Linearization of non-linear state equation
نویسنده
چکیده
The paper presents an overview of linearization methods of the non-linear state equation. The linearization is developed from the point of view of the application in the theoretical electrotechnics. Some aspects of these considerations can be used in the control theory. In particular the main emphasis is laid on three methods of linearization, i.e.: Taylor’s series expansion, optimal linearization method and global linearization method. The theoretical investigations are illustrated using the non-linear circuit composed of a solar generator and a DC motor. Finally, the global linearization method is presented using several examples, i.e. the asynchronous slip-ring motor and non-linear diode. Furthermore the principal theorem concerning the BIBS stability (bounded-input bounded state) is introduced.
منابع مشابه
Free Vibration Analysis of Quintic Nonlinear Beams using Equivalent Linearization Method with a Weighted Averaging
In this paper, the equivalent linearization method with a weighted averaging proposed by Anh (2015) is applied to analyze the transverse vibration of quintic nonlinear Euler-Bernoulli beams subjected to axial loads. The proposed method does not require small parameter in the equation which is difficult to be found for nonlinear problems. The approximate solutions are harmonic oscillations, whic...
متن کاملNonstationary Response Of Large, Non-Linear Finite Element Systems Under Stochastic Loading
A very efficient and straightforward numerical procedure for the computation of statistical second moment characteristics of large, non-linear finite element systems under stochastic loading is presented. For the modeling of both the loading and the response of the system an orthogonal series expansion of the corresponding covariance matrix, the so-called Karhunen-Loève expansion is applied, al...
متن کاملTime-Invariant State Feedback Control Laws for a Special Form of Underactuated Nonlinear Systems Using Linear State Bisection
Linear state bisection is introduced as a new method to find time-invariant state feedback control laws for a special form of underactuated nonlinear systems. The specialty of the systems considered is that every unactuated state should be coupled with at least two directly actuated states. The basic idea is based on bisecting actuated states and using linear combinations with adjustable parame...
متن کاملCoordinated Planning and Scheduling of Electricity and Natural Gas Systems
In this paper we propose a model for coordinated planning of power and natural gas systems, as a part of electricity supply chain. This model takes into account costs and constraints of both systems, and with hiring simplifications and linearization methods transforms initially nonlinear formulation to a mixed integer linear programming (MILP) problem. Natural gas would be assumed steady state,...
متن کامل