The dynamic behaviour of a coal slurry gasifier in an Integrated Gasification Combined Cycle is modelled by means of mass, energy and momentum conservation equations as well as reaction kinetics descriptions. The main phenomena taken into consideration are (i) slurry drying and devolatilisation, (ii) char and volatile gas combustion, char gasification and water-gas shift reaction, and (iii) syngas cooling. The proposed 0-dimensional description is sufficient to capture process dynamics and it is a useful starting point for control design and verification. In particular, basic control strategies are discussed. Both model and control implementation is carried out in the Matlab-Simulink environment. Simulation results are shown to support model reliability and control effectiveness.