Robust bounded control for uncertain nonlinear systems: application to a nonlinear strict feedback wind turbine model with explicit wind speed dynamics

Abstract

In this paper, a robust bounded control law for a class of uncertain nonlinear systems is proposed. The proposed bounded controller guarantees asymptotic stability, asymptotic tracking and asymptotic disturbance rejection of systems in strict feedback form with the sum of unmatched uncertainties and the unbounded exogenous disturbance. A feedback law emerged from Artstein's Theorem and Sontag's universal formulas are known to be useful to limit the control signal. However, the formulas are not robust as in many cases, being applied to the systems without uncertainties and disturbances. The controller proposed in this paper takes advantages of a mixed backstepping and Lyapunov redesign, which employed to enrich the Sontag's universal formulas. Therefore, the appealing feature of the proposed controller is that it satisfies small control property in order to preserve performance robustness and stability robustness with less control effort. Another advantage of the proposed controller is the formulas become applicable to higher order systems (i.e. order > 0). This paper also discusses fuzzy logic tuning approach for the controller parameters such that the closed loop system matrix remain Hurtwitz. For practicality, the proposed technique is applied to a variable speed control of a new strict feedback wind turbine system with wind dynamics appeared explicitly in the system model. The proposed controller guarantees the asymptotic tracking of the turbine rotor speed; maintains the optimal tip speed ratio and produces maximum power coefficient. This yields maximum power output from the turbine.