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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.

Flotation is multivariable process exhibiting uncertain and nonlinear dynamics as well as being perturbed by unmeasured disturbances. Optimization of this process is therefore a complex undertaking. Although real-time optimization (RTO) techniques for maximizing an objective function are aailable, steady-state assumptions in processes being frequently acted upon by unmeasured distrubances, strongly limit the optimization frequency, hierachical control systems allow to efficiently dealing with process uncertainty and complexity. In flotation processes, this has suggested to look at secondary variables correlated to performance variables that can be measured and regulated to indirectly optimize process operation. This research project feals with two major topics. The first one is the development of novel estimation algorithms to infer key secondary variables in flotation columns whereas the second topic deals with designing advanced control strategies towards process optimizacion. In the first part, techniques to measure on line froth depth and bias rate based on conductivity measurements were developed. A nonlinear dynamic observer for frother concentration estimation was also designed generating estimates with 1 ppm error. A Gaussian mixture model was used to on-line estimate bubble size distribution from sequential data coming from an image processing system. In the second part, a predictive control strategy was conceived to indirectly optimize column floration performance by maximizing gas holdup while ensuring a positive bias rate. Bubble size was then countrolled by an internal model controller based on Wiener model and the so-called frit and sleeve sparger. Good tracking and regulation against frother concentration and gas velocity variations were obtained. Results showed that using the frit and sleeve sparger, bubble size can be controlled independently from gas velocity, a key step to control bubble surface area flux. Moreover, gas holdup and bubble surface area flux were found to be highly correlated, initially implying that both variables can be used for control purpose. Finally, control of bubble size distributions is explored. It is shown that by using a Gaussian mixture model with fixed components to reprsent bubble size distribution turns the infinite dimensional problem of shaping it to a finite dimensional problem that can be approached using classical methods. Doctor en Ingeniería Eléctrica TERMINADA PFCHA-Becas 412p. PFCHA-Becas