On a generalized flat input definition and physical realizability

Fritzsche, Klemens; Röbenack, Klaus

doi:10.1016/j.ifacol.2020.12.1661

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…We do not need this general notion since, in our study, all functions

φ_{i}

depend on the state x only and singularities depend on x and/or u (but never on derivatives of u ). We send the reader to Reference 18, where a generalized definition of flat inputs is proposed that allows affine injections of the input and its derivatives in both the dynamics and the output equation.…”

Section: Definitions and Notationsmentioning

confidence: 99%

How to minimally modify a dynamical system when constructing flat inputs?

Nicolau

Respondek

Barbot

2021

Intl J Robust & Nonlinear

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In this paper, we study the problem of constructing flat inputs for multi-output dynamical systems, in particular, we address the issue of the minimal modification of the initial dynamical system (the measure of modification being the number of equations that have to be changed by adding flat inputs). We show that in the observable case, control vector fields that distort m equations only (where m is the number of measurements) can always be constructed (and this is the minimal possible number of equations that have to be modified by adding flat inputs), while in the unobservable case, the best that we can hope for is that m + 1 equations only are modified such that they involve flat inputs. We discuss when the original output is a flat output of minimal possible differential weight for the minimally modified control system (where by the differential weight, we mean the minimal number of derivatives of components of a flat output needed to express all states and controls). We propose a solution for constructing flat inputs leading to a minimally modified control system consistent with the minimal differential weight and, moreover, for which the observable part is affected by the minimal possible number of controls (this last property being important in applications). We show that, in that case, at least 2m − 1 equations have to be affected by the flat inputs.

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“…We do not need this general notion since, in our study, all functions

φ_{i}

Section: Definitions and Notationsmentioning

confidence: 99%

How to minimally modify a dynamical system when constructing flat inputs?

Nicolau

Respondek

Barbot

2021

Intl J Robust & Nonlinear

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“…u [q−r] . Therefore, the definition given in [3] where u and its derivatives are allowed to enter affinely only is not general enough.…”

Section: Examplementioning

confidence: 99%

“…However, flat input injection into the derivative array of the state space system structurally prevents a transformation back to a higher order system, and thus, obstructs so-called physical realizability. This problem can be solved using a generalized flat input definition [3] which we propose an algorithm for.…”

Section: Introductionmentioning

confidence: 99%

On the computation of physically realizable generalized flat inputs for nonlinear single‐output systems from a geometric point of view

Fritzsche

Guo

Röbenack

2021

Proc Appl Math & Mech

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Physical realizability is a structural property of (classical) flat inputs for state space systems which originate from higher order differential equations. These state space systems contain a derivative array, i.e., an integrator chain. Flat input injections into this array, however, structurally prevents from the reversal of the order reduction. Using a generalized flat input definition, we demonstrate how physical realizability can be achieved.

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“…Despite its significance and a large research effort [20]- [25], to date rather important questions regarding the existence and the computation of flat outputs have not been answered. Motivated by the question of ideal actuator placement, flat inputs have been introduced as a dual concept to flat outputs [26], [27] and the computation has been investigated [28]- [31]. Although, flat inputs have turned out to be valuable for control problems [32], [33], too, naturally one would assume that they play a role in state estimation.…”

Section: Introductionmentioning

confidence: 99%

Flat input based canonical form observers for non-integrable nonlinear systems

Fritzsche

Röbenack

Guo

2022

Syst. Theor. Control Comput. J.

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In this contribution, the design of canonical form observers for nonlinear non-integrable systems is investigated. These systems cannot be transformed into observer canonical form, therefore an exact observer error linearization cannot be achieved. However, using flat inputs and dynamic compensators, the original dynamics can be rendered into an integrable flat system. For this modified flat input system a canonical form observer can be designed. By utilizing a state transformation, it is then possible to obtain an estimate of the original state, where the observer error is approximately linearized. This procedure is exemplified by the Rössler system. Furthermore, we illustrate the relationship of this approach with high-gain observers.

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On a generalized flat input definition and physical realizability

Cited by 5 publications

References 19 publications

How to minimally modify a dynamical system when constructing flat inputs?

How to minimally modify a dynamical system when constructing flat inputs?

On the computation of physically realizable generalized flat inputs for nonlinear single‐output systems from a geometric point of view

Flat input based canonical form observers for non-integrable nonlinear systems

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