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If the parameter uncertainties are considered in the modeling and control of the FSHV, the following notation is introduced:
The yaw/roll dynamics of the FSHV with model uncertainties can be rewritten as follows:
The control objective is to stabilize the maneuvering dynamics of the FSHV for the task of course keeping based on time scale separation and singular perturbation control theory.
Multi-Time Scale Analysis of the FSHV. In this section, the multi-time scale decomposition of the full model (10) is analyzed.
Experience implies that the yaw and roll dynamics are slow relative to the dynamics of the servo system for flap mechanism among the state variables of the proposed mathematical model of the FSHV, which is the motivation to establish a singular perturbation control scheme as follows:
According to the two-time scale structure of the FSHV system with actuator dynamics, a hierarchical control strategy can be deployed for the maneuvering control of the FSHV.
where [eta] = [[[phi], [psi]].sup.T], in which [phi] and [psi] denote the roll angle and heading angle of the FSHV with coordinates in the earth-fixed frame, respectively; v = [[p, r].sup.T], in which p and r represent the angular velocities with coordinates in the body-fixed frame, respectively; [mathematical expression not reproducible] is the Jacobian transformation matrix related to the above frames; [mathematical expression not reproducible] is the inertia including added mass; and [mathematical expression not reproducible] denotes the Coriolis and centripetal matrix.
Considering the course keeping problem of the FSHV, the first equation in (1) can be simplified as [??] = v.
If the model uncertainties are considered in the modeling and control of the FSHV, the following notations are introduced:
When ships sail at a fixed speed, M(x), C(x), [D.sub.L](x), and G(x) are linear matrices with constant element parameters, so [F.sub.0]([x.sub.1], x[.sub.2]) is also a linear function, while [[zeta].sub.0]([x.sub.1], [x.sub.2]) represents the nonlinear damping of the coupling hydrodynamics of the FSHV.
Hence, the control objective is to design an observer based output feedback controller for the course keeping of the FSHV using an iterative learning approach.
As to the controller design, an ILO based sliding mode controller is proposed for the output feedback course keeping control problem of the FSHV based on an iterative learning sliding surface.
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