By Eure K.W.
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Extra info for Adaptive predictive feedback techniques for vibration control
This is in close agreement with the simulation results. Some of the differences between Figs. 7 can be accounted for by uncertainties in the identified ARX model parameters and noise in the experiment. However, in comparing the open-loop plot of Fig. 4 with the open-loop plot of Fig. 7 we see that the responses differ greatly between the frequencies 400 Hz to 1100 Hz. One contributing factor to this difference is that in the simulation of Fig. 4 the disturbance was white noise applied directly to the plant output.
11) The formulation given in Eq. 11) differs from that given in Ref.  in that it assumes the current control will be applied at the next time step rather than at the present time step. This is important in implementation because the present formulation allows time to perform computations. The above formulation also differs from that of Ref.  in the manner in which the controller coefficients are calculated. Rather than solving the Diophantine equation for future predictions, the above formulation uses a different recursive relationship.
19) represents the map from the system control input to the system output. If, however, the system ID is performed in the presence of the disturbance, then the following model may be obtained if the order of the ARX model is extended to infinity and the data length is infinite. The proof may be found in Ref. . 20) includes information about the disturbance which will be used to enhance performance in the controller design. Although neither the data length nor the system 47 order can actually approach infinity, Eq.