An extended linear quadratic dynamic matrix control (EQDMC) of a gibbsite crystallisation system is presented. The process model of the crystalliser is based on the conservation principles of mass and population balances, and kinetic relations including nucleation, growth and agglomeration correlations. It is shown that the process is non-linear with constraints and possesses interaction among its process variables. Practical concerns in crysallisation plants such as low flow rates and high, magma densities that I may lead to solids deposition and eventual line blocking are considered as the system's constraints. The controller is developed by combining extended linear dynamic matrix control (EDMC) and quadratic dynamic matrix control (QDMC) algorithms. Two types of control outputs are considered: controlled and associated variables. The capability of the controller in bringing the controlled variables to their setpoints while maintaining all process constraints within their limits is demonstrated via simulation. It is shown that increasing prediction horizon improves the control performance.