Robust Control of Nonlinear System with Input and Output Nonlinear Constraints

Abstract

With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.