A Trajectory-Based Approach to Discrete-Time Flatness

Diwold, Johannes; Kolar, Bernd; Schöberl, Markus

doi:10.1109/lcsys.2021.3071177

Cited by 20 publications

(28 citation statements)

References 10 publications

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“…which is common in the discrete-time literature and necessary for accessibility. Like in Diwold et al (2022b), we call a discrete-time system (1) flat if there exists a oneto-one correspondence between its solutions (x(k), u(k)) and solutions y(k) of a trivial system (arbitrary trajectories that need not satisfy any difference equation) with the same number of inputs. Before we state a more rigorous definition of discrete-time flatness, let us consider the coupling of the trajectories x(k) and u(k) by the system equations (1).…”

Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

“…Definition 3.1. (Diwold et al (2022b)) The system (1) is said to be flat around an equilibrium (x 0 , u 0 ), if the n + m coordinate functions x and u can be expressed locally by an m-tuple of functions…”

Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

“…, dδ R (ϕ)} which we shall use later. The uniqueness of the map ( 9) is a consequence of the fact that all forwardand backward-shifts of a flat output are functionally independent, see Diwold et al (2022b). Furthermore, the rows of the Jacobian matrix of the right-hand side of (9) with respect to y [0,R] are linearly independent, i.e., the map (9) is a submersion.…”

Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

“…The second approach is based on the one-to-one correspondence of the system trajectories to the trajectories of a trivial system. In contrast to the first approach, in this case the flat output may also depend on backward-shifts of the system variables, see Diwold, Kolar, and Schöberl (2022b) or Guillot and Millérioux (2020). Since it is more general, within the present paper we consider the second approach, and refer to the first one, which is included as a special case, as forward-flatness.…”

Section: Introductionmentioning

confidence: 99%

“…In Diwold et al (2022b), it has been shown that flat discrete-time systems can be exactly linearized by a dynamic feedback in such a way that the new input of the closed-loop system corresponds to the highest forward-shifts of the flat output that appear in the parameterization of the system variables. Similarly, in the continuous-time case it is always possible to perform an exact linearization such that the new input corresponds to the highest time derivatives of the flat output that appear in the parameterization of the system variables, see e.g.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the Exact Linearization and Control of Flat Discrete-time Systems

Kolar¹,

Diwold²,

Gstöttner³

et al. 2022

Preprint

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The paper addresses the exact linearization of flat nonlinear discrete-time systems. Two main questions are investigated: The first one is how to determine which forward-shifts of a given flat output can be chosen in principle as a new input, and the second one is how to actually introduce this new input by a suitable feedback. With respect to the choice of a feasible input, easily verifiable conditions are derived. Introducing such a new input requires a feedback which may in general depend not only on this new input itself but also on its forward-shifts. Hence, there occur similarities to the class of quasi-static feedbacks, which have already proven to be useful for the exact linearization of flat systems in the continuous-time case. For systems with a flat output that does not depend on forward-shifts of the input, it is shown how to systematically construct a new input such that the total number of the corresponding forward-shifts of the flat output is minimal. Furthermore, it is shown that in this case the calculation of a linearizing feedback is particularly simple, and the subsequent design of a discrete-time flatness-based tracking control is discussed. The presented theory is illustrated by the discretized models of a wheeled mobile robot and a 3DOF helicopter.

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Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

Section: Discrete-time Systems and Flatnessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Exact Linearization and Control of Flat Discrete-time Systems

Kolar¹,

Diwold²,

Gstöttner³

et al. 2022

Preprint

Self Cite

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Dynamic Tactile Synthetic Tissue: from Soft Robotics to Hybrid Surgical Simulators

Thurner,

Maier,

Kaltenbrunner

et al. 2024

Advanced Intelligent Systems

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Surgical simulators are valuable educational tools for physicians, enhancing their proficiency and improving patient safety. However, they typically still suffer from a lack of realism as they do not emulate dynamic tissue biomechanics haptically and fail to convincingly mimic real‐time physiological reactions. This study presents a dynamic tactile synthetic tissue, integrating both sensory and actuatory capabilities within a fully soft unit, as a core component for soft robotics and future hybrid surgical simulators utilizing dynamic physical phantoms. The adaptive surface of the tissue replica, actuated via hydraulics, is assessed by an embedded carbon black silicone sensor layer using electrical impedance tomography to determine internally or externally induced deformations. The integrated fluid chambers enable pressure and force measurements. The combination of these principles enables real‐time tissue feedback as well as closed loop operation, allowing optimal interaction with the environment. Based on the concepts of soft robotics, such artificial tissues find broad applicability, demonstrated via a soft gripper and surgical simulation applications including a dynamic, artificial brain phantom as well as a synthetic, beating heart. These advancements pave the way toward enhanced realism in surgical simulators including reliable performance evaluation and bear the potential to transform the future of surgical training methodologies.

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