Linear-Quadratic Optimal Boundary Control of a One-Link Flexible Arm

A linear-quadratic optimal control problem is considered for the infinite-dimensional model of a one-link flexible arm. Two boundary inputs are assumed to be available, namely the joint torque at the link base and a transverse force at the tip of the link. The problem is formulated and solved using semigroup theory and duality arguments. Simulation results are provided to support the theoretical findings, comparing the proposed optimal LQ law with a more conventional PD/state feedback controller in terms of cost and transient performance.