Operator-Based Nonlinear Control Systems with Smart Actuators

Smart materials such as piezoelectric elements, shape memory alloys (SMAs), and ionic polymer-metal composites (IPMCs), are applied widely to make actuators. However, backlash and hysteretic behaviors exist widely in the smart materials and affect the performance of actuators. To compensate the effect of the backlash and hysteretic behavior, operator-based nonlinear control designs are developed. This chapter discusses the design of operator-based controller based on the robust condition and the exponential iteration theorem. The stability and output tracking performance of the nonlinear plant with uncertain nonsymmetric backlash are guaranteed by the controller. The chapter describes a nonsymmetric Prandtl-Ishlinskii (PI) model hysteresis model using a nonsymmetric play hysteresis operator with unknown slopes was given to express hysteretic behavior. Nonlinear plants with the obtained hysteresis model are stabilized by a robust controller designed using the robust stability condition. Experimental results to control three types of actuators are also described in the chapter.