Precise trajectory tracking of a piezoactuator-driven stage using an adaptive backstepping control scheme

In this paper, an adaptive backstepping control scheme is proposed for precise trajectory tracking of a piezoactuator-driven stage. Differential equations consisting of dynamics of a linear motion system and a hysteresis function are investigated first for describing the dynamics of motion of the piezoactuator-driven stage with hysteresis behavior. Then, to identify the uncertain parameters designed in the differential equations, the Powell method of a numerical optimization technique is used. From the differential equations identified, an equivalent state-space model is developed, then a linear state-space model through a state transformation is established. In the linear state-space model, the hysteresis function is approximated by the first three terms of a Taylor series expansion. Based on the linear state-space model, we developed an adaptive backstepping control for the trajectory tracking. By using the proposed control approach to trajectory tracking of the piezoactuator-driven stage, improvements in the tracking performance, steady-state error, and robustness to disturbance can be obtained. To validate the proposed control scheme, a computer-controlled, single-axis piezoactuator-driven stage with a laser displacement interferometer was set up. Experimental results illustrate the feasibility of the proposed control for practical applications in trajectory tracking.     

压电驱动器的非对称迟滞模型

为了补偿压电驱动器的非对称迟滞,提出了改进型Maxwell迟滞模型.Goldfarb提出的经典Maxwell迟滞模型由多个基础单元并联叠加而成,其基础单元为单个弹簧-物块单元,迟滞特性为平行四边形,故只能描述对称迟滞.为了能描述压电驱动器非对称迟滞,提出了基础单元迟滞特性为梯形的模型.为了简化算法程序,将梯形单元优化为两个三角形单元组合而成.为了验证该模型,以压电工作台为实验对象,运用该迟滞模型的逆模型进行迟滞补偿控制.单独的迟滞逆模型前馈开环控制实验结果表明,位移跟踪相对误差从7.37％降到了1.56％,输入输出基本呈线性关系.逆模型结合PID复合反馈闭环控制实验结果表明,位移跟踪相对误差进一步降低到0.53％,输入输出呈很好的线性关系.这表明本文所建立的迟滞模型能很好地描述压电驱动器非对称迟滞特性.     

An adaptive recurrent radial basis function network tracking controller for a two-dimensional piezo-positioning stage

An adaptive recurrent radial basis function network (ARRBFN) tracking controller for a two-dimensional piezo-positioning stage is proposed in this study. First, a mathematical model that represents the dynamics of the two-dimensional piezo-positioning stage is proposed. In this model, a hysteresis friction force that describes the hysteresis behavior of one-dimensional motion is used; and a nonconstant stiffness with the cross-coupling dynamic due to the effect of bending of a lever mechanism in x and y axes also is included. Then, according to the proposed mathematical model, an ARRBFN tracking controller is proposed. In the proposed ARRBFN control system, a recurrent radial basis function network (RRBFN) with accurate approximation capability is used to approximate an unknown dynamic function. The adaptive learning algorithms that can learn the parameters of the RRBFN on line are derived using Lyapunov stability theorem. Moreover, a robust compensator is proposed to confront the uncertainties, including approximation error, optimal parameter vectors, higher-order terms in Taylor series. To relax the requirement of the value of the lumped uncertainty in the robust compensator, an adaptive law is investigated to estimate the lumped uncertainty. Using the proposed control scheme, the position tracking performance is substantially improved and the robustness to uncertainties, including hysteresis friction force and cross-coupling stiffness, can be obtained as well. The tracking performance and the robustness to external load of the proposed ARRBFN control system are illustrated by some experimental results.     

高线性度的二维无耦合纳米压电位移系统设计

设计了一套具有高线性度的二维无耦合纳米压电位移系统。提出了一种多个压电陶瓷同步线性操作的电荷控制方案,设计采用基于非线性反馈控制和相似控制相结合的具有接地配置功能的压电控制器。控制器中引入了T型电阻网络,使电容较小的压电致动器能够进行低频线性操作。并对压电陶瓷驱动的位移平台进行了机械结构设计,平台采用嵌套式串联结构来避免耦合位移。通过解析法和ANSYS Workbench有限元仿真两方面对位移平台进行了刚度及位移分析。搭建了一套干涉位移测量系统,对压电位移台的位移、耦合误差及线性度进行了验证测试。实验结果表明:系统满行程内二维位移台的耦合误差最大仅为0.098%,可以将迟滞不对称引起的剩余轨迹偏差减小到0.79%,两个压电陶瓷间的最大轨迹偏差仅为行程范围的0.23%,理论分析和实验验证了所设计多压电电荷控制器的可行性,且系统可有效抑制耦合位移并使定位精度得到明显提高。     

