This paper is a sequel of that published in the proceedings of Optima 2023, where the problem of stabilizing a chain of three integrators by a piecewise continuous constrained control in the form of three nested saturators was studied. In this work, we propose a more advanced stabilizing control law. The new feedback control is continuous and ensures the fulfillment of a phase constraint imposed on the third state variable. We study global stability of the closed-loop system and set an optimization problem of determining feedback coefficients that ensure the greatest convergence rate near the equilibrium while preserving global asymptotic stability of the system. We show that the loss of global stability is associated with arising hidden attractors, which come to existence when the convergence rate reaches a critical value depending on the control resource. A numerical procedure for constructing hidden attractors is developed, and the discussion is illustrated by numerical examples.