Robust Feedback Linearization Control for Reference Tracking and Disturbance Rejection in Nonlinear Systems

Most industrial processes are nonlinear systems, the control method applied consisting of a linear controller designed for the linear approximation of the nonlinear system around an operating point. However, even though the design of a linear controller is rather straightforward, the result may prove to be unsatisfactorily when applied to the nonlinear system. The natural consequence is to use a nonlinear controller. Several authors proposed the method of feedback linearization (Chou & Wu, 1995), to design a nonlinear controller. The main idea with feedback linearization is based on the fact that the system is no entirely nonlinear, which allows to transform a nonlinear system into an equivalent linear system by effectively canceling out the nonlinear terms in the closedloop (Seo et al., 2007). It provides a way of addressing the nonlinearities in the system while allowing one to use the power of linear control design techniques to address nonlinear closed loop performance specifications. Nevertheless, the classical feedback linearization technique has certain disadvantages regarding robustness. A robust linear controller designed for the linearized system may not guarantee robustness when applied to the initial nonlinear system, mainly because the linearized system obtained by feedback linearization is in the Brunovsky form, a non robust form whose dynamics is completely different from that of the original system and which is highly vulnerable to uncertainties (Franco, et al., 2006). To eliminate the drawbacks of classical feedback linearization, a robust feedback linearization method has been developed for uncertain nonlinear systems (Franco, et al., 2006; Guillard & Bourles, 2000; Franco et al., 2005) and its efficiency proved theoretically by W-stability (Guillard & Bourles, 2000). The method proposed ensures that a robust linear controller, designed for the linearized system obtained using robust feedback linearization, will maintain the robustness properties when applied to the initial nonlinear system. In this paper, a comparison between the classical approach and the robust feedback linearization method is addressed. The mathematical steps required to feedback linearize a nonlinear system are given in both approaches. It is shown how the classical approach can be altered in order to obtain a linearized system that coincides with the tangent linearized system around the chosen operating point, rather than the classical chain of integrators. Further, a robust linear controller is designed for the feedback linearized system using loop-