Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems

Lynch, Alan F.; Rudolph, Joachim

doi:10.1080/00207170210163640

Cited by 109 publications

(97 citation statements)

References 14 publications

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“…Under certain conditions on the growth of the time-derivatives of the prescribed flat output y * (t) (defined by its so-called Gevrey-class) and given a suitable set of system parameters p 0 , p 1 , q 0 , q 1 , ν, r 0 , and r 1 , it can be shown that the control input u * (t) converges for N → ∞ to a suitable control input for the DCRS (1)-(3), see, e. g., [10,19].…”

Section: Flatness-based State and Input Parametrizationmentioning

confidence: 99%

“…The temporal path of the transition can be provided either by a polynomial of suitable order or, especially with regard to the continuous limit of the parametrization, by any smooth function of an appropriate Gevrey-class, see, e. g., [10].…”

Section: Simulation Examplementioning

confidence: 99%

“…The flatness property allows for a parametrization of the state and input in terms of a so-called flat output and its time derivatives and therefore provides a systematic approach for feedforward control design. Originally proposed for finitedimensional systems, generalizations of the flatness concept have been successfully carried over to certain classes of PDEs, see, e. g., [7,10,12]. In these so-called late lumping approaches the parametrization is directly solved for the underlying PDE.…”

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confidence: 99%

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Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

Utz

Graichen

Kugi

2013

IFIP Advances in Information and Communication Technology

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Abstract. The tracking control design for setpoint transitions of a quasi-linear diffusion-convection-reaction system with boundary control is considered. For this a suitable model-based feedforward control is determined that relies on the flatness-based parametrization of the control input. A receding horizon feedback control is added within a two-degreesof-freedom control scheme to account for disturbances, model inaccuracies, and input constraints. The tracking performance of this control scheme is shown by means of simulation studies.A large class of chemical reactors with an interaction of diffusive, convective, and reactive effects leads to infinite-dimensional mathematical models in the form of nonlinear boundary-controlled parabolic partial differential equations (PDEs) [6]. The control design for setpoint transitions of chemical reactors, e. g., for ignition, extinction, or grade-transitions constitutes a challenging problem. In this contribution, the well-known two-degrees-of-freedom (2DOF) control scheme is applied in order to tackle this control task. The basic idea consists in first designing a feedforward control to steer the system along prescribed trajectories. The trajectory planning and feedforward control are complemented with a state feedback tracking control stabilizing the system about the desired trajectories.In the literature, there exists a variety of concepts for the design of both feedforward and feedback tracking controllers. For the feedforward control design, approaches using the flatness concept [2] have found widespread attention. The flatness property allows for a parametrization of the state and input in terms of a so-called flat output and its time derivatives and therefore provides a systematic approach for feedforward control design. Originally proposed for finitedimensional systems, generalizations of the flatness concept have been successfully carried over to certain classes of PDEs, see, e. g., [7,10,12]. In these so-called late lumping approaches the parametrization is directly solved for the underlying PDE. In contrast, the early lumping approach to control design is based on a

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Section: Flatness-based State and Input Parametrizationmentioning

confidence: 99%

Section: Simulation Examplementioning

confidence: 99%

mentioning

confidence: 99%

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Combined Feedforward/Model Predictive Tracking Control Design for Nonlinear Diffusion-Convection-Reaction-Systems

Utz

Graichen

Kugi

2013

IFIP Advances in Information and Communication Technology

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“…The length of the pipe is denoted by L. The state of this distributed parameter system is described at each time t by the function {T (z, t), 0 ≤ z ≤ L}. The dynamic planning problem consists (Lynch and Rudolph, 2002) of finding a control law (in the form of a time profile for u) driving the state between two states within the reachable set of the model.…”

Section: Introductionmentioning

confidence: 99%

“…Flatness based control design for distributed parameter systems is a subject of growing interest (Rouchon, 2001;Rudolph et al, 2003). In (Lynch, 2002) the problem is considered for quasilinear parabolic systems. A major difference with respect to the problem considered in this paper consists in the fact that, while most works refer to boundary control, here the manipulated variable is a flow.…”

Section: Introductionmentioning

confidence: 99%

Dynamic motion planning of a distributed collector solar field

Igreja¹,

Lemos²,

Rouchon³

et al. 2004

IFAC Proceedings Volumes

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This paper is concerned with motion planing for distributed collector solar fields. The problem consists in selecting the time profile of the manipulated variable (oil flow) such that the state (temperature distribution along the field) is driven from one value to another as specified. The problem is solved by using the methods of flat systems and a change of the time variable. Two solutions are provided, one directly for the distributed parameter model and another for a lumped parameter model resulting from space sampling of the distributed model.

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