On the linear control of nonlinear mechanical systems

Sira‐Ramírez, Hebertt; Ramírez‐Neria, Mario; Rodríguez-Ángeles, Alejandro

doi:10.1109/cdc.2010.5717691

Cited by 45 publications

(20 citation statements)

References 7 publications

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“…SiraRamírez, Ramírez-Neria, & Rodríguez-Ángeles, 2010;Zhao, Wang, Liu, & Wang, 2013) the boundedness of r (p) (t) is NOT assumed a priori, but it is formally proven.…”

Section: Preliminaries On the Gpi Control-observer Designmentioning

confidence: 98%

On the GPI approach with unknown inertia matrix in robot manipulators

Arteaga

Gutiérrez–Giles

2013

International Journal of Control

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This article discusses the design of generalised proportional integral observers for the tracking control of robot manipulators. The unknown, possibly state-dependent, additive nonlinearity influencing the input-output description, in terms of the tracking error dynamics is modelled for observer construction purposes, as an absolutely bounded, additive, unknown timevarying perturbation input signal. A disadvantage of the approach lies in the fact that the system inertia matrix is usually required for implementation. In this work, it is shown how the approach can be modified to avoid the use of the inertia matrix when it is unknown. A set of experiments with three different test beds is carried out to show the good performance of the proposed algorithm.

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“…SiraRamírez, Ramírez-Neria, & Rodríguez-Ángeles, 2010;Zhao, Wang, Liu, & Wang, 2013) the boundedness of r (p) (t) is NOT assumed a priori, but it is formally proven.…”

Section: Preliminaries On the Gpi Control-observer Designmentioning

confidence: 98%

On the GPI approach with unknown inertia matrix in robot manipulators

Arteaga

Gutiérrez–Giles

2013

International Journal of Control

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“…It is assumed that all the motors have identical features. Using equations (14), (15) in (13) leads tö…”

Section: A Gpi Control Designmentioning

confidence: 99%

“…The effects of the bounded perturbation input function on the performance of the observer estimation error dynamics may be adequately attenuated via high gain pole location. The method, known as Generalized Proportional Integral (GPI) observer based control (see [12]) has been applied and reported for several electrical and mechanical differentially flat systems with successful experimental results (see also [13], [14], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

An active disturbance rejection controller for a parallel Robot via Generalized Proportional Integral observers

Ramírez‐Neria¹,

Sira‐Ramírez

Rodríguez-Ángeles

et al. 2012

2012 American Control Conference (ACC)

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In this article, we address an active disturbance rejection controller design for the output reference trajectory tracking problem in a 3 degree of freedom (DOF) Delta Robot. The proposed method relies on purely linear high gain disturbance observation and linear feedback control techniques. The estimation tasks are carried out with the help of Generalized Proportional Integral (GPI) observers, endowed with output integral injection to counteract zero mean measurement noise effects. As the lumped exogenous and endogenous disturbance inputs are estimated, the observers deliver them to the controllers for on-line disturbance cancelation, while simultaneously the phase variables, related to the measured flat outputs, are being estimated by the same GPI observer. The gathered values of the phase variables are used to complete a linear multivariable output feedback control scheme. The proposed control scheme avoids the traditional computed torque method, reducing the computation time and bypassing the need for explicit, accurate, knowledge of the plant. The estimation and control method is only approximate as small as desired reconstruction, or tracking, errors are guaranteed. The reported results, including laboratory experiments, are significantly better than the results provided by the classical model-based techniques, when the system is subject to endogenous and exogenous uncertainties.

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“…As a consequence, the disturbance estimation error ξ(t) −ẑ 1 (t) = ξ(t) −ξ(t) is ultimately uniformly bounded by a small as desired neighborhood of zero. Proof: The proof is based on the fact that the estimation errorẽ = e δ − e 1δ satisfies the following perturbed linear differential equation (see [20]),…”

Section: B a Gpi Oberver-based Adrc For The Jumping Ringmentioning

confidence: 99%

“…Linear Generalized Proportional Integral observers, (GPI observers), dual to GPI controllers (see Fliess et al [6]), are used to approximately estimate in a self-updating manner the aggregate effects of exogenous and endogenous additive disturbances. The control input gain is assumed to be known and, at most, output dependent ( [20]). The approach has significant implications in nonlinear chaotic systems estimation as demonstrated in [17].…”

Section: Introductionmentioning

confidence: 99%

On the linear Active Rejection Control of Thomson's Jumping Ring

Ramírez‐Neria

García-antonio

Sira‐Ramírez

et al. 2013

2013 American Control Conference

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The problem of tracking a smooth time-varying reference trajectory for Thomson's ring is addressed from the perspective of Active Disturbance Rejection Control (ADRC). The tracking controller is designed on the basis of the tangent linearization model of the nonlinear system around a constant equilibrium point. The large height deviations, outside the region of validity of the approximate linearization, trigger the effect of unknown nonlinearities and exogenous perturbations. These disturbances are properly on-line estimated and canceled with the help of a linear extended observer-linear controller based output feedback control scheme. Experimental results are presented which validate the effectiveness of the proposed control scheme.

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On the linear control of nonlinear mechanical systems

Cited by 45 publications

References 7 publications

On the GPI approach with unknown inertia matrix in robot manipulators

On the GPI approach with unknown inertia matrix in robot manipulators

An active disturbance rejection controller for a parallel Robot via Generalized Proportional Integral observers

On the linear Active Rejection Control of Thomson's Jumping Ring

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