Mixing problems are common in science and engineering, the aim being to combine fluids as quickly and efficiently as possible. We consider the design of a simple controller to promote mixing in a Stokes' fluid flow. In this paper, a controlled stirring motion is represented by a velocity field consisting of the superposition of a steady base flow and a second field modulated by a saturating, time-dependent control variable. The problem can be formulated as an optimal control one, but the presence of a nonlinearity in the state dynamics and an input constraint make the construction of a feedback law difficult. The size of the problem means that receding horizon schemes, revolving around real-time optimization of even a simplified model, are currently not feasible for fast applications. To address this problem, we exploit theory for the control of bilinear systems to propose a simple, well-performing, explicit feedback law. There are several interesting design issues associated with applying this approach to a fluid mixing application. We demonstrate these by designing a controller for a two-dimensional fluid mixing problem with simple cellular flows and discuss the relevant implementation decisions. The closed-loop forcing fields have many features that are as expected: regions of the flow with large spatial velocity gradients target regular islands of concentration and the input favors velocity fields with contours aligned perpendicular to the scalar field. (C) 2010 Elsevier Ltd. All rights reserved.