3.2.1. General control design. It is obvious that the disturbance
signal is not controllable; hence, the only feasible
approach to suppress the vibrations is to define a
control signal minimizing the net input to the process.
This goal is readily fulfilled by measuring the disturbance
signal and realizing a control signal in the antiphase.
This is the underlying reason why the disturbance
is moved to the process input in the first place, as
now the control goal is achieved with simple feedforward
control. It is also desirable to have a control law
that guarantees the stability of the closed-loop system.
This secondary goal is readily achieved by utilizing
optimal LQ-regulator control for the stabilization of
the process states. Unfortunately, the disturbance is
not measurable and a state estimator has to be used
thereof. A plant model representing the process subject
to the input disturbance is introduced for the estimator
purposes. The dynamics of a multidimensional sinusoidal
disturbance are exactly the same as the dynamics
of the filter in Equation (5).The sinusoidal disturbances
are then realized by exciting the filters with white noise.
Now, the disturbance dynamics are given as (with the
slight violation of the notation for continuous time stochastic
signals)