Prescribed-Time Fuzzy Control for MIMO Coupled Systems With Unknown Structure and Control Direction: Application to Robotic Arm

Abstract

Due to model uncertainty, system coupling and external disturbance, the mathematical structure of control system is often constructed imprecisely. This unknown structure implies the unknown system dynamic and control input direction. Hence, it is difficult for unknown-structure Multiple Input Multiple Output (MIMO) coupled control systems to prescribe the settling time and control accuracy. To solve this problem, a novel prescribed-time robust direction-adjusting control method is proposed by adaptive Takagi-Sugeno (AT-S) fuzzy approximation. More specifically, by constructing an adaptive T-S fuzzy approximator under relaxed conditions, the mismatched uncertainty of systems can be transformed into the bounded matched uncertainty. It is a pre-condition for prescribed finite-time stability. After the prescribed time terminal, an adaptive robust control designed on AT-S fuzzy model is used for prescribed-accuracy convergence. Besides, compared with existing studies, the proposed method is independent of the structure information and initial control direction. Simulations and experiments verify its effectiveness. Note to Practitioners—The robot arm system with no or lowaccuracy Lagrange dynamic identification is a typical unknownstructure MIMO coupled system. It is difficult to achieve fastconvergence and high-accuracy control for this practical system, especially with no empirical pre-adjustment of the initial input direction. To solve this practical problem, a novel prescribedtime direction-adjusting adaptive T-S fuzzy control method is proposed. Firstly, the robotic arm system is decoupled into multiple joint subsystems by virtual dimension reduction strategy to avoid rule explosion, where system coupling is also converted to bounded unmatched uncertainty. Then, the inappropriate initial direction of the actuator input signal is addressed by control direction-adjusting algorithm. Meanwhile, based on adaptive TS fuzzy approximation theorem, the mismatched uncertainty is transformed into the bounded matched uncertainty. In the end, according to the prediction of approximation accuracy, a prescribed-accuracy robust controller is designed on AT-S fuzzy model. The proposed method is effective in a practical robotic arm control experiment without identification of Lagrange dynamics. Moreover, compared with other related methods, the control precision of the proposed method is higher.