TY - JOUR
TI - Observer-based force reconstruction technique
DO - https://doi.org/doi:10.7282/T3QJ7K0T
PY - 2015
AB - An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current input reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. To overcome these obstacles, linear dynamical systems theory and control systems theory are utilized in this work to develop a method that is asymptotically convergent to the exact solution. To address the inverse problem, multiple concepts are utilized. We perform an equilibrium analysis of linear dynamical systems with time-dependent inputs, and derive expressions for the dynamical equilibrium and remainder to provide a measure of the accuracy of the approximation. Then, concepts from control theory are used to define an unperturbed estimation system with observer feedback. We define an error system that consists of the difference between the estimate and actual system, and apply the concepts from our equilibrium analysis to develop a direct relationship between the system response and the applied force. Additionally, using an observer feedback gain, we are able to design the eigenvalues such that the derivatives of the applied force are filtered out and we obtain the input. This method was applied to lumped-parameter systems, continuous systems discretized using modal analysis, systems with probabilistic inputs, and a class of nonlinear systems. For each of these cases, we perform an error bounds analysis on bounded and unbounded inputs that are infinitely continuous and differentiable, and inputs with jump discontinuities to determine the quality of our estimate for the input. The results from these analyses demonstrate the capabilities of the proposed estimation method under various input conditions, and show the asymptotic nature of the estimate to the actual applied force. For each of these cases, examples are presented detailing the application of the proposed method under various loading conditions.
KW - Mechanical and Aerospace Engineering
KW - Linear systems
LA - eng
ER -