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The creation of low-order dynamic models for complex industrial systems is complicated by disturbances and limited sensor accuracy. This work presents a system identification procedure that uses machine learning methods and process knowledge to robustly identify a low-order closed-loop model of a municipal solid waste (MSW) grate incineration plant. These types of plants are known for their strong disturbances coming from fuel composition fluctuations. Using Bayesian optimization, the algorithm ranks and selects inputs from the available sensor data and chooses the model structure. This results in accurate models with low complexity while avoiding overfitting. The method is applied and validated using data of an industrial MSW incineration plant. The obtained models give excellent predictions and confidence intervals for the steam capacity and intermediate quantities such as supply air flow and flue gas temperature. The identified continuous-time models are fully given, and their step-response dynamics are discussed. The models can be used to develop model-based unit control schemes for grate incineration plants. The presented method shows great potential for the identification of over-actuated systems or disturbed systems with many sensors.