Flexible robotic manipulators are typical distributed parameter systems, and the resulting vibration deformation may affect their operation accuracy. This paper investigates the vibration attenuation and angular tracking control of a flexible robotic manipulator system subject to time-varying actuator faults, external disturbances, asymmetric input–output constraints, modeling uncertainties and unknown parameters. Two smooth nonlinear functions are adopted to eliminate potential chattering effects induced by controller switching and to address the problem of output signals violating constraints. The radial basis neural network function (RBNNF) is employed to compensate for modeling uncertainties, parameter uncertainties, and input nonlinearities. Furthermore, an adaptive fault-tolerant boundary vibration control scheme based on the Nussbaum function is proposed to guarantee the fault compensation and the permanent satisfaction of output constraints. By redefining appropriate operators and normed spaces, the well-posedness of the closed-loop PDE system is rigorously analyzed via operator semigroup theory. The uniform boundedness of the output variables is verified by Lyapunov stability theory. Numerical simulations under five test cases demonstrate that, under parametric perturbations, the proposed controller suppresses the maximum elastic vibration below 0.0047 and achieves tracking RMSE around $3.5220\times {10}^{-6}$ with positive constraint margins and acceptable control energy, which validates its effectiveness and superiority.