Adaptive contact-force control and vibration suppression for constrained flexible manipulator with unknown control direction and time-varying actuator fault

A contact-force control and vibration suppression problem for a constrained one-link flexible manipulator with unknown control direction and time-varying actuator fault is discussed in this paper. The manipulator is described by a Partial Differential Equation model. The Nussbaum function is used to solve the unknown control direction and time-varying actuator fault problems. A Nussbaum function provides an adaptive boundary controller constructed to control the contact force to a target and simultaneously eliminate the vibration of the flexible manipulator. The Variable Separation Technique is used along with system boundary conditions to prove the necessary existence and uniqueness of the system solution more concisely than using the common C-0 -semigroup contractions method. Because force sensors are not necessary, the noise caused by a force sensor can be avoided. Numerical simulations verify the effectiveness of the proposed controller-based solution.