To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are show...To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.展开更多
This paper develops an approach to control unstable nonlinear multi-inputs multi-output(MIMO) square plants using MIMO fractional order(FO) controllers. The controller design uses the linear time invariant(LTI) state ...This paper develops an approach to control unstable nonlinear multi-inputs multi-output(MIMO) square plants using MIMO fractional order(FO) controllers. The controller design uses the linear time invariant(LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix(TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function(TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D(Derivative) TF is related to a FO TF of the form Dδ, δ =[0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11572025,11202013 and 51420105008
文摘To shed light on the subgrid-seale （SGS） modeling methodology of nonlinear systems such as the Navier-Stokes turbulence, we define the concepts of assumption and restriction in the modeling procedure, which are shown by generalized derivation of three general mathematical constraints for different combinations of restrictions. These constraints are verified numerically in a one-dimensional nonlinear advection equation. This study is expected to inspire future research on the SGS modeling methodology of nonlinear systems.
文摘This paper develops an approach to control unstable nonlinear multi-inputs multi-output(MIMO) square plants using MIMO fractional order(FO) controllers. The controller design uses the linear time invariant(LTI) state space representation of the nonlinear model of the plant and the diagonal closedloop transfer matrix(TM) function to ensure decoupling between inputs. Each element of the obtained MIMO controller could be either a transfer function(TF) or a gain. A TF is associated in turn with its corresponding FO TF. For example, a D(Derivative) TF is related to a FO TF of the form Dδ, δ =[0, 1]. Two applications were performed to validate the developed approach via experimentation: control of the angular positions of a manipulator, and control of the car and arm positions of a translational manipulator.
