快速伺服刀架迟滞特性的Preisach建模

使用压电陶瓷作驱动元部件的快速伺服刀架是一种新的加工手段。本文介绍了基于Preisach模型的快速伺服刀架迟滞特性建模方法。作为快速伺服刀架的驱动元部件,压电陶瓷微位移器自身的迟滞、蠕变等非线性特性严重影响了快速伺服刀架的动态性能。为了精确建立快速伺服刀架的迟滞模型,给出了Preisach模型的数字表达方式,通过一系列实验测得的数据证明快速伺服刀架系统具有一致特性与擦除特性,满足Preisach模型的两个必要条件,最后在实验数据的基础上建立了基于Preisach模型的迟滞特性模型。实验表明,该迟滞模型可以很好地预测快速伺服刀架的迟滞位移曲线,其预测误差不超过0.65 μm。     

压电作动器的支持向量机迟滞模型

压电作动器被广泛应用于高精度定位领域,但是其固有的迟滞非线性会严重影响定位精度。为了准确地描述压电作动器的迟滞特性,提出了一种基于非线性自回归移动平均(NARMAX)的支持向量机(SVM)迟滞模型。为了建立SVM迟滞模型,首先需要将压电作动器的输入输出关系从一个多值映射问题转化为单值映射问题,对比了不同的单值映射对SVM迟滞模型精度及泛化能力的影响,提出了一种基于NARMAX构建单值映射的方法,建立了在全局上具有更高精度的压电作动器SVM迟滞模型。通过减小训练集中所包含输入信号频率的间隔,提高了模型在测试集上的精度。采用交叉验证的方法确定SVM模型中的参数,提高了迟滞模型在全局上的精度和泛化能力。结果表明,相比传统Bouc-Wen模型,所提出的模型在1 Hz处精度提高了8倍,在50 Hz处精度提高了60倍。通过位移跟踪实验,证明了基于SVM迟滞逆模型的前馈+反馈(FF+FB)控制能够有效提高跟踪精度,相较于PID反馈控制,其跟踪误差最多可降低73.9%。     

压电陶瓷执行器迟滞特性的 广义非线性Preisach模型及其数值实现

压电陶瓷执行器的迟滞非线性不具有经典Preisach模型的次环一致特性,直接利用该模型对压电陶瓷执行器的迟滞特性建模会产生较大误差。为了提高压电陶瓷执行器的迟滞特性建模精度,在非线性Preisach模型的基础上推导得到适用于压电陶瓷迟滞特性的广义非线性Preisach模型,并给出简化分类计算公式。广义非线性Preisach模型将经典Preisach模型表示定理中的次环一致特性修改为次环等弦长特性,放宽了对描述对象的限制要求。实验数据表明,与经典Preisach模型相比,广义非线性Preisach模型预测位移的误差绝对值的最大值降低了0.22 μm,均方根误差降低了0.11 μm,能够更精确地描述压电陶瓷的迟滞特性。     

基于最小二乘支持向量机的压电作动器迟滞非线性建模及参数辨识

为了辨识压电作动器应用中迟滞非线性特性,采用Preisach模型与最小二乘支持向量机（LS-SVM）的混合建模法构建压电作动器模型以表征其迟滞非线性。在Preisach模型基础上采用一阶回转曲线法求得α-β平面内的迟滞单元加权系数,以迟滞单元形心和加权系数作为训练模型的输入输出,利用遗传算法对模型参数进行了辨识。数值仿真验证了建立的模型能精确描述压电作动器迟滞非线性特性,仿真结果与实验结果的相对误差在0.12%~2.01%之间,证实了模型的有效性。     

在Preisach模型框架下的似对角动态神经网络压电陶瓷迟滞模型的研究

在Preisach模型的结构下,用一阶微分方程代替relay迟滞元,借鉴对角动态神经网络模型,提出压电陶瓷迟滞特性的一种新的数学模型。该模型既有Preissach模型的结构思想,又能反映其动态特性。在输入信号是周期性衰减信号的激励下,由Preisach模型产生的数据和压电陶瓷产生的数据分别进行建模和预测仿真,结果表明该模型用于压电陶瓷迟滞特性建模是有效的,并具有较高的模型精度。     

