In this paper a numerical model of a strongly nonlinear beam with attached vibration control system is presented. To reduce vibration a saturation controller is applied. Its input and output are time delayed signals. To estimate an influence of time delays on the control effectiveness, two indicators are proposed. The first indicator is quantitative, while the second one – qualitative is based on value of the largest Lyapunov exponent. The numerical procedure for estimating this exponent is developed and tested.