  In this paper, a nonlinear rotational inverted pendulum with time-varying
parameters is controlled using the indirect adaptive fuzzy controller design.
This type of controller is chosen because this particular system performance is
highly sensitive to unavoidable unknown model changes. So, a conventional
controller is firstly designed through feedback linearization method, and
applied to the system. Feedback linearization method here is used for two
purposes; to attain an approximation of necessary system dynamics and to assess
the performance of the proposed adaptive fuzzy controller by comparing the
results of both adaptive fuzzy and feedback linearization controllers. An
indirect adaptive fuzzy controller, resistant to parameter variations is then
proposed. The general structure of the adaptive controller is specified in the
first stage. In the second stage, its parameters are regulated with the aid of
two fuzzy systems. Lyapunov stability theorem is used to regulate the system
parameters such that the closed loop system is stabilized and zero tracking
error is attained. Finally, the results of the proposed and the conventional
approaches are compared. Results showed that the adaptive fuzzy controller
performed more efficiently than the classical controller, with existing
parameters variations.
