Higher Order Nonlinear Differential Equations Research Articles

Optimal control of nonlinear power systems by an imbedding method

Realistic models of power systems involve high-order non-linear differential equations. The application of optimal control theory in optimizing such systems involves a high-order nonlinear 2-point boundary-value problem whose solution is very cumbersome. In this paper the imbedding method of solving a free-end, fixed-time optimal control problem is applied to a sixth-order nonlinear power system. The optimal designs for both open and closed loop plants are presented. The results of this application are compared with those by the hybrid linearization method considered by other authors. The results indicate that the 2 methods follow quite closely.

On the optimal control solution of nonlinear power systems

Summary Realistic models of power systems involve high-order nonlinear differential equations. The application of optimal control theory in optimizing such systems involves a high-order nonlinear two-point boundary-value problem whose solution is very cumbersome. In this paper the imbedding method of solving free-end, fixed-time optimal control problem is applied to a sixth-order nonlinear power system. Both the open and closed-loop controllers are considered. The results of this application are compared with those by hybrid linearization method considered by other authors. The results indicate that the two methods follow quite closely.

The Phase-Space Method for Analysis of Nonlinear Control Systems

Abstract This paper gives a general procedure for the analysis of a feedback system with a nonlinear control function. Taking the actuating signal as the dependent variable, a single nonlinear differential equation is obtained, the order of which depends upon the complexity of the linear transfer functions. This high-order nonlinear differential equation is then solvable by the phase-space method developed by the author and detailed in his previous papers (1, 2, 3). The method is further extended to the analysis of a system with one nonlinear controller in the forward branch and another nonlinear controller in the feedback branch. The two phase-plane equations obtained from the simultaneous differential equations are then solvable by the method given in reference (4).

A method for solving third and higher order nonlinear differential equations

A method for solving third and higher order nonlinear differential equations