Nonlinear Fed-batch Reactor Pi Control with Constraints

This work studies the control of a fed-batch reactor for the production of penicillin and the design of suboptimal control strategies which result simple for their implementation. These strategies are able to (i) generate a suboptimal control that lead to the batch process towards its desired outputs, (ii) attenuate perturbations and noises always present in the operation of the process and, (iii) handle constraints upon the manipulated or control variable u(t). The control strategy always result a linear feedback, since proper assumptions on the costates of the nonlinear and Hamiltonian system are made, besides it is shown that this feedback law is a simple PI that actualize its suboptimal parameters ‘on-line’. Inside this scheme, basically, two strategies are designed. The former minimizes a quadratic cost plus a final (also quadratic) penalty on the states in a finite horizon fashion. The latter use linear matrix inequalities (LMIs) for incorporating constraints which were not considered in the value function of the first optimal control problem. Finally, the goodness of the proposed strategies is showed through numerical simulations.