Usually, simultaneous improvement of the transient performance and static accuracy is a challenging issue in saturated control systems. Employing an observer and the concept of composite nonlinear feedback, an integral controller is developed for constrained continuous-time systems. To achieve the control goal in the regulation purpose, a linear model is first derived by linearization about the operating point. Some parameters of the integral control are adjusted via the feedback passivation idea. The integral control law would be presented when a passivity condition is satisfied. Adding suitable damping terms to the existing one, the final controller is modified to enhance the response quality of the closed-loop system. The obtained results are evaluated in some numerical real examples. Although such a control method uses linearization, the outcomes of simulations, as well as the calculated performance indexes, discover the efficiency of the designed control system over the comparable ones.