Constrained extremum-seeking control in discrete-time with application to liquefier unit power minimization
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Given the increasing complexity of engineering systems, difficulties are often met in developing models that describe these systems accurately. If the model is used for the purpose of optimization, the true plant optimum cannot be achieved in the presence of plant-model-mismatch. Extremum-seeking control is a model free real-time optimization technique that is well suited for the optimization of uncertain processes. This work presents a constrained time-varying extremum seeking control approach for a class of discrete-time nonlinear systems. An interior point method is used to enforce the constraints. The proposed method has the ability to guarantee feasibility of a closed-loop system during optimization. The transient performance of the technique is compared to that of a constrained extremum-seeking approach in 1 dimension [Mills and Kristic, 2015]. Simulation results presented show the effectiveness of the proposed technique in solving constrained optimization problems within the stated constraints. The proposed technique is employed for the minimization of the unit power consumption of an operational nitrogen liquefier. In this thesis, the steady-state relationship between the manipulated variables, which include feed gas discharge pressure, turbine flow ratio, heat exchanger sub-cooler level set point, and the unit power consumption of the liquefier is investigated. The simulation model is used to estimate the steady-state unit power using varying values of the turbine flow ratio at different operating conditions. The simulation results demonstrate that a small but significant reduction in the unit power of the liquefier can be realized. This study clearly identifies the potential for the use of extremum-seeking control for the minimization of unit-power in real-time.