Conditions for the existence of a flat input

Waldherr, Steffen; Zeitz, Μ.

doi:10.1080/00207170701561443

Cited by 36 publications

(50 citation statements)

References 15 publications

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“…Consequently, it would be of great benefit to eliminate the numerical integration step. Here, the concept of flat inputs [Waldherr and Zeitz (2008)] comes into play. The main idea is to transform the DDE system (Eq.…”

Section: Flat Inputs For Parameter Identificationmentioning

confidence: 99%

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Parameter Identification Of Time-Delay Systems: A Flatness Based Approach

Schenkendorf

Reichl

Mangold

2012

IFAC Proceedings Volumes

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The use of mathematical models is widely established in various fields of application. To name but a few of their major applications, mathematical models can improve the controller design of complex technical systems or are able to facilitate the understanding of highly complex biochemical systems. No matter what mathematical models are used for, however, they fail to perform the intended task if they are badly parameterized. In general, during the process of parameterization one tries to make differences between simulation results and measurement data as small as possible. Under the assumption of a suitable model candidate this is done by choosing optimal model parameters. Unfortunately, the majority of used models cannot be solved analytically. For example, many dynamical processes are described by systems of ordinary differential equations (ODEs). Usually, analytical solutions do not exist. Although quite efficient numerical routines are available they usually slow down the parameterization process dramatically. The situation is even more demanding if one has to deal with processes that are described by delay differential equations (DDEs). Commonly, standard DDE solvers show a lack of efficiency as well as of robustness, i.e., they are likely to fail to solve the underlying DDE system. Consequently, it would be of great benefit to eliminate any need of numerical ODE/DDE solvers. Here, the concept of flat inputs comes into play. The key aspect is to transform the DDE system into an algebraic input/output representation, i.e., the inputs of the system are expressed analytically by the outputs and derivatives thereof. Now, the objective of parameterization is to minimize differences between these flat inputs and the physical inputs of the related process. As no numerical DDE solver is involved there is a significant speedup of the parameter identification step. In addition, the presented approach is closely linked to optimal experimental design for parameter identification. In particular, the reformulation of the cost function also affects parameter sensitivities. Using the same measurement data it is possible that previously insensitive model parameters become sensitive. To check this, global parameter sensitivities are determined by Sobol' Indices of first order. All results are demonstrated for the example of a mathematical model of the influenza A virus production.

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Section: Flat Inputs For Parameter Identificationmentioning

confidence: 99%

“…In fact, a necessary and sufficient condition for the existence of a flat input is only available for ODE systems with single input and single output [Waldherr and Zeitz (2008)]. For the more complex case of multiple inputs and multiple outputs no conditions at all are on hand currently [Waldherr and Zeitz (2010)].…”

Section: Determination Of Flat Inputsmentioning

confidence: 99%

Parameter Identification Of Time-Delay Systems: A Flatness Based Approach

Schenkendorf

Reichl

Mangold

2012

IFAC Proceedings Volumes

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“…Other techniques include: active control (Njah and Vincent 2008), adaptive control (Tang 2008), backstepping design (Peng and Chen 2008), flatness-based control (Marquez and Sira-Ramirez 1995) and sliding mode control (Yan, Hung, and Liao 2006) among others. The induction of the differential flatness property on Chua's circuit, via the prescription of an appropriate flat input channel (Waldherr and Zeitz 2008), allows for the trivialisation of the controller design task reducing the feedback control problem to that of a linear controllable time-invariant system. The original introduction of the flatness concept is due to (Fliess, Le´vine, Martin, and Rouchon 1995).…”

Section: Introductionmentioning

confidence: 99%

Flatness-based linear output feedback control for disturbance rejection and tracking tasks on a Chua's circuit

Sira‐Ramírez

Luviano‐Juárez

Cortés‐Romero

2012

International Journal of Control

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“…Recently, a new approach to solve the problem of a non-flat output has been proposed. The concept of flat inputs represents a dual approach to flat outputs [7]. Here, the control input and input vector field of the system are replaced such that the given output becomes the flat output.…”

Section: Introductionmentioning

confidence: 99%

Trajectory tracking control with flat inputs and a dynamic compensator

Stumper

Svaricek

Kennel

2009

2009 European Control Conference (ECC)

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This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output may be a non-flat output, or the system may be non-flat. The method is applicable to observable systems with stable internal dynamics. The performance of the new design is demonstrated on the variable-length pendulum, a non-flat nonlinear system with a singularity in the relative degree.This work was done at

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Conditions for the existence of a flat input

Cited by 36 publications

References 15 publications

Parameter Identification Of Time-Delay Systems: A Flatness Based Approach

Parameter Identification Of Time-Delay Systems: A Flatness Based Approach

Flatness-based linear output feedback control for disturbance rejection and tracking tasks on a Chua's circuit

Trajectory tracking control with flat inputs and a dynamic compensator

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