Real-time automatic regulation of gene expression is a key technology for synthetic biology enabling, for example, synthetic circuit's components to operate in an optimal range. Computer-guided control of gene expression from a variety of inducible promoters has been only recently successfully demonstrated. Here we compared, in silico and in vivo, three different control algorithms: the Proportional Integral (PI) and Model Predictive Control (MPC) controllers, which have already been used to control gene expression, and the Zero Average Dynamics (ZAD), a control technique used to regulate electrical power systems. We chose as an experimental testbed the most commonly used inducible promoter in yeast: the galactose-responsive GAL1 promoter. We set two control tasks: either force cells to express a desired constant fluorescence level of a reporter protein downstream of the GAL1 promoter (set-point) or a time-varying fluorescence (tracking). Using a microfluidics-based experimental platform, in which either glucose or galactose can be provided to the cells, we demonstrated that both the MPC and ZAD control strategies can successfully regulate gene expression from the GAL1 promoter in living cells for thousands of minutes. The MPC controller can track fast reference signals better than ZAD but with a higher actuation effort due to the large number of input switches it requires. Conversely, the PI controller's performance is comparable to that achieved by the MPC and the ZAD controllers only for the set-point regulation.