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This paper compares three different sets of translation equations of motion for a space launcher. Two of these schemes, the Cartesian and the polar approaches, are widely used and the third one, the full quaternion approach has just been recently introduced. This paper does not present the mathematical development leading to each of them, but it compares the three schemes in terms of accuracy, robustness and computation time. The three schemes produce the exact same trajectory, but the polar one is the best suited for an onboard guidance algorithm as it is quicker to solve.

A main problem in controlling bioprocesses is the lack of manipulated variables. Batch and fed-batch processes do not allow the bioreactor to be drained of the (often) toxic waste substances produced by the biomass. A chemostat (CSTR) only has the dilution rate as the manipulated variable, which allows a certain control over the biomass concentration with a risk, however, of instability if the dilution rate gets higher than the maximum growth rate. Perfusion processes with full biomass retention are somewhat similar to batches, as no steady-state is really obtained until biomass growth is stopped by nutrient limitations. Cell bleed is often used in perfusion processes to improve viability and prevent accumulation of dead cells. However, the idea of using the cell bleed stream as a manipulated variable for control has not previously been studied for perfusion systems. We propose here a control strategy with three degrees of freedom that can be used to control the reactor level, biomass concentration, and a metabolite concentration. In the end, we shall address that controlling these concentrations could be the key to metabolic flux-based optimizations in bioreactors., 4th International Conference on Engineering Applications and Computational Algorithms (DCDIS Conference 2005), July 27-29, 2005, Guelph, Ontario, Canada