On the control of an unstable periodic state in the repeated fed-batch operation of a biochemical system

In this paper we discuss the proportional feedback control of a repeated fe d-batch reactor around a desired but unstable periodic state. The flow rate in each cycle is assumed to be a constant. The unstable periodic state is determined using a shooting method technique and its stability is found usi ng the Floquet theory. The control action is based on the performance, i.e. , biomass concentration, at the end of the cycle. Two choices of the manipu lated variable are investigated, i.e., the cycle time and the flow rate. Th e concentration of the substrate in the feed is assumed to be a constant.