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Extremum seeking control (ESC) is a model-free control solution for real-time optimization of system operation where model acquisition is difficult and/or cost prohibitive. For many HVAC and refrigeration systems, there can be a large number of candidate inputs for ESC design; however, some inputs affect the performance measure to a greater degree than others. This article presents an online input selection method for multivariable ESC, which uses a singular value decomposition (SVD) analysis coupled with a dither-demodulation-based online Hessian estimate for the underlying static map. A subset of physical inputs or a new set of inputs via linear combination of the physical inputs can be determined using the proposed approach. We present an analysis for quantifying the loss bound of achievable optimum output with the underlying input selection. Further, the Hessian estimation error bound is quantified with perturbation analysis. The proposed method is evaluated with Modelica simulation models of chilled-water plants, one with a single chiller and the other with two parallel chillers. The simulation results validate the effectiveness of the proposed method of input selection.

Extremum-seeking control integrated online input selection with application to a chilled-water plant