压电陶瓷驱动器建模与控制技术的研究

由于压电致动器(PA)具有高带宽、高纳米位移分辨率和零机械摩擦等优点,其广泛应用于微/纳米操作、微/纳米定位和光学系统。然而,压电致动器的迟滞非线性却严重影响了其跟踪定位精度,甚至引起闭环系统失稳。为了模拟具有不对称特性的压电致动器的滞后特性和频率相关性,使用广义Bouc-Wen模型来描述压电致动器的滞后性并对该模型进行了参数辨识。然后,使用基于该模型的线性化反馈滑模控制器来改善压电致动器的迟滞非线性,最后采用MATLAB对压电致动器的位移与速度进行跟踪控制仿真,并对其位移误差进行仿真,以验证该模型的有效性,其显著提高了压电致动器的位移控制精度,有效提高了系统的鲁棒性,进而可显著提高双光子聚合加工系统的定位精度。     

压电驱动器的非线性模型及其精密定位控制研究

压电驱动器的非线性特性和迟滞特性是影响微动平台定位控制精度的主要因素。采用改进的Preisach模型对压电驱动器的迟滞特性进行建模，利用建立的Preisach模型进行开环精密定位控制和作为PID反馈控制的前馈环节的研究。实验结果表明，该模型能够有效地降低非线性迟滞特性对压电驱动器位移输出精度的影响，提高驱动器的动态响应特性。     

基于Preisach模型的压电陶瓷执行器线性插值法迟滞位移研究

论文介绍了基于Preisach模型的迟滞特性建模方法.通过一系列实验数据建立了Preisach模型,研究了如何应用线性插值法和BP神经网络方法进行任意Preisach函数X（α,β）值的求解,从而计算得到相应电压序列的位移,分析比较了两种方法的预测结果.实验表明,基于Preisach模型的线性插值方法方法可以更好地预测压电陶瓷执行器的迟滞位移.     

具有迟滞和蠕变特性压电作动器的模糊自适应逆控制方法

针对具有迟滞和蠕变特性的压电作动器非线性模型,提出了一种前馈控制和反馈控制相结合的自适应模糊逆控制方案。在前馈控制器中压电作动器的迟滞和蠕变非线性特性的逆模型由自适应模糊逻辑系统近似;在反馈控制器中比例控制器用来调节压电作动器的输出误差。该方法可以实时补偿压电作动器的迟滞和蠕变特性,减少作动器跟踪误差。仿真计算结果表明了该方法的有效性。     

压电驱动晶体的特性研究

压电陶瓷迟滞特性是影响压电陶瓷驱动器位移输出精度的主要因素。在仔细研究现有的解决方案的基础上，采用Preisach模型对压电的迟滞性进行建模，并进行了相应的实验研究。实验结果证明该方法可以很好地降低压电陶瓷迟滞特性对位移输出性能的影响。而且采用压电陶瓷位移输出不回复到初始0电压状态的处理方法能够更地吻合实际情况。     

Hybrid model based on Preisach and support vector machine for novel dual-stack piezoelectric actuator

This paper presents a hybrid model for piezoelectric actuators (PAs), which accounts for hysteresis and dynamic effects. The hybrid model is based on discrete Preisach model and Support Vector Machine (SVM). The Preisach model is generally implemented using a numerical technique basing on the first-order reversal curves (FORCs). The accuracy of the Preisach model mainly depends on the number of FORCs. However it is generally difficult to achieve enough number of FORCs in practice. In order to promote the modeling efficiency, firstly in Preisach modeling process, the storage method of prehistory and interpolation approach of output are improved; then SVM is employed in the work to circumvent the deficiency of the Preisach model resulting from the lack of FORCs, which produces a hybrid model based on the improved Preisach model and SVM. This hybrid model is implemented in calibration of a piezoelectric stack actuator and validated experimentally. Finally, a novel dual-stack PA is introduced and calibrated with this hybrid model. The results demonstrate that the presented hybrid model possesses the advantages both of SVM and Preisach model. In comparison with pure Preisach model, the hybrid model has higher accuracy and is easier to be obtained without increasing the number of FORCs. In addition, the inverse model for PA is derived from the hybrid model, which can be employed in active vibration control of structures.     

