压电陶瓷作动器非对称迟滞的建模与补偿控制

针对传统Bouc-Wen模型不能反映压电陶瓷作动器迟滞的非对称特性而导致其补偿控制精度难以提高的问题,提出了一种改进Bouc-Wen模型,通过修改形状控制参数使其能够模拟压电陶瓷作动器的非对称迟滞曲线.利用粒子群优化算法辨识了所需的模型参数,进一步研究了基于模型的前馈补偿控制、前馈加PI反馈补偿控制对于实现高精度位移输出的效果;在开环前馈补偿控制实验中,采用改进Bouc-Wen模型比传统Bouc-Wen模型的控制误差可降低约42％;在前馈加PI反馈补偿控制实验中,采用改进Bouc-Wen模型比传统Bouc-Wen模型的控制误差可降低约20％.研究结果表明:在相同的控制方式下,采用改进Bouc-Wen模型能够得到比传统Bouc-Wen模型更高的轨迹跟踪精度;与单纯采用基于模型的前馈补偿控制相比,采用基于模型的前馈加PI反馈补偿控制可显著提高压电陶瓷作动器的位移输出精度.     

叠堆式压电陶瓷驱动器的复合控制

提出了逆Bouc-Wen前馈控制与反馈控制相结合的复合控制算法,用于改善压电陶瓷驱动器对目标轨迹的跟踪性能。建立了压电陶瓷驱动器的Bouc-Wen迟滞动力学模型,并用粒子群算法(PSO)对该模型的参数进行识别。基于Bouc-Wen迟滞模型,提出了逆Bouc-Wen前馈补偿控制。最后,为消除迟滞模型的不确定性,引入比例积分(PI)反馈控制,并与前馈补偿控制构成复合控制算法。建立了基于dSPACE实时系统的压电陶瓷驱动实验平台,迟滞实验结果表明:压电陶瓷的迟滞误差量几乎为0,线性度高达96.5%;目标轨迹跟踪实验结果表明:复合控制算法的最大跟踪误差为0.180 5μm,均方根(RMS-Root mean square)跟踪误差为0.055 4μm,跟踪精度达到了10-8 m。相比于开环控制、前馈控制及PI反馈控制,提出的复合控制算法能够基本消除压电陶瓷的迟滞非线性,同时具有很好的轨迹跟踪性能。     

压电执行器的非对称动态迟滞特性建模研究

传统Bouc-Wen模型难以精确表征压电执行器固有非对称率相关动态迟滞非线性,因此提出一种广义Bouc-Wen(GBW)迟滞模型用于精确表征压电执行器的迟滞非线性。首先,基于传统Bouc-Wen迟滞模型引入两项非对称项和二阶IIR滤波器表征压电执行器非对称迟滞及高频相位滞后特性,进一步分析了模型参数值与频率变化规律并确定了模型的率相关参数。然后,搭建了基于NI CompactRIO测控系统的压电执行器精密定位实验平台,通过粒子群优化算法完成GBW模型的参数辨识,并对提出的GBW模型进行实验验证。实验结果表明,对于变频率正弦激励信号,GBW模型的最大误差为0.190 6μm,均方根误差为0.043 1μm仅占压电执行器位移行程的0.65%,相较于传统Bouc-Wen(CBW)模型及改进Bouc-Wen(EBW)模型分别下降了82.07%和62.10%。对比CBW模型和EBW模型,所提出的GBW模型精度和宽频性能均有显著提升,并且解析逆模型存在易于控制器设计,有助于实现压电执行器在超精密仪器设备中宽频、高速精密定位。     

