Research And Simulation Of Effective Reduction Strategies For Nonliear Systems

This paper involves the design and application in circuit simulation of methods for model reduction of nonlinear system. The reduced-order approach is based on projecting the dynamical system onto subspaces consisting of basis elements that contain characteristics of the expect solution. A major goal in this project is to develop accurate and effective numerical techniques for reduction computation, applicable to high-order systems.The purpose of Model Order Reduction is to replace a large model by a smaller one, which preserves the essential properties of the original model. This smaller system must be an approximation of the larger system, in a sense that the input-output behavior of this system is comparable to the original, within a certain accuracy. Therefore, the methods try to capture the essential features of the model in a small model and preferable as quick as possible.This research focus on two methods for nonlinear system reduction which are based on the existing reduction methods for linear system:Krylov subspace method and Balanced Truncation method. Krylov subspace method is one of the two larger groups of methods can be distinguished in the nowadays existing reduction methods, using a Krylov space to find the basic properties of a system. Krylov subspace methods are attractive for large-scale sparse systems, since only matrix-vector multiplications are required, and they can easily be generalized for descriptor systems. Drawbacks of this technique are that stability and passivity are not necessarily preserved in the reduced-order system and that there is no global approximation error bound. The other method-Balanced Truncation methods differ strongly from Krylov subspace methods, using a sort of singular value decomposition to select the important directions of the system and neglecting the others. An important property of this method is that the asymptotic stability is preserved in the reduced-order system.These two reduction method for linear system are of paramout importance so as to speed up the computation in large-scale science and engineering. They have their own advantages in the areas of application and computation. Combine the features and advantages of these methods to develop two reduction methods for nonlinear system:one method is use of a perturbative representation of the system and reduced by Krylov method. The other is empirical balanced truncation which is form empirical gramians to define a projection matrix to reduce the system.In the research, the order-reduction methods are simulated and analysed by MATLAB which allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, and Fortran. MATLAB language is an interactive mathematical script language and its syntax is similar with C/C++. It supports fifteen data type involving Boolean, numeric, text, function handle, heterogeneous container and each type is defined as matrix or array form(dimension of zero or zero upon). The simplest way to execute MATLAB code is to type it in at the prompt (>>) in the Command Window, one of the elements of the MATLAB Desktop. In this way, MATLAB can be used as an interactive mathematical shell. Sequences of commands can be saved in a text file, typically using the MATLAB Editor, as a script or encapsulated into a function, extending the commands available. The reduction methods are applied on a standard system and compared each other to present which one is more accuracy based on the evidence from MATLAB data analysis and plot generation. Realize the visualization of order-reduction thereby.