A method and apparatus for designing perturbation signals to excite a number of input variables of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller. The method begins with providing input parameters of the system. A plurality of binary multi-frequency (BMF) signals are generated based on these input parameters and the frequency spectra of these BMF signals are calculated. One BMF signal is selected out of the set of BMF signals so that the frequency spectrum of the selected BMF signal most closely matches a desired frequency spectrum specified by the input parameters. The selected BMF signal is used as a first perturbation signal for testing the system. The selected BMF signal is also shifted by predetermined amounts of samples to create delayed copies of the original BMF signal to be used as additional perturbation signals.