压电陶瓷作动器非对称迟滞建模与内模控制

压电陶瓷作动器被广泛应用于精密定位和控制中,但其本身存在的非对称迟滞非线性特性,严重影响了系统的定位和控制精度。针对这一问题,提出了一种基于广义Bouc-Wen模型的非对称迟滞建模方法,并利用差分进化算法辨识模型参数;基于所建的广义Bouc-Wen模型构建了其具有解析形式的迟滞逆模型,并设计了内模控制方案实现对压电陶瓷作动器的精密跟踪控制;最后在压电陶瓷作动器实验平台,对所提出的建模和控制方案进行了实验验证。对压电陶瓷作动器的建模结果表明,系统建模误差均小于0.051 0,比经典Bouc-Wen模型的建模误差降低约21%～46%;对100 Hz内幅值为20μm的期望位移信号的控制实验结果表明,所提出的控制方法具有良好的实时跟踪性能和跟踪控制精度。对100 Hz期望信号的跟踪控制均方根误差为0.491 6μm,相对误差为0.040 2μm,可以很好地满足实际工程需要。     

WTYD型压电陶瓷微位移器的迟滞特性模拟

为了模拟WTYD型压电陶瓷微位移器的输出位移与驱动电压之间的迟滞曲线,本文通过采用Bouc-Wen模型模拟迟滞分量提出了一种表征WTYD型压电陶瓷微位移器的输出位移与驱动电压之间的迟滞关系的Bouc-Wen模型并建立了相应的参数辨识方法。为了验证Bouc-Wen模型及其相应的参数辨识方法的有效性,建立了相应的实验装置并对模型进行了实验验证。研究结果表明,本文提出并研究的WTYD型压电陶瓷微位移器的Bouc-Wen模型及相应的参数辨识方法能较好地模拟WTYD型压电陶瓷微位移器的迟滞特性。     

压电陶瓷驱动器的复合控制方法研究

针对压电陶瓷驱动器中的迟滞非线性特性,提出一种提高压电陶瓷执行器定位精度的复合控制方法。建立了非等间隔阈值的Prandtl-Ishilinskii(PI)迟滞模型,通过自适应差分进化算法进行系统辨识,求取参数并建立逆模型。考虑到压电陶瓷迟滞非线性特性随输入信号频率变化的特点,采用融合PI逆模型前馈控制与滑模控制的复合控制方法用于压电陶瓷的精密驱动。实验结果表明,相比逆模型前馈和PID结合的复合控制方法,采用逆模型前馈和滑模复合控制方法,平均误差下降了0.0300μm,均方根误差下降了0.0346μm,能有效克服压电陶瓷迟滞非线性,提高系统跟踪性能。     

WTYD型压电陶瓷微位移器的迟滞特性建模与实验验证

为了模拟WTYD型压电陶瓷微位移器的输出位移与驱动电压之间的迟滞曲线,通过采用Bouc-Wen模型模拟迟滞分量,提出了一种表征WTYD型压电陶瓷微位移器的输出位移与驱动电压之间迟滞关系的Bouc-Wen模型并建立了相应的参数辨识方法。为了验证Bouc-Wen模型及其相应的参数辨识方法的有效性,建立了相应的实验装置并对模型进行了实验验证。研究结果表明,Bouc-Wen模型的最大绝对误差为3.78μm,最大相对误差为5.79%,表明Bouc-Wen模型及相应的参数辨识方法能较好地模拟WTYD型压电陶瓷微位移器的迟滞特性。     

压电陶瓷执行器迟滞非线性补偿与最优控制

为提高空间望远镜精密稳像系统中压电驱动快摆镜(FSM)的摆动精度,对压电陶瓷执行器迟滞非线性补偿和控制技术进行研究。针对压电迟滞的非对称性以及Duhem模型求逆过程复杂的问题,对Duhem模型中的微分方程进行变换,直接建立Duhem非对称逆迟滞模型作为迟滞前馈补偿器,并利用免疫差分进化算法辨识模型参数。在Duhem逆模型补偿压电静态迟滞非线性的基础上,引入基于优化参考跟踪的线性二次型高斯(LQG-ORT)控制方法进一步提高压电执行器的动态定位精度,采用动态迟滞率相关自回归各态历经模型(ARX)建立状态空间方程,用于卡尔曼滤波器预测状态变量和控制器计算状态变量的最优控制系数矩阵。实验结果表明：直接建立的Duhem非对称逆迟滞模型能有效描述压电执行器非对称逆迟滞曲线,拟合均方根误差为0.635 9 V(0.5 Hz),相对误差为0.79%(0.5 Hz);实时跟踪幅值为24μm,频率范围1～80 Hz的目标位移信号,LQG-ORT算法的跟踪误差为0.065 5μm,相对误差为0.27%。     

