Comparison of the Two Methods of Identification under Unknown-but-Bounded Disturbances

Considered are stable linear SISO plants subjected to unknown-but-bounded disturbances. For such plants, the potentials of the two methods of active identification are Compared—the instrumental variable method and the finite-frequency identification method. The relation between these methods is established in the situation where the measurable input is represented by a test signal in the form of the sum of harmonics, whose number is equal to the state space dimension of the plant. The advantages of the finite-frequency method are twofold: it reduces both the sensitivity of the estimates of the plant coefficients to the errors in experimental data and the effect of the dependence between the measurable input and exogenous disturbance on the accuracy of identification. These extra capabilities are provided by the self-tuning of the frequencies of the test signal.