A ‘positional’ multivariable self-tuning controller is derived and extended to admit an ‘incremental’ control policy. As a result of the choice of model representation, both multivariable self-tuning controllers are capable of multivariable-multirate self-tuning control. Thus different loops making up the multivariable control system can have different control actuation rates. Both ‘positional’ and ‘incremental’ algorithms were implemented in the dual-composition control of a pilot scale distillation column. The benefits of multirate self-tuning control were also evaluated. The results presented show that both algorithms gave good regulation. Multirate control also resulted in improved overall performances. The problem of commissioning self-tuning controllers is also discussed.