Feedforward and Feedback Tracking Control of Diffusion-Convection-Reaction Systems using Summability Methods

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

“…Furthermore, a shorter prediction horizon t f = 0.1 is considered for the receding horizon controller. This could be motivated by the need to reduce the computational cost for the solution of the OCP (12). It can be observed on the one hand that with the prediction horizon t f = 0.3, the receding horizon control carries out the transition within a transition time comparable to the one observed for the 2DOF control scheme.…”

“…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.…”

“…For the design of such stabilizing feedback controllers for infinite-dimensional systems, receding horizon optimal control, e. g., [9,15], constitutes a promising tool. This method is particularly attractive since it provides, in contrast to most state-of-the-art tracking control design methods for DCRSs, see, e. g., [12,13], the possibility to systematically include constraints as they are frequently encountered in technical systems.…”

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

“…The second inequality in (10) is trivial. After this preparatory discussion one may apply the following fixed-point theorem borrowed from [9] to obtain the desired result on existence and uniqueness of the solution of (5). …”

“…By contrast, available results for the nonlinear case almost exclusively apply to parabolic equations: As in the linear case, a new variablea flat output -is introduced in such a way that the boundary value problem reduces to a Cauchy problem with data on the time axis. Assuming the flat output trajectory, i.e., the Cauchy data, to be chosen from an appropriate space of smooth functions this problem can be solved using power series expansions and related techniques (see, e.g., [4][5][6]). Finally, the trajectory of the control variable can be read off from the boundary conditions.…”