Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.

Process Monitoring and Defect Detection of Additive Manufacturing Using Inline Coherent Imaging

With applications ranging from aerospace to biomedicine, additive manufacturing (AM) has been revolutionizing the manufacturing industry. The ability of additive techniques, such as selective laser melting (SLM), to create fully functional, geometrically complex, and unique parts out of high strength materials is of great interest. Unfortunately, despite numerous advantages afforded by this technology, its widespread adoption is hindered by a lack of on-line, real time feedback control and quality assurance techniques. In this thesis, inline coherent imaging (ICI), a broadband, spatially coherent imaging technique, is used to observe the SLM process in 15 - 45 $\mu m$ 316L stainless steel. Imaging of both single and multilayer builds is performed at a rate of 200 $kHz$, with a resolution of tens of microns, and a high dynamic range rendering it impervious to blinding from the process beam. This allows imaging before, during, and after laser processing to observe changes in the morphology and stability of the melt. Galvanometer-based scanning of the imaging beam relative to the process beam during the creation of single tracks is used to gain a unique perspective of the SLM process that has been so far unobservable by other monitoring techniques. Single track processing is also used to investigate the possibility of a preliminary feedback control parameter based on the process beam power, through imaging with both coaxial and 100 $\mu m$ offset alignment with respect to the process beam. The 100 $\mu m$ offset improved imaging by increasing the number of bright A-lines (i.e. with signal greater than the 10 $dB$ noise floor) by 300\%. The overlap between adjacent tracks in a single layer is imaged to detect characteristic fault signatures. Full multilayer builds are carried out and the resultant ICI images are used to detect defects in the finished part and improve upon the initial design of the build system. Damage to the recoater blade is assessed using powder layer scans acquired during a 3D build. The ability of ICI to monitor SLM processes at such high rates with high resolution offers extraordinary potential for future advances in on-line feedback control of additive manufacturing.