Some efficient open-loop control solution strategies for dynamic optimization problems and control co-design
Date
2021
Authors
Sundarrajan, Athul Krishna, author
Herber, Daniel R., advisor
Cale, James, committee member
Venayagamoorthy, Karan, committee member
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Abstract
This thesis explores strategies to efficiently solve dynamic optimization (DO) and control codesign (CCD) problems that arise in early-stage system design studies. The task of design optimization of dynamic systems involves identifying optimal values of the physical elements of the system and the inputs to effectively control the dynamic behavior of the system to achieve peak performance. The problem becomes more complex when designing multidisciplinary systems, where the coupling between disciplines must be accounted for to achieve optimal performance. Developing tools and strategies to efficiently and accurately solve these problems is needed. Conventional design practices involve sequentially optimizing the plant parameters and then identifying a control scheme for the given plant design. This sequential design procedure does not often produce system-level optimal solutions. Control co-design or CCD is a design paradigm that seeks to find system-level optimal design through simultaneous optimization of the plant and control variables. In this work, both the plant and controls optimization are framed as a integrated DO problem. We focus on a class of direct methods called direct transcription (DT) to solve these DO problems. We start with a subclass of nonlinear dynamic optimization (NLDO) problems for the first study, namely linear-quadratic dynamic optimization problems (LQDO). For this class of problems, the objective function is quadratic, and the constraints are linear. Highly efficient and accurate computational tools have been developed for solving LQDO problems on account of their linear and quadratic problem elements. Their structure facilities the development of automated solvers. We identify the factors that enable creating these efficient tools and leverage them towards solving NLDO problems. We explore three different strategies to solve NLDO problems using LQDO elements, and analyze the requirements and limits of each approach. Though multiple studies have used one of the methods to solve a given CCD problem, there isa lack of investigations identifying the trade-offs between the nested and simultaneous CCD, two commonly used methods. We build on the results from the first study and solve a detailed active suspension design using both the nested and simultaneous CCD methods. We look at the impact of derivative methods, tolerance, and the number of discretization points on the solution accuracy and computational times. We use the implementation and results from this study to form some heuristics to choose between simultaneous and nested CCD methods. A third study involves CCD of a floating offshore wind turbine using the levelized cost of energy (LCOE) as an objective. The methods and tools developed in the previous studies have been applied toward solving a complex engineering design problem. The results show that the impact of optimal control strategies and the importance of adopting an integrated approach for designing FOWTs to lower the LCOE.
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Subject
control co-design
floating offshore wind turbines
simultaneous CCD
dynamic optimization
active suspension
nested CCD