The paper first briefly reviews the analytical procedures for obtaining optimum PID controller settings for minimisation of time weighted integral performance criteria. The approach is then used to obtain formulae for setting the controller parameters for a first-order plus dead time plant model which is a common approximation used in the process industries. These results are further extended to obtain two procedures, which can be used with the relay autotuning approach, to find the required controller parameters for optimisation of the integral of time error squared criterion. Good results have been obtained when these criteria are used with other plant models.