Often the most difficult step in establishing a control system is the development of a suitable dynamic process model. As such a model is not available elsewhere, a first principle dynamic mathematical model was developed for a coal dense medium separation circuit. Each unit operation was modelled individually and then integrated together to form a complete non-linear state–space model for the circuit. This model was used to simulate the process and it was validated using real process data derived from a plant experiment. When developing models from first principles, it is necessary to estimate the model parameters. These parameters, specifically for non-linear state–space relationships, require a unique solution. A parameter identifiability method was used to show that the non-linear dynamic models developed have unique parameters for a specific set of input–output data.