Discrete-time flatness-based control of a gantry crane

Diwold, Johannes; Kolar, Bernd; Schöberl, Markus

doi:10.1016/j.conengprac.2021.104980

Cited by 13 publications

(6 citation statements)

References 17 publications

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“…The aim of this method is to generate a reference trajectory for the cart in order to achieve the payload positioning without sway [80]. This is mainly an openloop technique that can be combined with some closed-loop controllers [306,124,65]. Before explaining this topic, it should be noted that the desired trajectory is normally defined for the payload and not for the cart.…”

Section: Flatness Theorymentioning

confidence: 99%

Modeling and control of overhead cranes: A tutorial overview and perspectives

Mojallizadeh

Brogliato

Prieur

2023

Annual Reviews in Control

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Section: Flatness Theorymentioning

confidence: 99%

Modeling and control of overhead cranes: A tutorial overview and perspectives

Mojallizadeh

Brogliato

Prieur

2023

Annual Reviews in Control

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“…Since for practically relevant flat systems like e.g. the gantry crane, the VTOL aircraft, or the induction motor (see Diwold et al (2022a) or Diwold et al (2022b)) the corresponding equations would become rather extensive, for demonstrational purposes we use the simple academic example…”

Section: A Flat Systemmentioning

confidence: 99%

Discrete-time Flatness and Linearization along Trajectories

Kolar¹,

Diwold²,

Gstöttner³

et al. 2022

Preprint

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The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time case, where it is well-known that the linearization of flat systems along trajectories results in linear time-varying systems which are again flat. Since flatness implies controllability, this constitutes an important verifiable necessary condition for flatness. In the present contribution, it is shown that this is also true in the discretetime case: We prove that the linearized system is again flat, and that a possible flat output is given by the linearization of a flat output of the nonlinear system. Analogously, the map that describes the parameterization of the system variables of the linear system by this flat output coincides with the linearization of the corresponding map of the nonlinear system. The results are illustrated by two examples.

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“…One solution would be to implement Φ x as an analytically invertible neural network, but this restricts the approach to invertible activation functions, constant number of units in each layer n l , and to the input-state linearizable scenario with dim(x k ) = dim(z k ). Although this does not contradict the imposed assumptions, the planned extension of this data-driven control approach to flat systems in the discrete-time case, c.f., [3] and [4], would not be possible. Therefore, Φ x and Φ u as well as Φ −1…”

Section: Neural Canonical Control Structuresmentioning

confidence: 99%

A data-driven approach for the identification of nonlinear state-dependent switched systems using expectation-maximization

Ecker

Schöberl

2022

2022 17th International Conference on Control, Automation, Robotics and Vision (ICARCV)

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An indirect data-driven control and transfer learning approach based on a data-driven feedback linearization with neural canonical control structures is proposed. An artificial neural network auto-encoder structure trained on recorded sensor data is used to approximate state and input transformations for the identification of the sampleddata system in Brunovsky canonical form. The identified transformations, together with a designed trajectory controller, can be transferred to a system with varied parameters, where the neural network weights are adapted using newly collected recordings. The proposed approach is demonstrated using an academic and an industrially motivated example.

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Discrete-time flatness-based control of a gantry crane

Cited by 13 publications

References 17 publications

Modeling and control of overhead cranes: A tutorial overview and perspectives

Modeling and control of overhead cranes: A tutorial overview and perspectives

Discrete-time Flatness and Linearization along Trajectories

A data-driven approach for the identification of nonlinear state-dependent switched systems using expectation-maximization

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