Transfer functions for a single flexible link

Wang, D.; Vidyasagar, M.

doi:10.1109/robot.1989.100118

Cited by 97 publications

(64 citation statements)

References 6 publications

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“…In order to apply this technique to a flexible dynamic system Eq. (7) it is necessary to define an output vector as defined in (Moallem et al, 1997;Wang and Vidyasagar, 1989).…”

Section: Input-output Controlmentioning

confidence: 99%

A nonlinear high gain observer based input–output control of flexible link manipulator

Masoud

Ghayour

Sadigh

2012

Mechanics Research Communications

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“…In order to apply this technique to a flexible dynamic system Eq. (7) it is necessary to define an output vector as defined in (Moallem et al, 1997;Wang and Vidyasagar, 1989).…”

Section: Input-output Controlmentioning

confidence: 99%

A nonlinear high gain observer based input–output control of flexible link manipulator

Masoud

Ghayour

Sadigh

2012

Mechanics Research Communications

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“…Although some efforts have been made to address the real time execution issues of the noncausal inverse dynamics, it is still desirable that a causal solution can be obtained with bounded actuator torques [4,5]. One successful idea was proposed by Wang and Vidyasagar which modifies the output function [6]. In this method, the inverse solution is sought to achieve a prescribed trajectory at a virtual point close to the boundary tip [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…One successful idea was proposed by Wang and Vidyasagar which modifies the output function [6]. In this method, the inverse solution is sought to achieve a prescribed trajectory at a virtual point close to the boundary tip [5][6][7][8]. Stable solutions can be obtained but tip tracking is approximate.…”

Section: Introductionmentioning

confidence: 99%

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A Pseudo-rigid model for the inverse dynamics of an Euler beam

Mandali

Sun

Kanamiya

2011

Applied Mathematical Modelling

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a b s t r a c tInversion technique has been very successful in the tracking control of nonlinear dynamical systems. However, when applied to manipulators constructed with elastic links, inverse dynamics through direct integration in temporal space causes unbounded controller command. It has been suggested that seeking an inverse dynamics solution for a given tip trajectory with given initial conditions is an ill-posed problem. It has also been suggested that increasing model accuracy by including more terms in a truncated beam model worsens the controller's ability to stabilize the system dynamics. In this paper, we seek to understand the nature of the inverse dynamics instability and to find an alternative solution. We appeal to the notion of a pseudo-rigid model which describes the beam deflection by a homogeneous displacement field. Particularly, we derive the mode shape in order to yield a bounded inverse dynamics solution. Different from most of the existing solutions where solution stability was achieved through modifying the output function, we modified the inverse dynamics model. A bounded inverse solution and model simplicity provide much needed ease in the design and implementation of an inversion controller. Numerical simulations and experiments have both been conducted to prove the validity of the proposed method.

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“…[16] made comparisons between the stable inversion approach and some approximate tracking approaches [15] in the context of CTOL aircraft and found that the feedforward inputs via stable inversion have much larger magnitudes than those using the other approaches. In parallel, we have been interested in the tip tracking control of a flexible manipulator where the relative degree is ill-defined, arising from noncolocated sensor/actuator structures [17]. The endpoint tracking control of a flexible manipulator is nonminimum phase and its zero dynamics is also singularly perturbed [18,19].…”

Section: Introductionmentioning

confidence: 99%

Ill-conditioned stable inversion arising from singularly perturbed zero dynamics

Guo

Wang

2008

J. Control Theory Appl.

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The ill-conditioned stable inversion is studied for slightly nonminimum phase systems whose zero dynamics is singularly perturbed, that is, the relative degree is ill-defined. For these systems, we show that there exists an inherent limitation in the bandwidth of a reference trajectory to be tracked when a well-conditioned feedforward input via stable inversion is sought. We assert that, when the violation of this limitation occurs, the so-called reference trajectory redesign is called for. Our analysis results can provide an explicit assessment as well as useful guidance for the reference trajectory redesign if needed.

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Transfer functions for a single flexible link

Cited by 97 publications

References 6 publications

A nonlinear high gain observer based input–output control of flexible link manipulator

A nonlinear high gain observer based input–output control of flexible link manipulator

A Pseudo-rigid model for the inverse dynamics of an Euler beam

Ill-conditioned stable inversion arising from singularly perturbed zero dynamics

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