Quantized Time-Varying Fault-Tolerant Control for a Three-Dimensional Euler-Bernoulli Beam With Unknown Control Directions

In this study, quantization and time-varying actuator faults are considered for an uncertain three-dimensional Euler-Bernoulli beam system. The uncertainty is shown in that the control directions of the three actuators for the beam system may be unknown in practice. The three-dimensional Euler-Bernoulli beam is modeled as a distributed parameter system, where the system's governing equations are represented by a set of partial differential equations (PDEs) and boundary equations by ordinary differential equations (ODEs). Quantization is a necessary process in the network control field, and the quantized control algorithm is proposed and realized by logarithmic quantizers in this paper. Based on quantized control, the adaptive time-varying actuator fault-tolerant control scheme is designed with the aid of the Nussbaum functions and some auxiliary signals, which can also compensate for unknown control directions skillfully. Under the designed control scheme, all the signals are guaranteed to be bounded and the vibration of the beam is controlled. Finally, the simulation is done to verify the control effect.