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.
