Journal ArticleDOI
Stability of PID control for industrial robot arms
Paolo Rocco
- Vol. 12, Iss: 4, pp 606-614
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TLDR
A novel proof for the stability of rigid robot arms controlled by PID algorithms: the proof is based on a model of the robot where the nominal decoupled linear part is emphasized and the theoretical results are verified on a simple two DOF example.Abstract:
PID control is the most widespread technique for the control of industrial robot arms. However, the adoption of PID control is not adequately supported by a theoretical basis, since the results presented in the literature are of dubious interpretation and difficult, when not impossible, to verify. Motivated by this lack of theoretical support, this paper presents a novel proof for the stability of rigid robot arms controlled by PID algorithms: the proof is based on a model of the robot where the nominal decoupled linear part is emphasized. The main result consists in a simple condition between the exponential stability degree of the nominal closed loop system and the parameters of a bound on the nonlinear terms in the dynamic model of the mechanical manipulator. Some considerations are also worked out on the relations between the eigenvalues of the nominal system and the extension of the stability region. The theoretical results are finally verified on a simple two DOF example.read more
Citations
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Journal ArticleDOI
Six-DOF Impedance Control of Dual-Arm Cooperative Manipulators
TL;DR: In this paper, a general impedance control scheme is adopted, which encompasses a centralized impedance control strategy aimed at conferring compliant behavior at the object level, and a decentralized impedance control, enforced at the end-effector level, aimed at avoiding large internal loading of the object.
Journal ArticleDOI
A review of PID control, tuning methods and applications
TL;DR: This paper attempts to address the literature review of PID control in an era of control system and bio-medical applications by surveying the development of classical PID to the integration of intelligent control to it.
Journal ArticleDOI
Stability of PID control for industrial robot arms
TL;DR: A novel proof for the stability of rigid robot arms controlled by PID algorithms: the proof is based on a model of the robot where the nominal decoupled linear part is emphasized and the theoretical results are verified on a simple two DOF example.
Journal ArticleDOI
On the PID tracking control of robot manipulators
TL;DR: It is proved that under classical PID control, semiglobal stability can be assured with arbitrary small output tracking error, which means that, for any given set of initial conditions Wx, there exist PID control gains such that all trajectories starting in Wx converge to a residual set of arbitrary size.
Journal ArticleDOI
Neural PID Control of Robot Manipulators With Application to an Upper Limb Exoskeleton
Wen Yu,Jacob Rosen +1 more
TL;DR: Semiglobal asymptotic stability of the neural PID control and local asymPTotic stability for the linear PID control with a velocity observer are proved with standard weight training algorithms, which give explicit selection methods for the gains of thelinear PID control.
References
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TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
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Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems
Martin Corless,George Leitmann +1 more
TL;DR: In this article, a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state, and these feedback controls are continuous functions of the state.
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TL;DR: In this paper, the standard problem and performance bounds of model-matching theory are discussed. But the performance bounds are not defined. And they are not considered in this paper.
Journal ArticleDOI
A new feedback method for dynamic control of manipulators
Morikazu Takegaki,Suguru Arimoto +1 more
TL;DR: A new approach to the dynamic control of manipulators is developed from the viewpoint of mechanics and it is shown that a linear feedback of generalized coordinates and their derivatives are effective for motion control in the large.