A family of nonlinear PID-like regulators for a class of torque-driven robot manipulators equipped with torque-constrained actuators

Salinas, Adriana; Moreno–Valenzuela, Javier; Kelly, Rafael

doi:10.1177/1687814016628492

Cited by 31 publications

(17 citation statements)

References 27 publications

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“…It is worth mentioning that since both conditions V(q,q) > 0 anḋ V(q,q) < 0 are satisfied, then the proposed Lyapunov function candidate is a strict Lyapunov function. Consequently, the existence of a positive number 0 is ensured fulfilling inequality (14). Therefore, according to Lyapunov's direct method, we conclude asymptotic stability of the origin q,q T = 0 ∈ R 2n of the closedloop equation (7).…”

Section: Analysis Of Global Asymptotic Stabilitymentioning

confidence: 77%

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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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Section: Analysis Of Global Asymptotic Stabilitymentioning

confidence: 77%

“…Experimental tests on a two-dof robot manipulator are presented. In [14] a family of nonlinear PID-like controls is described. Lyapunov theory is used to establish conditions for local asymptotic stability.…”

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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“…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%

“…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]. In addition, Yarza introduced a nonlinear PID controller with bounded torques using a single saturation function that was globally asymptotically stable [15].…”

Section: Introductionmentioning

confidence: 99%

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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“…According to Moreno-Valenzuela and Guzman-Guemez (2016), the global asymptotic stability of a DC-to-DC boost converter system can be guaranteed by employing the proposed saturated observer-based controller. By applying a globally Lipschitz function, nonlinear PID-like control is designed to stabilize the saturated torque-driven robot manipulator system (Salinas et al, 2016). These works treat the input saturation problem of the ODE model.…”

Section: Introductionmentioning

confidence: 99%

Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

Liu

Huang

2018

Transactions of the Institute of Measurement and Control

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In this paper, the vibration suppression problem of a flexible satellite system is addressed. The dynamic model of the flexible satellite system is expressed by a set of non-homogeneous partial differential equations (PDEs). By using the theory of systems with uniform ultimate bounded (UUB) solutions and adaptive techniques, adaptive boundary control is presented to suppress the vibration of the flexible satellite with parametric uncertainties. A disturbance adaptive law is constructed to compensate for the effect of the boundary disturbance, and an auxiliary system is considered to mitigate the effect of input saturation. The well-posedness of the closed-loop system is discussed, and UUB stability can be ensured through a rigorous Lyapunov-like analysis. Numerical simulation results show the effectiveness of the proposed control scheme.

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A family of nonlinear PID-like regulators for a class of torque-driven robot manipulators equipped with torque-constrained actuators

Cited by 31 publications

References 27 publications

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

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

Global Asymptotic Nonlinear PID Control With a New Generalized Saturation Function

Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

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