In this paper, a digital PID controller, derived in the partial state reference model (PSRM) adaptive control spirit, is used to control the temperature in batch and semi-batch chemical reactors. This controller consists in the combination of a performance-oriented linear quadratic control design method and a robust parameter estimator within the delta operator formulation. Such a formulation is particularly motivated by the convergence of the performances to their continuous time counterpart as well as its numerical robustness when the sampling is required to be fast. Experiments on batch and semi-batch reactors are carried out to emphasize the performances of the aforementioned controller with respect to those of an auto-calibrated PID controller.