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Industrial robots are naturally equipped with classical PID controllers, which theoretically assure semi–global asymptotic stability of the closed–loop system equilibrium for the regulation case (see, e.g., Arimoto & Miyazaki (1984), Arimoto et al., (1990), Kelly (1995b), Ortega et al., (1995), Alvarez-Ramirez et al., (2000), Kelly et al., (2005), Meza et al., (2007)). Uniform ultimate boundedness of the closed–loop solutions can be concluded when the desired position is a function of time (some stability analyzes for this case can be found in the works of Kawamura et al. (1988), Wen & Murphy (1990), Qu & Dorsey (1991), Rocco (1996), Cervantes & Alvarez-Ramirez (2001), Choi & Chung (2004), and Camarillo et al., (2008)), but to the authors’ knowledge, so far there is not a proof of global regulation for such controller. In the search of a practical globally stable PID regulator, some nonlinear control structures based on the classical PID controller, which assure global asymptotic stability of the closed– loop system, have emerged. Some works that deal with global nonlinear PID regulators based on Lyapunov theory and passivity theory have been reported by Arimoto (1995), Kelly (1998), Santibanez & Kelly (1998a), and Meza & Santibanez (1999). Recently, a particular case of the class of nonlinear PID global regulators originally proposed in (Santibanez & Kelly, 1998a) was presented by Sun et al., (2009). On the other hand, it is well known that saturation phenomena in robot control systems are intrinsically present when the actuators are driven by sufficiently large control signals. If these physical constraints are not considered in the controller design they may lead to a lack of the stability properties. Even though no one of the controllers mentioned above considers the influence of the saturation phenomena, there are some works that have been reported to solve this saturation problem in PD-like controllers for the case of regulation tasks (Kelly & Santibanez, 1996; Colbaugh et al., 1997a; Loria et al., 1997; Santibanez & Kelly, 1997; 1998b). Solutions without considering velocity measurements and with gravity compensation are treated in (Loria et al., 1997). A full–state (position and velocity) feedback solution with adaptive gravity compensation is presented in (Zergeroglu et al., 2000). More recently, new schemes dealing with this regulation problem of robot manipulators with bounded inputs have been presented by Zavala & Santibanez (2006), Zavala & Santibanez (2007), Dixon (2007), Alvarez-Ramirez et al., (2003), and Alvarez–Ramirez et al., (2008). An adaptive

On Saturated PID Controllers for Industrial Robots: the PA10 Robot Arm as Case of Study