By Eure K.W.
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24) the system order is p + nd rather than p. This is due to the fact that the model given by Eq. 24) has imbedded within the parameters an exact model of the disturbance41. The value of nd is twice the number of periodic disturbances acting on the system. The resulting system model provides an exact input output map for the discretetime system being identified given that the periodic disturbance is the only disturbance acting on the system. A similar proof for MIMO systems with periodic disturbances may be found in Ref.
M2 < p+q-1. Beyond the control horizon the control input is assumed to be zero. The resulting controller is shown in Eq. 11). 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.
With both these random inputs applied, the system output y of Fig. 2 is measured. The two input data vectors and the one output vector are then used to approximate an ARMAX model of the system. It is important to note that the ARMAX model represents both the plexi- glass box and the filters and amplifiers used in the controller loop. The form of the model is that of Eq. 1). The ARMAX model was then used to find the GPC controller coefficients shown in Eq. 9). 2 shows the autospectrum of plant output (accelerometer signal, y) without control (gray line), feedback only (dotted line), and with feedback/feedforward control (solid line).