This work continues our studies reported in the proceedings of the Optima conference in 2022 and 2023 [1, 2], where the problem of stabilizing a chain of three integrators by a piecewise continuous control in the form of nested saturators was discussed. In this work, we propose a more advanced stabilizing control law. The new feedback control is continuous and guarantees 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. It is established that the loss of global stability results from arising a hidden attractor, which comes to existence when the convergence rate reaches a critical value. A numerical procedure for constructing hidden attractors is developed, and the discussion is illustrated by numerical examples.