Fractional-order boundary control of fractional wave equation with delayed boundary measurement using Smith predictor

In this paper, we consider boundary control of a fractional order wave equation. Both integer order and fractional order boundary control laws are investigated. When delayed boundary measurements are used for boundary control, the Smith predictor is applied. Through extensive hybrid symbolic and numerical simulation, combined with parameter optimization, for the first time, we confirmed that (1) small time delay in boundary control law can destabilize the controlled system; (2) the Smith predictor can compensate the delay effect; and (3) fractional order boundary control can outplay its integer counterpart in terms of transient performance.