An Observer-Based Indirect Adaptive Fuzzy Control for Rolling Cart Systems

Abstract

Rolling cart system is a highly nonlinear phenomenon in which links undergo tipping and rolling with no fixed base. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the rolling cart states by applying observer-based adaptive tracking control scheme based on fuzzy system and variable structure system (VSS) with system uncertainties, multiple time delayed state uncertainties, and external disturbances. A fuzzy modeling is used to approximate the dynamics of the rolling cart. The observer-based fuzzy adaptive control scheme is developed to override the nonlinearities, time delays, and external disturbances such that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> tracking performance is achieved. The advantage of employing adaptive fuzzy system is that we can utilize the linguistic information by setting the membership functions of fuzzy logical system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. Based on Lyapunov criterion and Riccati-inequality, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level to achieve <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> tracking performance. Finally, a numerical example of a two-links rolling cart is given to illustrate the effectiveness of the proposed control scheme.