The resulting controller is of the order of kþ2 dm,
where k, d and m are the number of process states,
disturbance tones and process inputs, respectively.
The controller is obtained by solving two separate
AREs. In the problem formulation there were some
possible issues related to nonsquare plants and the
insufficient degrees of freedom to represent some of
the output disturbances as input disturbances. It is
now evident that this does not become a problem, in
terms of the optimality, as the Kalman filter used for
the state estimation gives the lowest possible estimation
error for the given plant structure. Although it may
seem that by using output disturbances the possible
persistent estimation errors could be alleviated, the control
performance would be none the better. This is due
to the fact that the problem of finding a suitable control
law for output disturbances is dual to finding a suitable
estimator for input disturbances. Hence, both are capable
of providing similar performance. It is also worth
noting that even as the disturbance compensation can
be interpreted as a feedforward control, it is related to
the process output through the estimator dynamics,
hence ultimately being feedback control. This also
guarantees the closed-loop stability under the assumption
of stable estimator dynamics.
The resulting controller is of the order of kþ2 dm,where k, d and m are the number of process states,disturbance tones and process inputs, respectively.The controller is obtained by solving two separateAREs. In the problem formulation there were somepossible issues related to nonsquare plants and theinsufficient degrees of freedom to represent some ofthe output disturbances as input disturbances. It isnow evident that this does not become a problem, interms of the optimality, as the Kalman filter used forthe state estimation gives the lowest possible estimationerror for the given plant structure. Although it mayseem that by using output disturbances the possiblepersistent estimation errors could be alleviated, the controlperformance would be none the better. This is dueto the fact that the problem of finding a suitable controllaw for output disturbances is dual to finding a suitableestimator for input disturbances. Hence, both are capableof providing similar performance. It is also worthnoting that even as the disturbance compensation canbe interpreted as a feedforward control, it is related tothe process output through the estimator dynamics,hence ultimately being feedback control. This alsoguarantees the closed-loop stability under the assumptionof stable estimator dynamics.
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