Compensação de não linearidades via modelos

Abstract

The presence of nonlinear effects imposes significant limitations on a wide range of systems. Notably, hysteresis is a hard nonlinearity that enforces challenges in the context of control. Aiming to overcome these issues, the design of compensators is a recurrent approach in the literature. Based on a representative model, the compensator's purpose is to determine a compensation input that reduces the impact of the nonlinearity effects in the output. This work aims to design compensators for nonlinear dynamical systems. Firstly, theoretical fundamentals are presented, such as the Bouc-Wen (BW) model, NARX polynomials, the identification process, the mathematical formulation of the compensation, and a review of control for hysteretic systems. In the sequel, it has proposed an evolutionary algorithm for parameter estimation of BW models, which are inverted and used for the hysteretic compensation in a numerical example, Prandtl-Ishillinsky, and a pneumatic valve. As this algorithm facilitates the parameter estimation process, a term is added, generating modified models. Both classical and modified models are compared, showing that the last could improve the results, reducing the tracking error of about 30% for the experimental test. Next, it is presented the compensation approach based on NARX polynomials, the main contribution of this work. This approach aims to find compensation inputs iteratively for nonlinear systems in static (constant references) and dynamical contexts (time variant references) through identified NARX models. Besides, an adaptation of the dynamical strategy comes for hysteretic systems. In rewriting the NARX model as a polynomial in the desired compensation input, the polynomial roots are iteratively calculated. In this process, a decision-making procedure selects a suitable solution that will be the compensation input. This compensation strategy is presented in two numerical examples: the first one is a heating system with a static curve, while the second is a piezoelectric device modeled by a BW model. For both examples, it has been discussed relevant issues for the method like the impact of the initialization process in the compensation performance, the robustness of the approach to parameter variations, and the use of restrictions to deal with time-varying references which become constant. Finally, this method is applied to a physical example, the previous pneumatic vale. The results of the presented compensators are compared with well-established and recent works. For each compensator, it has discussed their benefits and limitations. The results show that the proposed NARX-based compensators produce relevant compensation inputs that can make the system approximately linear with a maximum tracking error of 3.9%. It has also been shown that the additional effort for the presented strategy tends to be less energetic and more regular.