Real-Time Optimization via Directional Modifier Adaptation, with Application to Kite Control

The steady advance of computational methods makes model-based optimization an increasingly attractive method for process improvement. Unfortunately, the available models are often inaccurate. The traditional remedy is to update the model parameters, but this generally leads to a difficult parameter estimation problem that must be solved on-line, and the resulting model may still poorly predict the process optimum. An iterative real-time optimization method called Modifier Adaptation overcomes these obstacles by directly incorporating plant measurements into the optimization framework, in the form of constraint values and plant-gradient estimates. Experimental gradient estimation is the main difficulty encountered when applying Modifier Adaptation. The experimental effort required to estimate plant gradients increases along with the number of plant inputs. This tends to make the method intractable for processes with many inputs. The main methodological contribution of this thesis is a new algorithm called ‘Directional’ Modifier Adaptation, which handles the gradient-estimation problem by estimating plant derivatives only in certain privileged directions. By spending less effort on gradient estimation, the algorithm can focus on optimizing the plant. A ‘Dual’ Directional Modifier Adaptation is proposed, which estimates these ‘directional’ derivatives using past operating points. This algorithm exhibits fast convergence to a neighborhood of the plant optimum, even for processes with many inputs. Modifier Adaptation also makes use of an approximate process model. Another difficulty which may be encountered is that this model’s inputs differ from those of the real process. The second methodological contribution is ‘Generalized’ Modifier Adaptation, a framework for dealing with the case where the model’s inputs differ from those of the plant. This approach circumvents remodeling the system. For example, Generalized Modifier Adaptation allows an open-loop process model to be used to optimize a closed-loop plant, without having to model the controller. The Dual Directional Modifier Adaptation method is applied to a purpose-built experimental kite system. Kites are currently being developed into a radical new renewable energy technology. Large-scale applications include pulling ships and generating electricity from wind at altitudes beyond the reach of conventional wind turbines. While kites were traditionally manually controlled, these new applications require autonomous operation. The first challenge is to design reliable control algorithms for kites, capable of dealing with noise, wind disturbances, and time delays. The control algorithm keeps the kite flying a periodic path, at very high speeds. The second challenge is to choose this path in order to maximize the energy extracted from the wind. During this thesis, a small autonomous kite system was constructed. Thirty days of experimental testing were carried out, over the space of two years. A new modeling hypothesis was validated, linking steering deflections to a decrease in the kite’s lift/drag ratio. A path-following controller was implemented, capable of achieving good, robust path-following performance, despite significant time delay. The only real-time measurement required by the control algorithm is the kite’s position, which, in this work, was obtained simply by measuring the angle of the kite’s tether. A two-layer optimizing control scheme was implemented on the experimental kite system. Dual Directional Modifier Adaptation was used to periodically update the reference path tracked by the path-following controller, in order to maximize the kite’s average tether tension. Despite extremely high noise levels, the algorithm was able to locate the optimal reference path in only 10 minutes, while ensuring that a minimum altitude constraint was never violated. The resulting average tether tension is about 20% higher than that obtained following the optimal path computed using the model. An experimental study comparing the average tether tension obtained using different reference paths confirms the importance of path shape, and validates the optimal solution reached by the Dual Directional Modifier Adaptation algorithm.