The usual plant structure assumed in self-tuning problems is not sufficiently general to cover some industrial control problems, such as autopilot design. An LQG-based control law is developed for this type of industrial situation. The cost function includes dynamic weighting elements, which allows integral action to be introduced and robustness characteristics to be modified. The system model involves a reference signal, disturbances which affect the output to be controlled and coloured measurement noise. The way in which the optimal control law is incorporated in a self-tuning control system is also described, using the ship steering problem to illustrate its utility in applications.