Model-Free Prescribed Performance Control of Pendulum Systems

The tracking control problem for torsional pendulum systems with unknown control directions and unknown disturbances is investigated in this paper. First, a class of orientation functions are introduced to cope with unknown control directions in lieu of the Nussbaum functions. Then, a prescribed performance controller is designed, which is robust to unknown disturbances. Furthermore, the proposed controller can effectively treat the unknown nonlinearities without invoking the tools for approximation, identification, and estimation. Based on dialectic by contradiction, it is proved that all the signals in the controlled systems are bounded and the tracking performance with the predefined convergence rate and accuracy is achieved. Finally, the feasibility of the proposed algorithm is verified by the simulation results.