菱形压电驱动器对称驱动形式的研究

为了提高压电堆栈的位移输出,该文设计了一种菱形压电驱动器。该机构以压电堆栈作为驱动元件,利用菱形位移放大器放大叠层压电陶瓷的输出位移。该文首先对三角放大原理进行了分析,接着对菱形压电驱动器在一端固定一端驱动负载和两端同时对称驱动负载两种不同的约束方式进行了理论分析,然后利用ANSYS软件对菱形压电驱动器的静、动态特性进行了有限元分析。通过分析结果可以得出,该机构的仿真放大倍数为6. 17,接近于机构的理论放大倍数7. 12,而对称驱动下的工作频率可远远高于一端驱动下的工作频率,并对该结果进行了进一步的分析与讨论。     

Modeling of hysteresis in piezoelectric actuators using neural networks

For the application of neural networks to the approximation of hysteresis which is characterized of multi-valued mapping and non-smooth nonlinearities, a novel modeling technique based on a transformation of one-to-one mapping is proposed in this paper. In this method, a special hysteretic operator is introduced to describe the change tendency of the hysteresis with regard to its input. Then an expanded input space is constructed for hysteresis with the introduction of such hysteretic operator, on which the multi-valued hysteresis is decomposed into a one-to-one mapping. Thus, neural networks model for hysteresis is derived, avoiding the calculation of the gradient of hysteresis. Subsequently, for approximation of rate-dependent hysteresis in piezoelectric actuators which is caused by the dynamic voltage excitations, a hybrid model, i.e. the dynamic extension of the proposed neural hysteresis submodel is developed. In the model, a linear dynamic block is introduced in series with the proposed neural model to allow for rate-dependent dynamics of the piezoelectric actuator simultaneously. Also the corresponding optimization algorithm by use of the modified Levenberg–Marquarqt (MLM) method is given. Finally, the experimental validation results of applying both the proposed neural hysteresis model and hybrid model to a piezoelectric actuator are presented.     

压电作动器非对称迟滞模型的建立和参数辨识

现有的众多基于传统Bouc-Wen改进的压电陶瓷非对称迟滞模型存在参数冗余,降低了模型参数辨识的准确性,而且常用的粒子群算法(PSO)在辨识压电陶瓷非对称迟滞模型参数方面收敛慢且容易陷入局部最优值。为此,首先提出了一种归一化的非对称迟滞模型,采用两个多项式达到非对称效果,利用归一化Bouc-Wen消除参数冗余;然后采用参数和变异策略自适应的差分进化算法进行迟滞参数辨识;建立了相应的测试系统,对压电陶瓷作动器进行了实验研究。结果表明,相比于传统的Bouc-Wen模型,所提出的模型能更精确地描述压电陶瓷实际电压位移曲线,而且消除了参数的冗余,降低了参数辨识的难度。相比于粒子群算法和传统差分进化算法,自适应差分进化算法能更快更精准地找到最优参数值。     

压电微动工作台的位移复合控制

为解决稳态精度和稳定性之间的矛盾,提高压电陶瓷执行器的控制性能,进而提高其驱动的微动工作台的定位精度,构造了一种前馈补偿同反馈调节相结合的复合控制算法。其中,前馈补偿为基于压电陶瓷执行器迟滞非线性模型的前馈控制,通过自学习算法来实现,用来补偿压电陶瓷执行器的迟滞非线性,提高对参考位移信号的跟踪能力;反馈调节为PID反馈控制,用来进一步校正前馈补偿没有消除的偏差以及由模型的不确定性所引起的误差,且为了减小积分饱和作用以及微分对扰动的敏感性,对PID算法进行了改进,使之成为一种变系数积分与加权微分的PID算法。试验验证了该算法的有效性,并将该算法同其他控制算法——开环控制、前馈控制、PID 反馈控制进行了对比试验研究,结果表明,复合控制算法比其他控制算法具有更好的性能。     

