An Estimate of the Domain of Attraction for the Pid Regulator of Manipulators

Meza, José Luis; Santibáñez, Víctor; Campa, Ricardo

doi:10.2316/journal.206.2007.3.206-2829

Cited by 26 publications

(18 citation statements)

References 10 publications

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“…The entries of the dynamics of this two degrees-of-freedom direct-drive robotic arm are given by (Meza et al, 2007): The PID tuning method is based on the stability analysis presented in (Santibáñez & Kelly, 1998). The tuning procedure for the PID controller gains can be written as:…”

Section: Simulation Resultsmentioning

confidence: 99%

“…A open problem is the lack of a proof of global asymptotic stability (Arimoto, 1994). The stability proofs shown until now are only valid in a local sense (Arimoto, 1994;Arimoto et al, 1990;Arimoto & Miyazaki, 1983;Arimoto, 1996;Dorsey, 1991;Kelly, 1995;Kelly et al, 2005;Rocco, 1996;Wen, 1990) or, in the best of the cases, in a semiglobal sense (Alvarez et al, 2000;Meza et al, 2007). In (Ortega et al, 1995a), a so-called PI 2 D controller is introduced, which is based on a PID structure but uses a filter of the position in order to estimate the velocity of the joints, and adds a term which is the integral of such an estimate of the velocity (this added term motivates the name PI 2 D); for this controller, semiglobal asymptotic stability was proved.…”

Section: Classical Pid Regulatorsmentioning

confidence: 99%

See 1 more Smart Citation

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

Meza¹,

Santibáñez²,

Soto³

et al. 2011

Advances in PID Control

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Classical Pid Regulatorsmentioning

confidence: 99%

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

Meza¹,

Santibáñez²,

Soto³

et al. 2011

Advances in PID Control

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“…It is well known that industrial robots are equipped with PID controllers which practically assure the semiglobal asymptotic stability of the closed-loop equilibrium for the regulation case [1][2][3][4][5][6][7][8]. Also, it is known that real-life actuators are unable to supply unlimited torque, and their output is bounded.…”

Section: Introductionmentioning

confidence: 99%

A practical PID regulator with bounded torques for robot manipulators

Santibáñez

Camarillo

Moreno–Valenzuela³

et al. 2010

Int. J. Control Autom. Syst.

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This paper proposes a saturated nonlinear PID regulator for industrial robot manipulators. Our controller considers the natural saturation problem given by the output of the control computer, the saturation phenomena of the internal PI velocity controller in the servo driver, and the actuator torque constraints of the robot manipulator. An approach based on the singular perturbations method is used to analyze the exponential stability of the closed-loop system. Experimental essays show the feasibility of the proposed controller. Furthermore, the theoretical results justify why the classical PID used in industrial robots preserves its exponential stability despite the saturation effects of the electronic control devices and the actuator torque constraints.

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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.…”

Section: Introductionmentioning

confidence: 99%