Persons at STU
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|Language of final thesis:||English|
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|Title of the thesis:||Embedded Optimal Estimation for Fast Mechatronic Systems|
|Summary:||A fast mechatronic system belongs to the class of processes, which usually need a short sampling time for discretization---in the range of milliseconds. Sometimes their system dynamics cannot be fully expressed by a linear or linear time-varying (LTV) model, a set of nonlinear differential equations is required. In addition, some of the states and time-varying parameters might not be accessible through measurement, hence an advanced estimation method needs to be employed. Nonlinear state estimation techniques are intended to improve the quality of estimated state and parameters by explicitly utilizing the nonlinear dynamics, compared to the methods that use linear or linearized models. In an optimal estimation framework, there is not a unique approach that certainly outperforms all other methods. Estimation accuracy, computational complexity and availability of the numerical solver are among the factors that should be considered before choosing the right estimation method for a specific application. Moreover, with the increased interest in embedded systems for implementing advanced estimation methods, it is quite challenging to trade off these properties. To address the nonlinear estimation problem, several approaches have been proposed, where most of them lack global stability and optimality. Among the existing nonlinear estimation methods, the extended Kalman filter (EKF) and the moving horizon estimation (MHE) are the most popular, where the latter one, as a candidate for constrained optimization-based estimation technique, is rarely implemented in real-time for fast mechatronic systems.
In this work, two vibration systems are considered as case studies; a linear cantilever beam setup and a nonlinear vibration energy harvesting system. The performance of the optimization-based MHE compared to the standard and widelyaccepted EKF is demonstrated in real time. Thanks to the current advancements in numerical solvers for optimization problems, this implementation is carried out on a low-cost computing device with a sampling time in the range of milliseconds. Furthermore, the weaknesses of the two nonlinear estimation methods are studied in detail: none of them guarantee global stability or optimality. To recover these properties, a nominally globally valid model transformation method is introduced, where the resulting LTV model is equivalent to the nonlinear dynamics, with sub-optimal consideration of input and output disturbances. Utilizing this model re-formulation, several multi-stage nonlinear estimation methods with global convergent properties are developed; two-stage Kalman filtering, homotopy-based MHE and double MHE. The stability analysis of these methods are discussed and their improved performance is validated in several simulation studies. One of the proposed estimation methods, the two-stage Kalman filtering, has been experimentally validated in a globally convergent adaptive vibration attenuation scheme, on an embedded micro-controller unit. The main purpose of designing the other advanced estimation approaches, namely multi-stage MHE, not only is to improve the quality of estimation, but to achieve computational complexity that is less than the one needed for solving nonlinear optimization-based estimation methods. To this end, several simulation studies are performed to verify that the computational complexity of the proposed multi-stage MHE is an order of magnitude less than nonlinear MHE and its estimation performance is improved.|
|Key words:||nonlinear estimation, embedded optimization, adaptive control, non-convex optimization problem, real-time implementation|
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