This paper presents an adaptive path following control law to steer underactuated ships along a predefined path at a constant forward speed with uncertain parameters due to changes of added mass matrices.The proposed ...This paper presents an adaptive path following control law to steer underactuated ships along a predefined path at a constant forward speed with uncertain parameters due to changes of added mass matrices.The proposed controller is based on analytic model predictive control and model reference adaptive control.The SerretFrenet frame is used to describe the ship dynamics.The analytic model predictive control provides a systematic method rather than try-and-error method to get appropriate control parameters to guarantee the stability of the closed-loop system,and the well-defined relative degree is guaranteed by introducing output-redefinition.An identification algorithm based on model reference adaptive control is used to identify the uncertain parameters.Numerical simulations are provided to demonstrate the validity of the proposed control law.展开更多
This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natura...This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.展开更多
In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directr...In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.展开更多
基金the National Natural Science Foundation of China (No. 50779033)the National High Technology Research and Development Program (863) of China (No. 2007AA11Z250)
文摘This paper presents an adaptive path following control law to steer underactuated ships along a predefined path at a constant forward speed with uncertain parameters due to changes of added mass matrices.The proposed controller is based on analytic model predictive control and model reference adaptive control.The SerretFrenet frame is used to describe the ship dynamics.The analytic model predictive control provides a systematic method rather than try-and-error method to get appropriate control parameters to guarantee the stability of the closed-loop system,and the well-defined relative degree is guaranteed by introducing output-redefinition.An identification algorithm based on model reference adaptive control is used to identify the uncertain parameters.Numerical simulations are provided to demonstrate the validity of the proposed control law.
文摘This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.
文摘In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.