压电微定位台的率相关动态迟滞建模及参数辨识

针对压电微定位台固有的率相关迟滞非线性严重限制其微定位精度的问题,研究了基于Backlash-Like的Hammerstein率相关迟滞非线性模型及其建模方法。以改进的Backlash-Like分段辨识模型描述压电微定位台的静态非线性特性,结合ARX(Auto Regressive eXogenous)模型,建立描述压电微定位台的率相关动态迟滞模型。同时,针对传统的粒子群算法(Particle Swarm Optimization,PSO)进行模型参数辨识时易陷入局部最优的问题,提出一种具有交叉变异策略的改进型粒子群算法进行模型的参数辨识。实验结果表明:与传统的Backlash-Like模型相比,改进的Backlash-Like分段辨识模型在输入电压为60V,频率为2Hz的信号时,模型辨识的最大误差由0.68μm下降到了0.104μm,最大相对误差由2.69%下降为0.35%。当压电微定位台输入电压为60V,频率分别为30Hz,60Hz和90Hz的单频信号时,Hammerstein率相关迟滞模型较Backlash-Like分段辨识模型,均方根误差由0.393 1～0.700 6μm下降至0.054 1～0.190 4μm,相对误差由1.721%～3.087%下降至0.236%～0.831%。验证了基于改进Backlash-Like的Hammerstein率相关迟滞模型较传统的Backlash-Like静态迟滞模型能精确地描述压电微定位台的率相关动态迟滞特性,具有较好的频率泛化能力,提高了压电微定位平台的定位精度。     

压电执行器的Bouc-Wen模型在线参数辨识

现有的定参数Bouc-Wen模型由于无法表征压电执行器迟滞具有的频移和时变性,极易产生较大的模拟误差。为了精确地模拟压电执行器的迟滞特性,本文建立了压电执行器的Bouc-Wen模型,并采用递推最小二乘在线辨识方法来实时辨识Bouc-Wen模型的参数。为了避免出现数据饱和现象,使用限定记忆来限定辨识方法所使用的数据组数。为验证该辨识方法的有效性,建立了相应的实验系统对其进行实验验证。实验结果表明,限定记忆递推最小二乘在线辨识方法能使Bouc-Wen模型也呈现频移和时变特性。以100 Hz的驱动电压为例,其最大绝对模拟误差从1.38μm降为0.51μm。因此,与传统的离线参数辨识方法相比,限定记忆递推最小二乘在线辨识方法能够有效地提高Bouc-Wen模型的模拟精度。     

Real-time inverse hysteresis compensation of piezoelectric actuators with a modified Prandtl-Ishlinskii model

This paper presents a novel real-time inverse hysteresis compensation method for piezoelectric actuators exhibiting asymmetric hysteresis effect. The proposed method directly utilizes a modified Prandtl-Ishlinskii hysteresis model to characterize the inverse hysteresis effect of piezoelectric actuators. The hysteresis model is then cascaded in the feedforward path for hysteresis cancellation. It avoids the complex and difficult mathematical procedure for constructing an inversion of the hysteresis model. For the purpose of validation, an experimental platform is established. To identify the model parameters, an adaptive particle swarm optimization algorithm is adopted. Based on the identified model parameters, a real-time feedforward controller is implemented for fast hysteresis compensation. Finally, tests are conducted with various kinds of trajectories. The experimental results show that the tracking errors caused by the hysteresis effect are reduced by about 90%, which clearly demonstrates the effectiveness of the proposed inverse compensation method with the modified Prandtl-Ishlinskii model.     

