Suboptimal Control Strategies Applied to Nonlinear Batch Reactor with Constraints

PABLO S. RIVADENEIRA; EDUARDO J. ADAM

Rosario

Congreso; RPIC 2009 - XIII Reunión de Trabajo para el procesamiento de la Información y Control; 2009

Universidad de Rosario - RPIC

This work studies the control of a semibatch reactor for theproduction of penicillin. For this purpose, it is proposed an initial designof two control strategies which result simple for their implementation.These strategies are developed inside the optimal control framework appliedto non-linear systems. The first one, based on finite horizon optimalcontrol theory, minimizes a quadratic cost derived from the linearapproximation of the co-states from the Hamiltonian associated to thesystem. The resulting suboptimal law is a proportional law and, due to theoffset produced for this controller, an integral mode is incorporated as anew state. As a consequence, the controlled output is feedback.The second strategy use linear matrix inequalities (LMIs) for incorporatingrestrictions which were not considered in the value function of the optimalcontrol problem. The new restrictions are boundaries for the states and themanipulated variable. However, the design of this strategy is restricted toan infinite horizon optimal control problem and, the proportional-integral(PI) modes resulting have constant gains. Finally, the goodness of the twoproposed strategies is showed through numerical simulations.