Saturated Nonlinear Pid Global Regulator for Robot Manipulators: Passivity Based Analysis

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

“…Remark 1. Note that _ q is not involved in any of the expressions in equations (11)- (13). In fact, _ q is estimated online through the auxiliary subsystem in equations (13), driven by q as input variable.…”

“…Consider system (1),(10) taking u ¼ uðq; #; Þ as defined through equations (11)- (13). Let us define the variable transformation…”

“…For instance, let K D 2 R n be a positive definite diagonal matrix. An SP-SI-SD type algorithm 13,28 is obtained by defining …”

“…Such efforts gave rise, for instance, to the Saturating-Proportional SaturatingIntegral Saturating-Derivative (SP-SI-SD) type algorithm. 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.…”

Analysis via Passivity Theory of a Class of Nonlinear PID Global Regulators for Robot Manipulators

“…Recently, a particular case of the class of nonlinear PID global regulators originally proposed in (Santibáñez & Kelly, 1998) was presented by (Sun et al, 2009). Few saturated PID controllers (that is, bounded PID controllers taking into account the actuator torque constraints) have been reported: for the case of semiglobal asymptotic stability, a saturated linear PID controller was presented in (Alvarez et al, 2003) and (Alvarez et al, 2008); for the case of global asymptotic stability, saturated nonlinear PID controllers were introduced in (Gorez, 1999), (Meza et al, 2005), . The work introduced by (Gorez, 1999) was the first bounded PID-like controller in assuring global regulation; the latter works, introduced in (Meza et al, 2005) and , also guarantee global regulation, but with the advantage of a controller structure which is simpler than that presented in (Gorez, 1999).…”