This paper presents he development and implementation of a branch-and-bound on-off model-based predictive control (MPC) strategy aimed at controlling pH and minimising CO2 losses in a microalgal tubular photo bioreactor. These kinds of photobioreactors are usually controlled by means of an on-off valve and thus classical on-off switching controllers are implemented, without taking into account plant dynamics. In the considered operating range, the nonlinearity of the system is not severe and thus a linear model of the pH evolution in spite of changes in CO2 injection and in solar radiation has been obtained and used within a MPC framework to achieve desired regulation properties trying to minimise CO2 losses, as one of the major costs in this installation is the supply of carbon dioxide and its transfer to the culture, amounting to about one-third the cost of the largest scale systems. The paper also shows the results obtained when applying the technique to the real photobioreactor. (C) 2003 Elsevier Ltd. All rights reserved.