Adaptive identification of hysteresis and creep in piezoelectric stack actuators

The adaptive identification of the non-linear hysteresis and creep effects in a piezoelectric actuator is proposed in this paper. Model uncertainties related to the hysteresis and creep effects, most prominently in the high frequency zone (to 100 Hz), large operating amplitude and/long operating time, can make a piezoelectric actuator-driven micro-positioning system unstable in the closed loop. Furthermore, these uncertainties may lead to inaccurate open-loop control and frequently cause harmonic distortion when a piezoelectric actuator is driven with a sinusoidal input voltage signal. In order to solve the above issues, it is important to determine an accurate non-linear dynamic model of a piezoelectric actuator. An unscented Kalman filter-based adaptive identification algorithm is presented, which accurately determines the non-linear dynamics of a piezoelectric stack type actuator such that the non-linear hysteresis and creep effects can be accurately predicted. Since hysteresis and creep are dominant in open loop, the actuator is driven in an open-loop mode in this investigation.     

Modeling of piezoelectric actuator for compensation and controller design

This work proposes a novel method for describing the hysteretic non-linearity of a piezoelectric actuator. The hysteresis behavior of piezoelectric actuators, including the minor loop trajectory and the residual displacement near zero input, are modeled by a set of hysteresis operators, including a gain and an input-dependent lag, as well as the parameter scheduling method. A hysteresis model, using the identified parameters, and containing only the dominant hysteresis operator, is presented herein. Based upon a simplified hysteresis model, tracking is controlled to reduce the non-linear effects in the characteristics of the piezoelectric actuator. A proportional-integral (PI) controller, with inverse model feed-forward, suppresses the tracking error to within ±1% full span range (FSR) of the actuator, noticeably improving the tracking performance of the piezoelectric actuator.     

基于PI迟滞模型的单压电变形镜开环控制

压电非线性迟滞导致压电变形镜的开环控制精度及闭环工作带宽降低,限制了其在自适应光学系统中的应用。为克服迟滞影响,提出采用PI迟滞模型描述单压电变形镜的迟滞非线性特性,实现单压电变形镜的高精度开环控制。首先建立PI迟滞数学模型,利用最小二乘法辨识PI迟滞模型的权值,计算出PI逆模型的权值和阈值,从而获得消除迟滞后的变形镜控制电压;接着搭建了基于哈特曼波前传感器的自适应光学测试平台,采用单压电变形镜的环形致动器进行离焦面形的开环控制实验。实验结果表明,经过迟滞消除后变形镜的电压-变形迟滞由9.3%降低到1.2%,离焦面形的开环重构精度提高70%以上,证明该迟滞模型可有效应用于单压电变形镜的开环控制。     

压电执行器动态迟滞建模与LQG最优控制器设计

为提高空间天文望远镜稳像系统中压电快摆镜(Fast Steering Mirror,FSM)的动态性能,对压电执行器(Piezoelectric Actuator,PZT)动态迟滞补偿和控制进行研究。鉴于基于广义Play算子Prandtl-Ishlinskii(PI)模型的求逆复杂性和迟滞曲线的非对称性,构造一种基于广义Stop算子PI逆模型来补偿压电执行器迟滞非线性。采用Hammerstein模型对压电执行器动态迟滞特性进行建模,以广义PI模型和自回归遍历模型(Auto-regressive Exogenous Model,ARX)分别表征Hammerstein迟滞模型中的静态非线性和率相关性,并针对迟滞率相关模型不确定性问题,提出一种前馈补偿和线性二次型Gauss最优控制算法(Linear Quadratic Gaussian,LQG)相结合的复合控制策略。利用自适应差分进化算法(Adaptive Differential Evolution algorithm,ADE)辨识和整定模型及控制器参数。实验结果表明:该动态迟滞模型能够有效描述1～100Hz频率范围内压电执行器迟滞曲线,拟合均方根误差为0.077 1μm(@1 Hz)～0.512 3μm(@100Hz),相对误差为0.31%(@1Hz)～2.09%(@100Hz);实时跟踪幅值为24.5μm的变频目标位移,LQG控制算法的跟踪精度相比于直接前馈控制和PID控制分别提高48.6%和27.02%。