Global Asymptotic Stability of the Classical PID Controller by Considering Saturation Effects in Industrial Robots

Yarza, Antonio; Santibáñez, Víctor; Moreno–Valenzuela, Javier

doi:10.5772/45688

Cited by 23 publications

(35 citation statements)

References 35 publications

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“…(sat(PDdgc)) Controller Design. The sat(PDdgc) feedback controller used for comparison with hybrid ILC has the following modified control law computed off-line [12,16,39,52,54]:…”

Section: Saturated Pd With Desired Gravity Compensationmentioning

confidence: 99%

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Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

Ernesto¹,

Pedro²

2015

Mathematical Problems in Engineering

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This paper proposes the design of a hybrid iterative learning controller for a four-degree-of-freedom (DOF) robotic machining manipulator (RMM). It combines a nonlinear saturated (sat) proportional + integral + derivative (PID) control with desired gravity compensation (dgc) and proportional + derivative-(PD-) based iterative learning control (ILC). The sat(PID) control is the primary component that maintains the local stability of the entire RMM system and the PDILC component provides robustness to parameter variations and uncertainties in the robot dynamics. Global asymptotic stability of the proposed control algorithm is conducted using Lyapunov direct method and LaSalles invariance principle. Simulation results show the effectiveness and robustness of the proposed hybrid iterative learning controller. It is also shown that the proposed controller achieved better tracking performances compared to conventional sat(PDdgc) feedback controller.

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“…(sat(PDdgc)) Controller Design. The sat(PDdgc) feedback controller used for comparison with hybrid ILC has the following modified control law computed off-line [12,16,39,52,54]:…”

Section: Saturated Pd With Desired Gravity Compensationmentioning

confidence: 99%

“…Most of the industrial robots control applications are PID [11,39,40], PD [12,13,41], and PI [42] based, due to their simplicity and clear physical meaning. Despite these advantages, the design of these controllers is still a challenge [43][44][45] for multi-input/multi-output (MIMO) system.…”

Section: Introductionmentioning

confidence: 99%

Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

Ernesto¹,

Pedro²

2015

Mathematical Problems in Engineering

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“…In order to ensure that the positions reach the desired setpoints in less time than those shown in Figure 18, it might be required to protect the devices against damage due to overvoltage and/or overcurrent peaks caused by high gains, for example, by using saturated controls [18]. …”

Section: Regulation Control Simulationmentioning

confidence: 99%

Stability Analysis of a Voltage-Based Controller for Robot Manipulators

Orrante-Sakanassi

Santibáñez

Moreno–Valenzuela

2013

International Journal of Advanced Robotic Systems

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A voltage-based control scheme for robot manipulators has been presented in recent literature, where feedback linearization is applied in the electrical equations of the DC motors in order to cancel the electrical current terms. However, in this paper we show that this control technique generates a system of the form ,where is a singular matrix, that is to say, a generalized state-space system or singular system. This paper introduces a formal stability analysis of the respective system by considering the state-space equation as a singular system. Furthermore, in order to avoid the singularity of the closed-loop system, modified voltage-based control schemes are proposed, whose Lyapunov stability analyses conclude semiglobal asymptotic stability for the set-point control case and uniform boundedness of the solutions and semiglobal convergence of the position, as well as velocity errors for the tracking control case. The proposed control systems are simulated for the tracking and set-point cases using the CICESE Pelican robot driven by DC motors.

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“…This is the case for instance of [20], [21], [22] where state-feedback and output-feedback schemes were presented, and [23] where a controller with the same structure as the state-feedback algorithm presented in [22] was previously proposed. Such PID-type algorithms are not only independent of the exact knowledge of the system parameters, but also disregard the structure of the system dynamics (or of any of its components).…”

Section: Introductionmentioning

confidence: 99%

Output-Feedback Adaptive SP-SD-Type Control with an Extended Continuous Adaptation Algorithm for the Global Regulation of Robot Manipulators with Bounded Inputs

López-Araujo

Zavala‐Río

Santibáñez

et al. 2013

International Journal of Advanced Robotic Systems

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In this work, an output-feedback adaptive SP-SD-type control scheme for the global position stabilization of robot manipulators with bounded inputs is proposed. Compared with the output-feedback adaptive approaches previously developed in a boundedinput context, the proposed velocity-free feedback controller guarantees the adaptive regulation objective globally (i.e. for any initial condition), avoiding discontinuities throughout the scheme, preventing the inputs from reaching their natural saturation bounds and imposing no saturation-avoidance restrictions on the choice of the P and D control gains. Moreover, through its extended structure, the adaptation algorithm may be configured to evolve either in parallel (independently) or interconnected to the velocity estimation (motion dissipation) auxiliary dynamics, giving an additional degree of design flexibility. Furthermore, the proposed scheme is not restricted to the use of a specific saturation function to achieve the required boundedness, but may involve any one within a set of smooth and non-smooth (Lipschitz-continuous) bounded passive functions that include the hyperbolic tangent and the conventional saturation as particular cases. Experimental results on a 3-degree-of-freedom manipulator corroborate the efficiency of the proposed scheme.

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Global Asymptotic Stability of the Classical PID Controller by Considering Saturation Effects in Industrial Robots

Cited by 23 publications

References 35 publications

Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

Iterative Learning Control with Desired Gravity Compensation under Saturation for a Robotic Machining Manipulator

Stability Analysis of a Voltage-Based Controller for Robot Manipulators

Output-Feedback Adaptive SP-SD-Type Control with an Extended Continuous Adaptation Algorithm for the Global Regulation of Robot Manipulators with Bounded Inputs

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