Integration of Extremum Seeking and Model Predictive Control for Discrete Time Systems
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This thesis considers a time-varying extremum seeking control algorithm that adjusts set-points provided to a model predictive controller for a vapour compression system. While perturbation-based extremum seeking methods have been known for some time, they suffer from slow convergence rates---a problem emphasized in application by the long time constants associated with thermal systems. The proposed method uses time-varying extremum seeking, which has faster and more reliable convergence properties for this application. In particular, we regulate the compressor discharge temperature using a model predictive controller with set-points selected from a model-free time-varying extremum seeking algorithm. We show that the relationship between compressor discharge temperature and power consumption is convex (a requirement for this class of real-time optimization), and use discrete-time extremum seeking control to drive these set-points to values that minimize power. The results are compared to the traditional perturbation-based extremum seeking approach. Further, because the required cooling capacity (and therefore compressor speed) is a function of measured and unmeasured disturbances, the optimal compressor discharge temperature set-point must vary according to these conditions. We show that the energy optimal discharge temperature is tracked with the time-varying extremum seeking algorithm in the presence of disturbances.