Flatness based trajectory planning for a semi‐linear hyperbolic system of first order p.d.e. modeling a tubular reactor

Abstract

Trajectory planning and open loop control design for semi-linear hyperbolic systems in one space dimension is considered. A "flatness based" method is introduced on an example of a convection dominated tubular reactor with heat exchanger. More generally, the method applies to boundary value problems that can be translated into Cauchy problems w.r.t. the spatial coordinate.

Minimum time control of heterodirectional linear coupled hyperbolic PDEs

“…The generalization of this result to an arbitrary number m of controlled negative velocities is presented in [14]. There, the proposed control law yields finite-time convergence to zero, but the convergence time is larger than the minimum control time, derived in [17], [25]. This is due to the presence of nonlocal coupling terms in the targeted closed-loop behavior.…”

“…jean.auriol@mines-paristech.fr florent.di meglio@mines-paristech.fr time, derived in [17], [25]. This is due to the presence of nonlocal coupling terms in the targeted closed-loop behavior.…”

“…More precisely, a proposed boundary feedback law ensures finite-time convergence of all states to zero in minimum-time. This minimum-time, defined in [17], [25] is the sum of the two largest time of transport in each direction.…”

Output-feedback control of an underactuated network of interconnected hyperbolic PDE–ODE systems

“…For instance, the well-known PI controller has been extended in [5] to a chain of linear hyperbolic systems. Flatness-based analysis is used to design a state-feedback controller for hyperbolic PDEs networks in [6,7,8]. The dynamics of characteristic lines are studied in [9] to design an output feedback control law for semilinear hyperbolic systems interconnected in series.…”