Microlithographic illumination system includes individually drivable elements to variably illuminate a pupil surface of the system. Each element deviates an incident light beam based on a control signal applied to the element. The system also includes an instrument to provide a measurement signal, and a model-based state estimator configured to compute, for each element, an estimated state vector based on the measurement signal. The estimated state vector represents: a deviation of a light beam caused by the element; and a time derivative of the deviation. The illumination system further includes a regulator configured to receive, for each element: a) the estimated state vector; and b) target values for: i) the deviation of the light beam caused by the deviating element; and ii) the time derivative of the deviation.