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%。     

Using the modified PSO method to identify a Scott-Russell mechanism actuated by a piezoelectric element

This paper mainly proposes an efficient modified particle swarm optimization (MPSO) method, to identify a Scott-Russell (SR) magnification mechanism driven by a piezoelectric actuator (PA), in which Bouc-Wen model is employed to describe the hysteresis phenomenon. In system identification, we adopt the MPSO to find parameters of the SR mechanism and the PA. This new algorithm is added with “distance” term in the traditional PSO's fitness function to avoid converging to a local optimum. It is found that the MPSO method can obtain optimal high-quality solution, high calculation efficiency, and its feasibility and effectiveness are demonstrated for the modified IEEE 30-bus system. Finally, the comparisons of numerical simulations and experimental results prove that the MPSO identification method for the SR magnification mechanism is feasible.     

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.     

基于扩张状态观测器的迟滞非线性系统辨识

针对一类迟滞非线性系统提出一种参数辨识新方法。通过构造合适的周期输入信号,分析Bouc-Wen模型的积分特性,该特性在后续线性参数与迟滞参数辨识中起到重要作用。利用扩张状态观测器获得系统状态和等效扰动构造方程组,实现线性参数和非线性参数的分离辨识,所有参数通过线性方程组求解得到。通过数值仿真验证了方法的有效性。最后,方法应用于一类压电系统的迟滞非线性模型辨识,所得模型能够很好地反应实际系统的特性。     

Identification of nonlinear hysteretic systems by artificial neural network

An identification method is developed for nonlinear hysteretic systems by use of artificial neural network in the paper. Employing the Bouc–Wen differential model widely used for memory-type nonlinear hysteretic systems, the approach sets up a Bouc–Wen model-based neural network. The weights of the designed specifically network correspond to the Bouc–Wen model parameters and are thus physical ones. Taking advantage of powerful function approximation capability of neural network, the nonlinear hysteretic systems can be identified with the proposed approach by network training. The identification scheme is validated by a simulated case and thereafter applied to modeling of a wire cable vibration isolation experimental system. The results show that the presented identification method can identify the nonlinear hysteretic systems with high accuracy.     

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。     

Direct identification of generalized Prandtl–Ishlinskii model inversion for asymmetric hysteresis compensation

In this study, we present an identification-based direct construction of the inverse generalized Prandtl–Ishlinskii (P–I) model to facilitate inverse model-based feedforward compensation of asymmetric hysteresis nonlinearities. Compared with the derivation of the inverse model analytically from a generalized P–I model, this direct modeling approach has the following advantages. First, direct inverse model identification is formulated as a nonlinear optimization problem, which is not subject to the constraint condition on the generalized P–I model's threshold and density functions, where this is indispensable for the analytical model inversion procedure. Second, this approach may be a simple and attractive alternative when the identification precision of a generalized P–I model is limited by the constraint condition, which necessarily results in insufficient hysteresis compensation functionality for the analytically derived inverse model. Finally, direct inverse model identification can overcome the drawbacks of the analytical inversion method, including the accumulation of parameter estimation errors in an analytical inverse model because these parameters are computed from the generalized P–I model's parameters in a recursive manner. Our experimental results demonstrated that the implementation of open-loop control with the directly identified inverse generalized P–I model as a feedforward compensator achieved precise compensation for the asymmetric hysteresis nonlinearities of a piezoelectric stack actuator.     

动压缸电液伺服压力系统自适应差分进化辨识

根据轨道路基测试装置工作原理,建立了动压缸电液伺服压力系统AMESim模型,理论推导出该系统传递函数。针对标准差分进化算法早熟问题,构造了一种可以自动调节变异因子、变异算子和交叉因子的自适应差分进化算法。设计了基于该系统AMESim模型的参数辨识方案,进行了自适应差分进化算法与其他算法的对比仿真,验证了该算法具有良好的辨识精度和收敛性,给出了动压缸负载开环传递函数辨识参数,并通过自适应差分进化算法获得了伺服阀系统开环传递函数辨识参数。最后给出了动压缸电液伺服压力系统传函参数,通过与该系统AMESim模型对比仿真,验证了该辨识参数的有效性。     

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.