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The aim of this study is to provide a full comprehensive study of the singular linear parameter‐varying (LPV) systems and observer synthesis in a real process. The states and unknown inputs estimation problem for a binary distillation column is solved by using an LPV proportional‐integral observer (PI‐Observer). A singular LPV model of the process is developed. This model facilitates the design of the PI‐Observer for singular LPV systems. The observer proposed is tested using experimental data of a distillation column separating an ethanol–water mixture. The results indicate that the observer is able to accurately reconstruct the product composition dynamics and the unknown inputs of the process.