On necessary and sufficient conditions for differential flatness

Lévine, Jean

doi:10.1007/s00200-010-0137-x

Cited by 163 publications

(129 citation statements)

References 48 publications

Supporting

Mentioning

124

Contrasting

Unclassified

Order By: Relevance

“…where τ cm is the mechanical input torque, τ cp is the load torque [10] (16) where k t , R cm and k v are motor constants, η cm is a coefficient that denotes the motor's mechanical efficiency. C p is the specific heat capacity of air and W cp is the compressor mass flow rate.…”

Section: Nonlinear Dynamics Of Pem Fuel Cellsmentioning

confidence: 99%

“…First it is proven that the dynamic model of the fuel cells is a differentially flat one. This means that all its state variables and its control inputs can be expressed as differential functions of a primary variable which is the so-called flat output [14][15][16][17][18]. Differential (linear) independence is another property that holds between the flat output and its derivatives.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A PEM Fuel Cells Control Approach Based on Differential Flatness Theory

et al. 2016

View full text Add to dashboard Cite

The article presents an approach to nonlinear control of fuel cells using differential flatness theory and Kalman filtering. First, it is proven that the dynamic model of fuel cells is a differentially flat one which means that all its state variables and control inputs can be expressed as differential functions of specific stare variables which are the so-called flat outputs of the system. By exploiting the differential flatness properties of the model its transformation to an equivalent linear form (canonical Brunovsky form) becomes possible. For the latter description of the system's dynamics the design of a state-feedback controller is achieved. This control scheme should be also robust to model uncertainties and external perturbations. To cope with this problem the state-space description of the PEM fuel cells is extended by considering as additional state variables the derivatives of the aggregate disturbance input. Next, a Kalman filter-based disturbance observer is applied to the linearized extended model of the fuel cells. This estimation method enables to identify the disturbance and model uncertainty terms that affect the system and to introduce a complementary control element that compensates for the perturbations' effects. The efficiency of the proposed control scheme is evaluated through simulation experiments.B G. Rigatos

show abstract

Section: Nonlinear Dynamics Of Pem Fuel Cellsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A PEM Fuel Cells Control Approach Based on Differential Flatness Theory

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Next,the differential flatness properties of this model are proven using as flat output the rotation angle of the motor. Differential flatness means that all state variables and the control input of the system can be expressed as functions of the flat output and its derivatives [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

et al. 2016

View full text Add to dashboard Cite

The article proposes a method for nonlinear control of the dynamical system that is formed by a DC-DC converter and a DC motor, making use of differential flatness theory. First it is proven that the aforementioned system is differentially flat which means that all its state vector elements and its control inputs can be expressed as differential functions of primary state variables which are defined to be the system's flat outputs. By exploiting the differential flatness properties of the model its transformation to a linearized canonical (Brunovsky) form becomes possible. For the latter description of the system one can design a stabilizing feedback controller. Moreover, estimation of the nonmeasurable state vector elements of the system is achieved by applying a new nonlinear Filtering method which is known as Derivative-free nonlinear Kalman Filter. This filter consists of the Kalman Filter recursion applied on the linearized equivalent model of the system and of an inverse transformation that is based on differential flatness theory and which enables to obtain estimates of the initial nonlinear state-space model. Moreover, to compensate for parametric uncertainties and external perturbations the filter is redesigned as a disturbance observer. By estimating the perturbation inputs that affect the joint model of the DC-DC converter and of the DC motor their compensation becomes possible. The efficiency of the proposed control scheme is further confirmed through simulation experiments.

show abstract

“…Next it is shown that the system of the nonlinear ODEs is a differentially flat one. This means that all its state variables and the control inputs can be written as differential functions of one single algebraic variable which is the flat output [31][32][33][34][35][36]. Actually, by examining independently each nonlinear ODE it is shown that this stands again for a differentially flat system, for which a virtual control input can be computed as in the case of flatness-based control for the trivial system.…”

Section: Introductionmentioning

confidence: 99%

Differential Flatness Properties and Feedback Control of the Fokker–Planck PDE

2016

View full text Add to dashboard Cite

The Fokker-Planck PDE describes the dynamics of several biochemical and biological processes, as well as of phenomena at molecular scale. In this paper, the problem of feedback control of the Fokker-Planck PDE is studied. It is shown that the procedure for numerical solution of Fokker-Planck PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Fokker-Planck PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the Fokker-Planck PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem's dynamics and can eliminate the subsystem's tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the Fokker-Planck PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the Fokker-Planck PDE system so as to assure that all its state variables will converge to the desirable setpoints.

show abstract

On necessary and sufficient conditions for differential flatness

Cited by 163 publications

References 48 publications

A PEM Fuel Cells Control Approach Based on Differential Flatness Theory

A PEM Fuel Cells Control Approach Based on Differential Flatness Theory

Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

Differential Flatness Properties and Feedback Control of the Fokker–Planck PDE

Contact Info

Product

Resources

About