Continuous-time non-linear flatness-based predictive control: an exact feedforward linearisation setting with an induction drive example

Abstract

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.

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“…Once the nominal T ¤ i in (23) are expressed in function of the reference trajectories F ¤ i ,the profile of F ¤ i can be tuned to drive the system as fast as possible from an initial position to a final one without hitting actuator constraints. This profile depends on the coefficients a i j of the reference trajectories which are defined as polynomial functions of fixed degrees in (22) and (23). The coefficients are in function of the initial and final conditions as well as t 0 and t f where the final time t f is the sole unknown parameter and thus, they can be obtained by determining t f .…”

&#x210B;<inf>&#x221E;</inf>-suboptimal tracking control for bilinear power systems with dynamic feedback - theory and experiment

“…As we have to consider the load disturbance τ d which enters (5) via (14), we usē τ (t) = τ l +τ d (t) in (10), whereτ d (t) would be the "reference load disturbance" which obviously is unknown in advance, but may be handled as in [17]. This yields…”

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“…This system is differential flat if there exists such a flat output vector z(t) ∈ R m that has the following properties [21][22][23]:…”

“…The concept of differential flatness has been exploited to design feedforward control schemes for nonlinear systems [22][23][24], which normally form a specific combination of a nominal feedforward input and a local feedback controller. In this paper, the differential flatness property is adopted in the receding horizon framework to facilitate the online optimisation.…”