced to transform the stability condition, the best square approximation method is applied to enhance the performance of the traditional ARMA model. Combining with the established hysteresis model, a series of tracking control tests is successfully conducted. Comparing to the traditional Prandtl–Ishlinskii model, the FTS’s motion accuracy is greatly improved by 20 times. The fast tool servo system has the capability to achieve millimeter stroke and nanometer scale precision, since its performance can be further improved by using other actuators and sensors with larger travel range and higher resolution. In summary, its potential applications will be promising.