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

Zavala‐Río, Arturo; Mendoza, Marco; Santibáñez, Víctor; Reyes, Fernando

doi:10.1177/1729881416663368

Cited by 7 publications

(5 citation statements)

References 25 publications

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“…where g(qd) is the desired gravity torque vector. By substituting (13) and (14) into the robot dynamics (7), we obtain…”

Section: A Stability Analysis Of Linear D + Nonlinear Pimentioning

confidence: 99%

“…Furthermore, Zavalario proposed a natural saturated extension of PD with desired gravity compensation control law and constrained input that was globally asymptotically stable [11,12]. Then, an outputfeedback PID with multiple saturating structures and constrained inputs guaranteed the global stability [13]. Salinas put forward a family of locally asymptotically stable nonlinear PID control law, where stability conditions were independent of the saturation levels of actuators [14].…”

Section: Introductionmentioning

confidence: 99%

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Global Asymptotic Nonlinear PID Control With a New Generalized Saturation Function

Niu

Qu²

2020

IEEE Access

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In order to solve the problem of the strict condition of traditional saturation function, a new generalized saturation function was proposed and applied in nonlinear PID (Proportion-Integration-Differentiation) control laws, which consisted of linear D + nonlinear PI and linear PD + nonlinear PI. The new generalized saturation function has powerful reaction near the equilibrium point, and has the capability to make the control converge to the equilibrium point swiftly. The global asymptotic stability condition of nonlinear PID control laws were derived by employing Lyapunov's method and LaSalle's invariance principle. In order to improve the accuracy of nonlinear PID control laws, time integration of the absolute value of position tracking error and time integration of the absolute value of torque error were chosen as the objective functions. Global asymptotic stability conditions and rated driving torque of each motor were set as the constraint conditions. Nonlinear PID controller parameters were tuned by employing multi-objective genetic algorithm, non-dominated sorted genetic algorithm-II (NSGA-II). Compared with the optimization results of nonlinear PID with traditional saturation function, the accuracy of position tracking using the proposed method was improved by nearly one order of magnitude. The new generalized saturation functions with minimum time integration of position tracking error were selected to study the robustness of the nonlinear PID controller in modeling uncertainty, input torque disturbance, and noise. The position tracking accuracy of the proposed method compared to those of the traditional PID controller and nonlinear PID controller with traditional saturation function was improved by nearly two orders of magnitude and one order of magnitude, respectively. The introduced saturation function significantly improves position tracking accuracy and robustness of the nonlinear PID controller.

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“…where g(qd) is the desired gravity torque vector. By substituting (13) and (14) into the robot dynamics (7), we obtain…”

Section: A Stability Analysis Of Linear D + Nonlinear Pimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Asymptotic Nonlinear PID Control With a New Generalized Saturation Function

Niu

Qu²

2020

IEEE Access

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“…But until now, the PID control lacks of global asymptotic stability. It is valid only in a local sense [2,4,5].…”

Section: Introductionmentioning

confidence: 99%

An asinh-type regulator for robot manipulators with global asymptotic stability

Reyes-Cortés

Al‐Hadithi

2020

Automatika

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In this paper, a new asinh-type control scheme with gravity compensation for the position control problem of robot manipulators in joint space is presented. The properties and characteristics of the asinh control structure make the position error and the motion velocity asymptotically converge to the equilibrium point. A strict Lyapunov function to formally prove global asymptotic stability is developed. The tuning of the control gains is obtained by PSO (Particle Swarm Optimization) technique without saturating the servomotors. To illustrate the effectiveness and performance of the proposed scheme, an experimental comparative analysis between the proportional-derivative (PD) and atanh controls against the proposed algorithm on a three degrees of freedom direct-drive robot manipulator is carried out.

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“…The proportional-derivative (PD) and proportional-integral-derivative (PID) control algorithms are the most simplest regulators to achieve regulation of robot manipulators. For the case of PD control guarantees the global regulation objective [31]; while that, the PID control lacks of it, until now asymptotic stability is valid only in a local sense [13,33]. On the other hand, there is an implicit assumption in the linear PD and PID control schemes, they are able to provide any requested joint torque, because these schemes do not incorporate input constraints from manipulator actuator limitations on their applied torques.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, in [3] has proposed a bounded proportional control plus Hammerstein strictly positive real compensator control term to ensure that the applied torque of each servomotor is bounded by a value that is less then maximum torque, it has a asymptotically stable behavior. In [33] a PID-type control for the global regulation with constrained inputs is proposed; this controller can adopt multiple saturating structures, the global stabilization objective is guaranteed. Furthermore, experimental tests on a two degrees-of freedom are presented.…”

Section: Introductionmentioning

confidence: 99%