轻工业包装物品搬运机器人路径跟踪控制

目的 为了提高直角坐标搬运机器人的定位精度,保证机器人能够按照预定路径运动。方法 介绍直角坐标机器人工作原理,并基于模糊控制理论,提出一种基于模糊PID的直角坐标机器人轨迹跟踪控制算法,并将其应用于机器人运动轨迹跟踪控制中。结果 仿真和实验结果表明,基于模糊PID的机器人控制器能够保证机器人沿预定路径运动,机器人轨迹跟踪误差能够很快收敛于0附近,该轨迹跟踪方法具有较好的抗干扰性和鲁棒性。结论 所提方法能够明显提高直角坐标机器人的路径跟踪能力,对于提升机器人运动精度具有参考价值。     

Position precision compensation method of a micro-manipulation stage based on fuzzy control

The hysteresis nonlinearity of piezoelectric micro-manipulation stage leads to the decrease of its position accuracy and dynamic performance, and it is hard to establish the accurate hysteresis model. A position accuracy compensation method was adopted based on the fuzzy control strategy to get rid of the dependence on hysteretic model. As for a one-dimensional micro-manipulation stage, the position deviation and deviation variation rate of the stage was used as fuzzy input, and the input voltage change of piezoelectric actuator was used as fuzzy output. A method of developing fuzzy rules was presented based on experiment data of PID control to acquire experience. The fuzzy relationship between the stage input and output by fuzzy reasoning and de-fuzzy process was established, and the adaptive compensation of hysteresis could be realized. In order to illustrate the feasibility of the proposed method, the experimental comparative analysis with PID control was carried out. The position errors were compared when the stage was tracking the sine signals with different frequencies. The experimental results show that the proposed fuzzy control method can make the stage have higher position tracking accuracy and faster tracking speed, and has better adaptability.     

基于模糊控制的微操作平台位置精度补偿方法

由于压电式微操作平台的迟滞非线性会导致其位置精度和动态性能下降,且难以建立精确的迟滞非线性模型,采用一种基于模糊控制策略的位置精度补偿方法,以摆脱对迟滞模型的依赖。以一种一维压电式微操作平台为对象,以平台的位置偏差与偏差变化率为模糊输入,压电驱动器输入电压变化量为模糊输出,提出采用基于PID控制的实验数据获取经验来制定模糊规则的方法。通过模糊推理和解模糊过程,建立平台输入量与输出量之间的模糊关系,实现了可消除迟滞现象的自适应补偿。为了说明所提出的位置精度补偿方法的可行性,通过实验与PID控制进行比较,分析平台跟踪不同频率正弦信号的位置误差。实验结果表明,所提出的模糊控制方法能使平台具有更高的位置跟踪精度和更快的跟踪速度,并具有较好的自适应性。     

Adaptive control with hysteresis estimation and compensation using RFNN for piezo-actuator

Because the control performance of a piezoactuator is always severely deteriorated due to hysteresis effect, an adaptive control with hysteresis estimation and compensation using recurrent fuzzy neural network (RFNN) is proposed in this study to improve the control performance of the piezo-actuator. A new hysteresis model by modifying and parameterizing the hysteresis friction model is proposed. Then, the overall dynamics of the piezo-actuator is completed by integrating the parameterized hysteresis model into a mechanical motion dynamics. Based on this developed dynamics, an adaptive control with hysteresis estimation and compensation is proposed. However, in the designed adaptive controller, the lumped uncertainty E is difficult to obtain in practical application. Therefore, a RFNN is adopted as an uncertainty observer in order to adapt the value of the lumped uncertainty E on line. And, some experimental results show that the proposed controller provides high-performance dynamic characteristics and is robust to the variations of system parameters and external load.     

基于迟滞观测器的压电工作台自适应控制

为提高压电陶瓷驱动的微定位工作台的精度和速度,设计了一种基于迟滞状态观测器的自适应控制系统.在分析压电陶瓷迟滞非线性特性和工作台结构的基础上,建立了压电工作台的动态迟滞模型.迟滞观测器用于估计由位移偏差、传递函数、迟滞变量和扰动而产生的不确定误差,对神经网络控制器的输出量进行补偿,使工作台的位移跟随参考值.基于李雅普诺夫稳定理论推导了迟滞观测器的自适应调节律.实验结果表明,采用带有迟滞观测器的自适应控制系统时,在30μm、1 Hz正弦信号作用下,工作台的平均定位误差从之前的0.39μm减小到了0.19μm,对迟滞特性的非对称拟合平均误差由0.42μm减小到0.22μm,在10μm阶跃输入时的平均定位误差从0.22μm减小到了0.13μm,稳定时间由0.19 s缩短为0.08 s,定位工作台的性能得到明显的改善,能够满足实验要求.     

