Collaborative Research: Hysteresis Compensation Using Linear Parameter Varying Control Methods

摘要：本项目旨在开发控制系统中滞后非线性的精确补偿方法。在宏观、中微观和纳米尺度上，许多机电、结构和材料系统由于摩擦、间隙、相变或材料特性而表现出滞后行为。在这些系统中，迟滞会导致许多不良影响，包括性能差、稳态误差、极限环行为和稳定性损失。在这个项目中，提出了一种新的线性变参数（LPV）控制综合方法来补偿滞后。该方法构造了适当的状态增广和变换，将一般非线性滞回系统转化为相对于滞回非线性的小信号局部线性增益的等效LPV系统。该滞回的局部线性增益被提出作为LPV反馈控制增益更新的调度参数。此外，提出了适当的迟滞建模和在线识别，从而在无法直接测量迟滞信息的系统中得到理想的LPV公式。为此，提出了一种新的Preisach算子加权函数辨识方法，该方法提供了一种计算效率高的滞回非线性局部线性行为在线估计方法。所提出的方法被认为解决了以前开发的方法的许多局限性，因为它可以应用于具有多个迟滞非线性的一般非线性系统，该系统基于每个时刻迟滞的小信号线性增益的知识。提出的迟滞识别和补偿方法将应用于莱斯大学动力系统实验室的大型迟滞变刚度和阻尼结构系统，以及休斯顿大学智能材料和结构实验室的压电陶瓷Thunder致动器微定位系统。此外，该项目还建议开发一个交互式智能材料实验显示器，用于招聘、外展活动和高中演示。精确的迟滞补偿将大大有利于高性能机电和材料系统的精确控制。此类系统的例子包括智能材料（形状记忆合金、压电陶瓷材料、磁致伸缩材料、电活性聚合物、电流变和磁流变流体）、混凝土加固结构、齿轮系统和许多振动系统。智能材料的迟滞补偿在许多高技术领域具有至关重要的意义，包括自适应光学、高精度制造和微定位致动器，在显微外科、精密仪器、微泵和微操作等领域都有应用。参与该项目的学生将获得从基础工程科学到实验、测试和实际实施的先进控制、机电系统和智能材料的广泛跨学科培训和教育。

Abstract: This project seeks to develop methodologies for precise compensation of hysteresis nonlinearities in controlled systems. Many electromechanical, structural and material systems at the macro-, meso- micro- and nano-scale exhibit hysteretic behavior due to friction, backlash, phase transition or material properties. Hysteresis in these systems can cause a number of undesirable effects including poor performance, steady-state errors, limit cycle behavior and loss of stability. In this project, the development of a novel Linear Parameter Varying (LPV) control synthesis approach to hysteresis compensation is proposed. In this approach an appropriate state augmentation and transformation is constructed to transform a general nonlinear hysteretic system to an equivalent LPV system with respect to the small-signal local linear gain of the hysteresis nonlinearity. This local linear gain of the hysteresis is proposed as a scheduling parameter to update the LPV feedback control gains. Furthermore, appropriate modeling and on-line identification of hysteresis is proposed that leads to a desired LPV formulation in systems where direct measurement of hysteresis information is not available. To this end, a new method for identification of the Preisach operator weighting function is proposed that provides a computationally efficient on-line estimate of the local linear behavior of the hysteresis nonlinearity. The proposed approach is seen to address many of the limitations of previously developed methods since it can be applied to general nonlinear systems with multiple hysteresis nonlinearities based on knowledge of the small-signal linear gain of the hysteresis at each instant of time. The proposed hysteresis identification and compensation methods will be applied to a large-scale hysteretic variable stiffness and damping structural system at the Rice Universitys Dynamic Systems Laboratory, and to a piezoceramic Thunder actuator micro-positioning system at the University of Houstons Smart Materials & Structures Laboratory. In addition, the project proposes the development of an interactive smart material experiment display that will be used for recruitment, outreach activities and high school demonstrations.Precise hysteresis compensation will greatly benefit the precise control of high performance electromechanical and material systems that exhibit hysteretic behavior. Examples of such systems include smart materials (shape memory alloys, piezoceramic materials, magnetostrictive materials, electro-active polymers, and electro-rheological and magneto-rheological fluids), concrete reinforced structures, gear systems and many vibrating systems. Hysteresis compensation in smart materials is of paramount importance in many high technology areas, including adaptive optics, high precision manufacturing and micro-positioning actuators with applications in micro-surgery, precision instrumentation, micro-pumps and micro-manipulation. The students involved in the project will acquire a broad interdisciplinary training and education in advanced controls, electromechanical systems and smart materials ranging from fundamental engineering sciences to experimentation, testing, and practical implementation.