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This paper proposes an alternative to the saturated nonlinear PID controller previously presented by Santibaez et al. (2010) which, also, results from the practical implementation of the classical PID controller, by considering the natural saturations of the electronics in the control computer, servo drivers, and actuators. The stability analysis of the closed loop system is carried out by using the singular perturbation theory. Based on auxiliary Lyapunov functions, we prove local exponential stability of the equilibrium point of the closed loop system. It is also guaranteed that, regardless of the initial conditions, the delivered actuator torques evolve inside the permitted limits. Experimental results confirm the proposed analysis. Furthermore, the theoretical result explains why the classical linear PID regulator used in industrial robot manipulators preserves the exponential stability in spite of entering the saturation zones inherent to the electronic control devices and the actuator torque constraints.