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This study focuses on state estimation of nonlinear discrete time systems with constraints. Physical processes have inherent in them, constraints on inputs, outputs, states and disturbances. These constraints can provide additional information to the estimator in estimating states from the measured output. Recursive filters such as Kalman Filters or Extended Kalman Filters are commonly used in state estimation; however, they do not allow inclusion of constraints in their formulation. On the other hand, computational complexity of full information estimation (using all measurements) grows with iteration and becomes intractable. One way of formulating the recursive state estimation problem with constraints is the Moving Horizon Estimation (MHE) approximation. Estimates of states are calculated from the solution of a constrained optimization problem of fixed size. Detailed formulation of this strategy is studied and properties of this estimation algorithm are discussed in this work. The problem with the MHE formulation is solving an optimization problem in each iteration which is computationally intensive. State estimation with constraints can be formulated as Extended Kalman Filter (EKF) with a projection applied to estimates. The states are estimated from the measurements using standard Extended Kalman Filter (EKF) algorithm and the estimated states are projected on to a constrained set. Detailed formulation of this estimation strategy is studied and the properties associated with this algorithm are discussed. Both these state estimation strategies (MHE and EKF with projection) are tested with examples from the literature. The average estimation time and the sum of square estimation error are used to compare performance of these estimators. Results of the case studies are analyzed and trade-offs are discussed.
ContributorsJoshi, Rakesh (Author) / Tsakalis, Konstantinos (Thesis advisor) / Rodriguez, Armando (Committee member) / Si, Jennie (Committee member) / Arizona State University (Publisher)
Created2013
Description
Microbial fuel cells(MFC) use micro-organisms called anode-respiring bacteria(ARB) to convert chemical energy into electrical energy. This process can not only treat wastewater but can also produce useful byproduct hydrogen peroxide(H2O2). Process variables like anode potential and pH play important role in the MFC operation and the focus of this dissertation are pH and potential control problems.
Most of the adaptive pH control solutions use signal-based-norms as cost functions, but their strong dependency on excitation signal properties makes them sensitive to noise, disturbances, and modeling errors. System-based-norm( H-infinity) cost functions provide a viable alternative for the adaptation as they are less susceptible to the signal properties. Two variants of adaptive pH control algorithms that use approximate H-infinity frequency loop-shaping (FLS) cost metrics are proposed in this dissertation.
A pH neutralization process with high retention time is studied using lab scale experiments and the experimental setup is used as a basis to develop a first-principles model. The analysis of such a model shows that only the gain of the process varies significantly with operating conditions and with buffering capacity. Consequently, the adaptation of the controller gain (single parameter) is sufficient to compensate for the variation in process gain and the focus of the proposed algorithms is the adaptation of the PI controller gain. Computer simulations and lab-scale experiments are used to study tracking, disturbance rejection and adaptation performance of these algorithms under different excitation conditions. Results show the proposed algorithm produces optimum that is less dependent on the excitation as compared to a commonly used L2 cost function based algorithm and tracks set-points reasonably well under practical conditions. The proposed direct pH control algorithm is integrated with the combined activated sludge anaerobic digestion model (CASADM) of an MFC and it is shown pH control improves its performance.
Analytical grade potentiostats are commonly used in MFC potential control, but, their high cost (>$6000) and large size, make them nonviable for the field usage. This dissertation proposes an alternate low-cost($200) portable potentiostat solution. This potentiostat is tested using a ferricyanide reactor and results show it produces performance close to an analytical grade potentiostat.
Most of the adaptive pH control solutions use signal-based-norms as cost functions, but their strong dependency on excitation signal properties makes them sensitive to noise, disturbances, and modeling errors. System-based-norm( H-infinity) cost functions provide a viable alternative for the adaptation as they are less susceptible to the signal properties. Two variants of adaptive pH control algorithms that use approximate H-infinity frequency loop-shaping (FLS) cost metrics are proposed in this dissertation.
A pH neutralization process with high retention time is studied using lab scale experiments and the experimental setup is used as a basis to develop a first-principles model. The analysis of such a model shows that only the gain of the process varies significantly with operating conditions and with buffering capacity. Consequently, the adaptation of the controller gain (single parameter) is sufficient to compensate for the variation in process gain and the focus of the proposed algorithms is the adaptation of the PI controller gain. Computer simulations and lab-scale experiments are used to study tracking, disturbance rejection and adaptation performance of these algorithms under different excitation conditions. Results show the proposed algorithm produces optimum that is less dependent on the excitation as compared to a commonly used L2 cost function based algorithm and tracks set-points reasonably well under practical conditions. The proposed direct pH control algorithm is integrated with the combined activated sludge anaerobic digestion model (CASADM) of an MFC and it is shown pH control improves its performance.
Analytical grade potentiostats are commonly used in MFC potential control, but, their high cost (>$6000) and large size, make them nonviable for the field usage. This dissertation proposes an alternate low-cost($200) portable potentiostat solution. This potentiostat is tested using a ferricyanide reactor and results show it produces performance close to an analytical grade potentiostat.
ContributorsJoshi, Rakesh (Author) / Tsakalis, Konstantinos (Thesis advisor) / Rodriguez, Armando (Committee member) / Torres, Cesar (Committee member) / Spanias, Andreas (Committee member) / Arizona State University (Publisher)
Created2018