Search

This communication presents a longitudinal model-free control approach for computing the wheel torque command to be applied on a vehicle. This setting enables us to overcome the problem of unknown vehicle parameters for generating a suitable control law. An important parameter in this control setting is made time-varying for ensuring finite-time stability. Several convincing computer simulations are displayed and discussed. Overshoots become therefore smaller. The driving comfort is increased and the robustness to time-delays is improved.

This communication is devoted to a “practical” comparison between high-order sliding modes and the recently introduced model-free control. The perfect knowledge of the relative degree of the output variable, which is a standard assumption for sliding modes, is assumed here. Our comparisons are based on two concrete case-studies and on numerous computer simulations. The smoothness of the input variables, the robustness with respect to noises and the straightforward extendibility of the model-free controllers to MIMO systems are highlighted.

This paper simplifies several aspects of the practical implementation of the newly introduced model-freecontrol and of the corresponding intelligentPID controllers (M. Fliess, C. Join, “Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control?,” 15thIFAC Symp. System Identif, Saint-Malo, 2009). Four examples with their computer simulations permit to test our techniques.

This paper deals with real time and possibly closed loop identification of delay systems. It is based on non-asymptotic algebraic estimation techniques initiated in (Fliess M., 2003). Numerical simulations with noisy data are provided.

We derive PID-like regulators utilizing flatness-based predictive control (M. Fliess and R. Marquez, 2000, Continuous-time linear predictive control and flatness: a module-theoretic setting with examples, vol. 73, 606-623), generalized PI controllers (M. Fliess, R. Marquez, E. Delaleau, and H. Sira-Ramirez, 2001, Correcteurs proportionnels-intégraux généralisés, ESAIM: Control, Optimisation, and Calculus of Variations) and a kind of predictors which are reminiscent of Smith predictors. Our formalism is analogous to the two-sided Laplace transform.

Two important control schemes, PID and Model Predictive Control, are analyzed. Their respective characteristics are combined to propose a PID strategy based on predicted system trajectories. It is shown that predicted input and output trajectories can be easily generated using the flat outputs of the system. Our approach is illustrated by two examples, a simple DC motor and an identified cement mill model.

R.E. Kalman introduced the concept of controllability for finite-dimensional linear systems at the beginning of the sixties. It has played since then a key role. A vast literature has been devoted to various extensions to nonlinear and infinite-dimensional systems. We first interpret Kalman's controllability in a new module-theoretic language, which is independent of any distinction between the system variables. Its nonlinear extension leads to the notion of differentially flat systems, which were introduced in 1992 by J. Lévine, P. Martin, P. Rouchon, and the author. They permit a straightforward trajectory tracking, which has been illustrated by numerous applications. In 1995 H. Mounier worked out the case of linear delay systems and discovered a new type of controllability which is verified by most realistic case-studies. We will conclude with some examples of systems governed by partial differential equations, which were recently studied by H. Mounier, P. Rouchon, J. Rudolph, and the author.

The motion planning and the synthesis of a tracking controller of a flexible robot arm is studied in an algebraic framework using Mikusiński's operational calculus. Experimental results are reported.

A module-theoretic approach to linear controllability is shown to be equivalent to Willems' trajectory characterization. We also sketch a computational-free derivation of Brunovsky's canonical form and show how to relate the notion of numerical state-space to our algebraic standpoint.

The controllability of linear delay differential systems is attacked via module theory. Many of the notions which have been proposed in the literature are interpreted and compared via a change of the ground ring. New definitions are also suggested which, as demonstrated by several case studies, turn out to be often encountered in practice.

In engineering, as well as in physics, one often encounters implicit systems of ordinary differential equations of the form Fi(ẏ1…ẏm, y1…ym) = 0, i = 1,…, m, in the unknowns y1…ym, where the Jacobian matrix (∂Fi/∂ẏj)i,jis identically singular. We first state a condition under which the above equation may be solved. Then, we give a decomposition, which provides as a byproduct a clear-cut definition of the index. Since the Fi's must be differentiated an arbitrary number of times, we employ tools stemming from the differential geometry of infinite jets and prolongations like Lie-Bäcklund morphisms.

Tensoring the module of a linear system with the quotient field of the ring of linear differential operators yields an algebraic framework where transfer matrices most naturally appear and which easily applies to the time-varying case. Several basic structural properties are examined : transfer algebra, matrix fraction decompositions and their connections with controllability and observability, realization, input-output inversion, model-matching.