Two new dimensionless parameters (Phi and Omega) are proposed for calculating the proportional, integral, and derivative constants of a dissolved oxygen proportional integral-derivative (PID) feed-back control algorithm from knowledge of the growth rate, bioreactor design and operation variables. The values of Phi and Omega were determined for a broad range of Reynolds numbers (between 1000 to 40 000) during the exponential growth phase of two highly different processes: fermentations of recombinant Escherichia coli and cultures of human hematopoietic cells. The utility of Phi and Omega for use in dissolved oxygen self-tunning adaptive control algorithms is discussed.