“…These feedback parts can be of different type as, for instance: sliding mode (Sira-Ramı´rez 2000), based on Lyapunov stability theory (Chelouah et al 1996), backstepping (Martin et al 2000), H 1 or -analysis of the linearised system around the predicted trajectory (Cazaurang 1997), classic PID (Le´vine 1999), or extended PID (Hagenmeyer and Delaleau 2003b,c). The only condition is Ã(0) ¼ 0, which implies that the restriction of É Ã to ÁZ ¼ 0 is precisely equal to :…”
Section: Flat Systems Without Perturbationsmentioning
To cite this article: V. Hagenmeyer & E. Delaleau (2008) Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive exampleA general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.
“…These feedback parts can be of different type as, for instance: sliding mode (Sira-Ramı´rez 2000), based on Lyapunov stability theory (Chelouah et al 1996), backstepping (Martin et al 2000), H 1 or -analysis of the linearised system around the predicted trajectory (Cazaurang 1997), classic PID (Le´vine 1999), or extended PID (Hagenmeyer and Delaleau 2003b,c). The only condition is Ã(0) ¼ 0, which implies that the restriction of É Ã to ÁZ ¼ 0 is precisely equal to :…”
Section: Flat Systems Without Perturbationsmentioning
To cite this article: V. Hagenmeyer & E. Delaleau (2008) Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive exampleA general flatness-based framework for non-linear continuous-time predictive control is presented. It extends the results of Fliess and Marquez (2000) to the non-linear case. The mathematical setting, which is valid for multivariable systems, is provided by the theory of flatness-based exact feedforward linearisation introduced by the authors (Hagenmeyer and Delaleau 2003b). Thereby differential flatness does not only yield an easy calculation of the predicted trajectories considering the respective system constraints, but allows to use simple linear feedback parts in a two-degree-of-freedom control structure. Moreover, this formalism permits one to handle non-minimum phase systems, and furthermore to deal with parameter uncertainties and exogenous perturbations. Respective robustness analysis tools are available. Finally, an induction drive example is discussed in detail and experimental results for this fast electro-mechanical system are presented.
“…Thus, a feedforward signal will be applied such that the ICE reaches the angular velocityφ 1,ref =φ 2 from initial velocitẏ ϕ 1,0 within a given transition time T t . For the design of the feedforward control law, the differential flatness approach is applied [18][19][20][21][22][23][24] since it promises a straightforward design approach, especially for controllable linear systems. We will design a trajectory y f ,d for a flat output y f such that the resulting feedforward controller T sc,d (s) = G −1 ice Y f ,d (s) can be easily incorporated within current electronic control units.…”
Section: Flatness-based Feedforward Control For Synchronisationmentioning
In this article, a new drivetrain configuration of a parallel hybrid electric vehicle is considered and a novel model-based control design strategy is given. In particular, the control design covers the speed synchronisation task during a restart of the internal combustion engine. The proposed multivariable synchronisation strategy is based on feedforward and decoupled feedback controllers. The performance and the robustness properties of the closed-loop system are illustrated by nonlinear simulation results.
“…The modeling of this system has been undertaken in [8] which concludes to an implicit model. The dynamics of the load are given by…”
Section: Nonlinear Crane Modelmentioning
confidence: 99%
“…Section 2 recalls basic stability definitions and main theorems that assess this property. In Section 3, we recall from [8,9] the model of the crane used in this study. Then Section 4 gives the controller for equilibrium stabilization with its proof of stability.…”
Abstract:A simple output feedback PD controller is proposed that stabilizes a nonlinear crane. Global asymptotic stability is achieved at any equilibrium point specified by the controller. The control scheme relies solely on the winches position and velocity and hence no cable angle measurement, or no direct measurement of the load position, is needed. The controller can be extended to many different kinds of existing cranes.
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