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Gas compressor stations are vital components of natural gas pipelines. Their compressors are often arranged in parallel or serial configurations to achieve a designated mass flow or pressure ratio. The machines have different, time-varying performance characteristics and by applying carefully chosen inputs to them, the station’s energy consumption of can be reduced. In the industry, a two-step real-time optimization method is frequently used to do so. However, in practice this method rarely achieves optimal plant operation due to structural plant-model mismatch. To tackle the issues caused by plant-model mismatch, other controllers are needed. The performance of a recently proposed feedback optimization algorithm for this type of optimization problems is investigated with a simplified, generic load sharing problem and a compressor load sharing problem. A setup of three machines arranged in parallel is considered for both problems. In the compressor load sharing problem, plant-model mismatch is included by fitting Gaussian process regression models to efficiency maps from manufacturers to serve as hidden, true plant models in simulations. Second order polynomials, fitted to the same data, are used as the models available to the optimizing controllers. The performance of feedback optimization and the two-step optimization method is compared to an equal load sharing controller. Feedback optimization achieves lower energy consumptions than the two-step optimization method and converges steadily, whereas the two-step approach exhibits jumps between local minima. By tuning the feedback optimization controller adaptively, good convergence rates are possible for all operating points. Therefore, using feedback optimization to solve load sharing problems that involve mechanical systems and structural plant-model mismatch can lead to significant reductions in energy consumption.