Model-based controllers are now beginning to gain widespread acceptance in industry. However, the majority of these controllers are based on linear models and performance in controlling the non-linear processes common in the chemical industry is sub-optimal. The use of a non-linear model could yield significant improvements in control performance. In this study a relational model from a fuzzy input space to a crisp output space is constructed by applying a least-squares identification technique to past process data. This model is termed a crisp-consequent fuzzy relational model (ccFRM) and is capable of giving an accurate representation of a non-linear system. A novel inversion method is presented which allows the ccFRM to be inverted and used within the well-known IMC structure. This new controller is termed a fuzzy internal model controller (FIMC) and test results are presented showing the FIMC performing both servo and regulatory action on a multi-variable simulated pH system. This process is extremely non-linear and exhibits severe interaction effects and is consequently a very difficult system to control. The simulation is introduced in detail, as are the tests carried out, and the performance of the FIMC in these tests is found to be encouraging.