The present paper is concerned with the design of dynamic anti-integrator-windup controllers for critically stable linear systems with a single pole at the origin. The constant gain term in the conventional anti-windup controller is extended to have dynamics represented by a transfer function. The proposed dynamic anti-windup compensator is similar to the one based on co-prime factorization of the plant. The overall controller includes an internal model for constant signals and achieves regulation for constant disturbance and reference inputs as long as the asymptotic control input stays within the saturation limits. The effectiveness of the proposed method is demonstrated on a one-link flexible arm through simulations and experiments.