In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is c...In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.展开更多
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hy...In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.展开更多
In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hys...In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.展开更多
This paper discusses the generalized play hysteresis operator in connection with the KdV equation. Results from the nonlinear semigroup theory are applied to assure the existence and uniqueness. The KdV equation with ...This paper discusses the generalized play hysteresis operator in connection with the KdV equation. Results from the nonlinear semigroup theory are applied to assure the existence and uniqueness. The KdV equation with hysteresis is reduced to a system of differential inclusions and solved.展开更多
The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the us...The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.展开更多
基金supported by the National Natural Science Foundation of China(61203229)
文摘In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.
基金the Natural Science Foundation of the Education Committee of Anhui Provinc
文摘In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
文摘In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.
文摘This paper discusses the generalized play hysteresis operator in connection with the KdV equation. Results from the nonlinear semigroup theory are applied to assure the existence and uniqueness. The KdV equation with hysteresis is reduced to a system of differential inclusions and solved.
文摘The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.
