In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown tim...In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown time-varying coefficients and unknown force function. In this scheme, the control law is constructed in terms of estimated values for the bounds of the unknown coefficients, where these values are continuously updated by adaptive laws to ensure asymptotic convergence to zero for the output function. The proposed controller is applied to solve the problem of pitch angle regulation for a floating wind turbine with dynamic uncertainty and external disturbances. Numerical simulations are performed to demonstrate the validity of the designed controller to achieve the desired pitch angle for the floating turbine＇s body.展开更多
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonl...The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.展开更多
文摘In this paper, a modified sliding-mode adaptive controller is derived to achieve stability and output regulation for a class of dynamical systems represented by a non-homogeneous differential equation with unknown time-varying coefficients and unknown force function. In this scheme, the control law is constructed in terms of estimated values for the bounds of the unknown coefficients, where these values are continuously updated by adaptive laws to ensure asymptotic convergence to zero for the output function. The proposed controller is applied to solve the problem of pitch angle regulation for a floating wind turbine with dynamic uncertainty and external disturbances. Numerical simulations are performed to demonstrate the validity of the designed controller to achieve the desired pitch angle for the floating turbine＇s body.
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
