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Since the dynamic characteristics of a nonlinear inverted-pendulum mechanism are highly nonlinear, it is difficult to design a suitable control system that realizes real time stabilization and accurate tracking control at all time. In this study, a robust fuzzy-neural-network (FNN) control system is implemented to control a dual-axis inverted-pendulum mechanism that is driven by permanent magnet (PM) synchronous motors. The energy conservation principle is adopted to build a mathematical model of the motor-mechanism-coupled system. Moreover, a robust FNN control system is developed for stabilizing and tracking control of the dual-axis inverted-pendulum system. In this control system, a FNN controller is used to learn an equivalent control law as in the traditional sliding-mode control, and a robust controller is designed to ensure the near total sliding motion through the entire state trajectory without a reaching phase. The salient advantages of this FNN-based control scheme are as follows. 1) It does not require a perfect knowledge of system uncertainties so that this brings a high level of autonomy to the overall system and make the use of this control scheme very attractive for real time applications. 2) All adaptive learning algorithms in this control system are derived in the sense of Lyapunov stability analysis, so that system-tracking stability can be guaranteed in the closed-loop system. 3) Not only the weight vector in the rule-to-output layer are adjusted on line but also the mean and the standard deviation of Gaussian functions in the membership function layer. This training scheme will increase the learning capability of the FNN. 4) An adaptive bound estimation algorithm is investigated to relax the requirement for the bound of uncertain term including the minimum reconstructed error, higher-order term in Taylor series, and network parameters approximation error. The effectiveness of the proposed control strategy can be verified by numerical simulation and experimental results.
Wai et al. (Wed,) studied this question.