超声波电机面向控制的非光滑混合模型分步辨识与非线性补偿

The dynamic behavior of the ultrasonic motor(USM) correlates closely with the hysteresis effect of piezoelectric materials within its stator and the friction involved with the contact layer. Aiming at the servo-control application of the USM, this project studies the techniques for identification of a hybrid model capable of describing both the hysteresis and friction nonlinearities in the USM, and the model-based nonlinear compensation from an improvement of the control performance view point. The main contents are as follows. 1) For the description of the non-smooth nonlinearites, i.e. the hysteresis and the friction, we study the characteristic parameters and mathmatical description with the non-smooth blocks. Then a non-smooth hybrid model is derived for the USM. 2) By defining the effective space of the characteristic parameters with the non-smooth blocks, the hybrid model can be decomposed into several functional modules, and the system is degraded to relative simple transitional forms for the parameters optimization under separable exciation signals. Then the overal model is constructed through a stepwise identification along with a specific decomposition and synthesis approach. 3) For the undifferentiable and multi-valued property with the non-smooth hysteresis, the completion of the input space by introducing requisite basis functions is studied to construct the hysteresis model and inverse compensator. With the feed-forward inverse compensation strategy, a simple control-oriented model of the USM is derived. Meanwhile, by constructing a direct relationship between the choice of the stepwise algorithm and the controller design strategy, a model based controller is studied through the block-oriented principle with the consideration of the robustness and the dynamic response performance. This project will contribute greatly to the control of the nonlinear dynamic systems with memory non-smoothness both in theory and practical applications.

超声波电机的动态特性与定子压电陶瓷迟滞、接触层摩擦有密切联系。本项目面向超声波电机的伺服控制应用，研究能够描述迟滞、摩擦等非线性在内的超声波电机混合模型的辨识及其非线性补偿方法，改善超声波电机的控制性能。主要内容包括：1）针对超声波电机中迟滞、摩擦等非光滑非线性，研究其特征量参数提取和数学描述方法，构建超声波电机的非光滑混合模型结构；2）结合模型分解-合成的方法，研究针对各非光滑环节的工作空间，可分离输入激励信号和辨识算法的设计，分步辨识各职能环节；3）针对非光滑多值映射迟滞非线性，研究完备其辨识输入空间的算子基函数，建立迟滞模型和补偿逆，结合逆模型补偿策略，简化超声波电机的控制模型，并通过建立分步辨识与基于模型的控制器设计之间的联系，提高控制系统的鲁棒性和动态响应性能。研究成果能为含有记忆特性的非光滑非线性动态系统的辨识和控制提供重要的理论支持，同时具有重要的工程应用价值。

为了克服超声波电机固有的非线性影响，得到较好的转速控制特性，提高电机的伺服控制性能，从面向控制的角度分析了对控制精度有重要影响的迟滞等非光滑因素的补偿方法，结合非光滑混合模型的分步辨识算法和逆补偿策略，研究了超声波电机中的摩擦层死区、定子压电陶瓷迟滞典型非光滑特性的辨识和补偿方法。1）通过输入激励信号的设计，分析了超声波电机的非线性动态特性和数学描述形式，提出了一种用以描述超声波电机分段线性死区和非对称动态特性Wiener- Hammerstein三明治模型结构。分别针对死区的分段线性特性、静态多项式混合非线性以及转子动态环节的非对称特性，利用广义最小二乘法对改进的Hammerstein模型的参数进行了递推估计。2）针对压电陶瓷执行器中存在的非光滑多值映射迟滞非线性，构造了能够描述迟滞输出随输入变化规律的迟滞算子并引入辨识空间，在扩展的迟滞输入空间上构建了逼近非光滑迟滞的紧致集及模型优化算法，建立迟滞模型和补偿逆。3）进一步，采用NARX (nonlinear autoregressive model with exogenous inputs)模型结构表示迟滞的频率依赖性特性，并给出此模型的权值优化算法。结合提出的基于扩展空间的迟滞逆模型和动态迟滞NARX 模型，分别构建内模控制的控制器与内部模型，构造了压电陶瓷迟滞非线性系统的神经网络内模控制策略。4）针对超声波电机所具有的非对称ARX模型结构，从分段线性的角度研究了其模型辨识及控制问题，对不同线性工作区间的子线性系统进行多模型PID控制器的设计。超声波电机非光滑混合模型分步辨识与非线性补偿的方法，充分利用了模型的动态信息，可以有针对性地设计补偿器对系统进行整体的优化控制，提高了控制系统的综合性能。研究成果能为含有记忆特性的非光滑非线性动态系统的辨识和控制提供了重要的参考价值。

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