Dual-Loop Adaptive Iterative Learning Control for a Timoshenko Beam With Output Constraint and Input Backlash

In this paper, vibration control and output constraint are considered for a Timoshenko beam system with input backlash and external disturbances. By integrating iterative learning control (ILC) into adaptive control, two dual-loop adaptive ILC 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 barrier composite energy function, all the signals are proved to be bounded in each iteration. Along the iteration axis: 1) the endpoint transverse displacements and the endpoint angle displacements are restrained; 2) the transverse vibrations and the rotation vibrations are suppressed to zero; and 3) the spatiotemporally varying disturbance and the time-varying disturbances are rejected. Simulations are provided to manifest the effectiveness of the proposed control laws.