A DAE Formulation for the Dynamic Analysis and Control Design of Cranes Executing Prescribed Motions of Payloads

Blajer, Wojciech; Kołodziejczyk, K.

doi:10.1007/978-1-4020-5684-0_5

Cited by 5 publications

(13 citation statements)

References 20 publications

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“…1b, and C = ∂Φ/∂y is the associated 1 × n constraint matrix (Jacobian). By contrast, the crane dynamic equations in independent coordinates q, whose symbolic form is M q (q)q + d q (q,q) = f q (q,q) − B T q u, are of much more complex explicit form and are much more laborious to derive (see [10,11] for the details).…”

Section: Modeling Preliminariesmentioning

confidence: 99%

“…where 0 and I are the zero and identity matrices of dimension m × m. As shown in [5,[10][11][12], the use of independent coordinates q results in the much more complex servoconstraint equations, which must then be twice differentiated with respect to time (further substantial complexity) when involved in the governing equations for the inverse dynamics analysis. The present formulation is free from those demanding derivation tasks.…”

Section: Modeling Preliminariesmentioning

confidence: 99%

“…The mathematical models of cranes, used in both the flatness-based and DAE formulations of the inverse simulation studies, are typically built using minimal sets of independent coordinates [5,[7][8][9][10][11][12], leading to the minimal-dimension constraint reaction-free dynamic equations. The equations are of relative high complexity, however, assisted with further complexity of the so-called servo-constraints [12][13][14] or control constraints [5,15] on the system, resulted from the specified motion requirements expressed in the independent variables.…”

mentioning

confidence: 99%

“…By contrast, the use of dependent (nonminimal) coordinates may lead to some simplifications in formulation of the problem, which was exploited in, e.g., [16] and [17] for the flatness based solution of control of kinematically undetermined cable suspension manipulators. In this paper, we adopt this idea to improve our previous DAE formulation [11] for the dynamics and control of cranes executing prescribed motions of payloads. In the dependent variable formulation, the robot (crane without the load) dynamics and the load dynamics are initially described separately, and are then coupled through a simple passive constraint due to the inextensible hoisting cable.…”

mentioning

confidence: 99%

“…In the dependent variable formulation, the robot (crane without the load) dynamics and the load dynamics are initially described separately, and are then coupled through a simple passive constraint due to the inextensible hoisting cable. Since the load motion is explicitly specified, the followed formulation of the inverse dynamics problem simplifies compared to the independent variable formulations [5,[10][11][12] in many modeling and computational issues. The advantages are emphasized in the sequel with reference to a three-dimensional rotary crane model executing a specified motion of the load.…”

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confidence: 99%

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Improved DAE formulation for inverse dynamics simulation of cranes

Blajer

Kołodziejczyk

2010

Multibody Syst Dyn

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Cranes are underactuated systems with less control inputs than degrees of freedom. Dynamics and control of such systems is a challenging task, and the existence of solution to the inverse dynamics simulation problem in which an r-degree-of-freedom system with m actuators, m < r, is subject to m specified motion task (servo-constraints) is conditioned upon the system is differentially flat (all the system states and control inputs can be algebraically expressed in terms of the outputs and their time derivatives up to a certain order). The outputs are often designed as specified in time load coordinates to model a rest-to-rest maneuver along a trajectory in the working space, from the initial load position to its desired destination. The flatness-based methodology results then in the required control inputs determined in terms of the fourth time derivatives of the imposed outputs, and the derivations are featured by substantial complexity. The DAE formulation motivated in this contribution offers a more convenient approach to the prediction of dynamics and control of cranes executing prescribed load motions, and only the second time derivatives of the specified outputs are involved. While most of the inverse simulation formulations, both flatness-based and DAE ones, are performed using independent state variables, the use of dependent coordinates and velocities may lead to substantial modeling simplifications and gains in computational efficiency. An improved DAE formulation of this type is presented in this paper.

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Section: Modeling Preliminariesmentioning

confidence: 99%

Section: Modeling Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Improved DAE formulation for inverse dynamics simulation of cranes

Blajer

Kołodziejczyk

2010

Multibody Syst Dyn

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Inverse dynamics of underactuated mechanical systems: A simple case study and experimental verification

Blajer

Dziewiecki

Kołodziejczyk

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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Payload motion control of rotary gantry and luffing cranes using mechanical wave concepts

Habibi

O’Connor

2016

Transactions of the Institute of Measurement and Control

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A new solution is presented to the problem of controlling the motion of a crane's suspended load through arbitrarily complex, 3D paths through the crane's manoeuvre space. A generalized boom crane arrangement is considered, so that gantry and luffing arrangements are included as particular cases. Thus the crane's boom slews about a central, vertical (tower) axis. This boom is either a horizontal gantry with a trolley moving radially along it, from which the load can be winched, or a jib, which can rotate in the vertical plane, with the hoisting cable passing over a pulley attached at its end point. In either case, there are three directly controlled motion variables, the effects of which on the suspended payload's motion are strongly crosscoupled. The challenge is to enable the payload to follow the desired 3D path as closely as possible during the manoeuvre, and come to rest rapidly at target, by directly controlling these three actuating motions. Thus the controller must achieve position control combined with active swing suppression throughout the manoeuvre and on arrival at the desired end point. A model is developed of the generalized crane for both gantry and luffing crane types. The proposed control strategy is then applied and tested on this model. The controller is based on mechanical wave concepts. When applied to the model, it is shown to be very effective. It is accurate, robust to system changes and actuator limitations, very stable, requires sensing only at the trolley (and not at payload), and is easy to implement.

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A DAE Formulation for the Dynamic Analysis and Control Design of Cranes Executing Prescribed Motions of Payloads

Cited by 5 publications

References 20 publications

Improved DAE formulation for inverse dynamics simulation of cranes

Improved DAE formulation for inverse dynamics simulation of cranes

Inverse dynamics of underactuated mechanical systems: A simple case study and experimental verification

Payload motion control of rotary gantry and luffing cranes using mechanical wave concepts

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