漂浮基柔性空间机械臂关节运动的分块神经网络控制及柔性振动模糊控制

讨论了载体位置不受控、姿态受控情况下,漂浮基柔性空间机械臂关节运动及柔性振动主动抑制的控制问题。由系统动量守恒关系及假设模态法,利用拉格朗日方法建立了漂浮基柔性空间机械臂的系统动力学方程。之后采用奇异摄动理论,将其分解为表示刚性运动的慢变子系统和柔性振动的快变子系统。据此,设计了柔性空间机械臂系统载体姿态及机械臂关节铰协调运动的组合控制器。针对慢变子系统——柔性空间机械臂的刚性运动,设计了分块神经网络控制器,以完成系统参数未知情况下关节空间协调运动的轨迹跟踪;而对于快变子系统——柔性臂的振动,则设计了模糊控制器来主动抑制柔性杆的振动。数值仿真证实了提出方法的有效性。     

压电致动快速刀具伺服迟滞非线性的分数阶模型

在复杂曲面或功能结构的超精密车削以及主动误差校正车削中,利用快速刀具伺服(FTS)受到了学术界和工程界的广泛关注.然而,无论采用哪一种驱动方式,FTS皆存在难以模型化的迟滞非线性,从而制约了FTS跟踪性能的提高.本文利用分数阶微积分理论,针对压电致动型FTS的迟滞非线性建立了等效的分数阶动力学模型,得到了压电致动型FTS的传递函数.利用一种改进的差分进化算法进行了模型参数的辨识.通过正弦波及三角波信号激励的实验结果表明,针对压电致动型FTS所提出的分数阶模型建模误差小于4％,具有预期的模型精度.本研究为FTS的迟滞非线性建模提供了一种简单有效的新方法,对于提高FTS运动轨迹的跟踪控制性能具有重要意义.     

基于位移传感器的包装机械手运动跟踪方法设计

目的为提高包装机械手末端执行器轨迹跟踪精度,提出一种三维运动轨迹跟踪方法。方法获取拉绳式位移传感器在预先建立的三维坐标系中坐标数据和拉线长度。利用坐标和拉线长度计算运动物体的三维坐标数据,进而形成所述运动物体的三维运动轨迹。同时,给出基于ARM的轨迹跟踪控制器结构以及软件实现方法。结果实验结果表明,与传统示教盒相比,该方法可将定位精度提高1倍,相关误差可控制在0.3 mm以内。该方法在执行效率方面大约能够提升33%,提高了包装机械手的执行速度和分拣效率。结论所述轨迹跟踪方法能够提高包装机械手末端执行器的定位精度和定位速度,符合包装、食品、化工等行业的工艺要求。     

Robust adaptive numerical compensation for friction and forceripple in permanent-magnet linear motors

This paper describes a robust adaptive compensation method for friction and force ripple present in the dynamics of permanent-magnet linear motors. The method is used in ultraprecise positioning applications. The compensation algorithm consists of a PID component and an adaptive component for estimating friction and force ripple. The adaptive component is continuously refined on the basis of just prevailing input and output signals. Computer simulations and real-time experimental results verify the effectiveness of the proposed scheme for high-precision motion trajectory tracking     

压电式二维微动工作台的迟滞补偿与解耦控制

为了提高压电式二维微动工作台的定位精度,基于改进的Prandtl-Ishlinskii模型设计了前馈与解耦控制器,并结合反馈控制器开发了复合控制系统.在分析x与y方向电压与位移之间迟滞关系的基础上,前馈控制器通过改进的Prandtl-Ishlinskii模型描述迟滞的逆过程,分别补偿了x与y方向的迟滞.解耦控制器通过改进型Prandtl-Ishlinskii模型估算耦合位移值,修正驱动电压,抵消耦合效应引起的位移.复合控制系统结合了前馈与解耦控制器,并加入PID反馈控制进一步提高定位精度.实验结果表明:控制前,x方向与y方向定位误差的最大绝对值分别是4.16μm和4.18μm,而采用复合控制后定位误差的最大绝对值降为0.06μm和0.07μm.这种复合控制方法能够补偿压电式微动工作台的迟滞非线性,无需改变结构或更换零件就能减小耦合效应,有效地提高微动工作台定位精度.     

