The behaviour of a roughening surface under time delayed feedback control is investigated by means of stochastic growth equations. We demonstrate for the Kardar-Parisi-Zhang equation and for the molecular beam epitaxy equation that the roughness can be tuned by two different feedback control schemes, i.e., digital control and differential control. It is shown that the local growth exponent beta, and thus the temporal evolution of the RMS (root mean square) surface roughness, can be adjusted within certain ranges for both types of growth equations. This indicates the possibility of in situ control of the surface roughness in experiments. (C) 2006 Elsevier B.V. All rights reserved.