Increased cycle time achieved by fractional derivatives in the adaptive control of the Brusselator model

In the control of chemical reactions the goal is to stabilize the control and take care of the design that has to integrate engineering aspects, as restrictions concerning the control signals, and the phenomenological limits that are not necessarily expressed by the reaction kinetic equations (e.g. no negative concentrations can be physically interpreted, and the reactants at the side of ingress cannot be purely extracted from the stirring tank reactor). In this paper the Robust Fixed Point Transformation (RFPT)-based adaptive approach was chosen for the control of an approximately modeled Brusselator reaction. The main reason of that was the fact that this methodology concentrates on the primary design goals as precise realization of the prescribed concentrations while the more conventional design methods that apply some Lyapunov function mainly concentrate on guaranteeing global stability without providing quasi-optimal solutions for the primary goals. Though the RFPT-based design has only local stability, its region of stability may be quite satisfactory for several practical applications. For controlling chemical reactions Continues Stirring Tank Reactors (CSTR) are widely used engines. The Busselator model will be represented in a CSTR in the simulations. In the present example two different reactants can be injected into the tank and the mixture is taken out in a single outlet. The necessary sampling frequency is a practically important design factor. It is shown that by the use of fractional order derivatives in the prescribed error relaxation considerably increases the necessary sampling time so it decreases the sampling frequency. This statement is substantiated by simulation results.