应用于圆饼工件分拣的码垛机器人自适应积分滑模控制

目的 针对存在系统未建模特性和负载变化下码垛机器人关节空间轨迹跟踪控制的问题,设计一种基于结合时延估计技术与自适应积分滑模面的控制策略。方法 根据圆饼工件分拣需求,设计一款桌面式码垛机器人系统,推导机器人的运动学与动力学模型,给出关节空间轨迹规划算法,并基于无模型思想设计关节空间轨迹跟踪控制器。结果 利用雅克比伪逆法可反解出机器人的关节角;通过所提的轨迹规划算法能有效获得各关节运动轨迹;与PID控制器和积分滑模控制器相比,文中所提控制器具有较好的控制精度、较强抗干扰性和较高的鲁棒性。结论 仿真和实验结果表明,所设计的基于时延估计技术的自适应积分滑模控制器是合理的,能使得码垛机器人完成圆饼工件的分拣任务,具有一定的工程应用价值。     

面向微装配的压电陶瓷微夹钳建模与控制

建立了悬臂梁位移与外电场和外力之间的动静态模型以及压电陶瓷迟滞环的Backlash算子模型.以所建立的迟滞模型为前馈环节与PID反馈构成复合控制对悬臂梁进行位置控制.现场测试数据验证了该模型的正确性和复合控制方法的可行性,并分别用逆控制、PID控制以及复合控制方法进行了正弦曲线跟踪实验,这些控制方法的比较结果表明,复合控制策略具有最高的控制精度.     

压电陶瓷片迟滞补偿建模及悬臂梁主动控制研究

为增强压电悬臂梁振动控制效果,提出一种基于最小二乘法的逆迟滞补偿控制算法。在不同电压下对压电陶瓷片位移进行实测,应用最小二乘法对其迟滞环进行多项式拟合建模,并利用压电片逆迟滞补偿模型对控制电压进行补偿。通过悬臂梁振动主动控制试验系统研究PID控制器在有、无逆迟滞补偿时的控制效果。结果表明:经过PID逆迟滞补偿后的主动控制效果比传统PID提高10.083%。因此,该逆迟滞补偿方法能够有效增强压电陶瓷片的主动控制效果,对于压电悬臂梁振动主动控制具有重要参考价值。     

汽车半主动悬架的滑模变结构控制

在1／4汽车动力学模型的基础上，运用滑模变结构方法设计了汽车半主动悬架滑模控制器。基本思想是以半主动悬架的近似天棚阻尼系统作为参考模型，把被控系统和参考模型间的广义误差动力学引入渐近稳定的滑动模态中；采用极点配置法确定滑模切换面参数；用等速趋近率改善滑模运动段的动态品质；根据滑模面上的等效控制力，确定半主动悬架的实时控制阻尼力。仿真结果表明：该滑模控制器性能稳定，具有较好的鲁棒性和跟踪性，对模型参数的变化和外界扰动有一定的适应性。仿真证实了滑模控制器设计的有效性。     

下肢外骨骼矫形器的动力学建模与运动控制研究

对用于步行训练的下肢外骨骼矫形器的动力学与运动控制进行了研究.首先利用拉格朗日法建立了下肢外骨骼矫形器在跑步机上双足步行的动力学模型;在此基础上,设计了实现下肢外骨骼矫形器的轨迹跟踪控制的计算力矩加比例微分反馈控制系统,并采用Lyapunov方法,分析了控制系统在建模存在误差情况下的稳定性和收敛性;最后,在Adams-Matlab虚拟样机协同仿真平台上进行了下肢外骨骼矫形器的步行仿真实验,结果表明该控制方法对下肢外骨骼矫形器的轨迹跟踪控制是有效的.     

Minimizing Scanning Errors in Piezoelectric Stack-Actuated Nanopositioning Platforms

Piezoelectric stack-actuated parallel-kinematic nanopositioning platforms are widely used in nanopositioning applications. These platforms have a dominant first resonant mode at relatively low frequencies, typically in the hundreds of hertz. Furthermore, piezoelectric stacks used for actuation have inherent nonlinearities such as hysteresis and creep. These problems result in a typically low-grade positioning performance. Closed-loop control algorithms have shown the potential to eliminate these problems and achieve robust, repeatable nanopositioning. Using closed-loop noise profile as a performance criterion, three commonly used damping controllers, positive position feedback, polynomial-based pole placement, and resonant control are compared for their suitability in nanopositioning applications. The polynomial-based pole placement controller is chosen as the most suitable of the three. Consequently, the polynomial-based control design to damp the resonant mode of the platform is combined with an integrator to produce raster scans of large areas. A scanning resolution of approximately 8 nm, over a 100 mum times 100 mum area is achieved.