Iterative learning control for a timoshenko beam with input backlash

In this paper, vibration control is addressed for a Timoshenko beam system with input backlash and external disturbances. By integrating iterative learning control into adaptive control, two dual-loop adaptive iterative learning control schemes are proposed in the presence of the input backlash. Two observers are designed to estimate two bounded terms, which are divided from the backlash inputs. Based on the defined composite energy function, all the signals are proved to be bounded in each iteration. Along the iteration axis, (I) the input backlash is tackled; (II) the transverse displacements and the angle displacements are suppressed to zero; and (III) the spatiotemporally varying disturbance and the time-varying disturbance are rejected. Simulations are provided to manifest the effectiveness of the proposed control laws.