Global Asymptotic Saturated PID Control for Robot Manipulators

Output-feedback proportional-integral-derivative-type control with multiple saturating structure for the global stabilization of robot manipulators with bounded inputs

“…Observe that the input-saturation-avoidance conditions for the particular control structures presented in this appendix, that is inequalities (32), (34), (36) and (38), imply that M Pi þ M Ii < T i . On the other hand, the satisfaction of inequalities (14) implies that M Pi þ M Ii > 3B gi . Hence, for the specific choices of s d presented in equations (31), (33), (35) and (37), the feasibility of the simultaneous fulfillment of inequalities (14) and the corresponding inputsaturation-avoidance condition-(32), (34), (36) or (38), respectively-is ensured by requiring the satisfaction of Assumption 1 with ¼ 3.…”

“…On the other hand, the satisfaction of inequalities (14) implies that M Pi þ M Ii > 3B gi . Hence, for the specific choices of s d presented in equations (31), (33), (35) and (37), the feasibility of the simultaneous fulfillment of inequalities (14) and the corresponding inputsaturation-avoidance condition-(32), (34), (36) or (38), respectively-is ensured by requiring the satisfaction of Assumption 1 with ¼ 3. Other particular choices of s d in the generalized scheme (11) could require different values of !…”

“…This arises as a requirement to guarantee the feasibility of the simultaneous fulfillment of (15b) and inequalities (14). For instance, in the particular control structure cases presented in Appendix 1, such a feasibility is achieved by requiring ¼ 3, as pointed out in Remark 5.…”

“…This was developed by Meza et al 13 via passivity theory and later on by Su et al 14 through Lyapunov stability analysis. A Saturating-Proportional-Derivative Saturating-Integral (SPD-SI) type controller was further proposed by Santibáñez et al 15 More recently, a state-feedback PID-type scheme with a generalized saturating structure, that includes both the SP-SI-SD and SPD-SI as particular cases, was presented by Mendoza et al 16 In particular, Su et al's work 14 includes a velocity-free version of the presented controller by involving the dirty derivative. Further concerns on the bounded input problem have led to the additional consideration of the saturation effects of the electronic control devices of practical PID regulators.…”

Adaptive Gain PID Control for Mechanical Systems

“…The design and use of PID controllers is a part of what has been denominated Classical Control, which as the name implies, has been studied for many years (DiStefano et al 1996), however it continues to be a source for research (Alvarez et al 2008), (Ang et al 2008), (Su et al 2010). The structure of the controller contains a differential term to aid in the reduction of system friction and an integral term to attenuate steady state error.…”