The Research Of The Approach Of Model Transformation In Linear Systems

All control methods are besed on a special model such as state equation, transfer matrix, difference equation and so on. So the aim of this paper is mainly analyse and study the transfer approach of many different kinds of control models, in order to find a model transfer method which is simple, effective and useful.Firstly, the paper discussed the description of each kind of models. It studied not only the definition of common used models in both continuous system and discrete system, also the mathematical theory the model based on and how to establish the model. This part is the basic for the study of the model transfer methods in the following chapters.In the study of the approach transfer state equation into transfer matrix, the paper introduced a useful algorithm based on the iteration. The core of that algorithm is to compute the characteristic polynomial. Three different kinds of methods are discussed and compared. With the comparation of these algorithms, the most adaptive usage fields of each approach are known.Presently, most algorithms of the transfer matrix realization are deal with the transfer matrix whose elements are zero-pole models and the models they deal with are the ones without time delay. To resolve these problems, a new algorithm which can deal with a MIMO system transfer matrix (rational fraction matrix form) with time delay is proposed in this paper. The controllability and observability of a state equation tansfor from a rational fraction matrix form transfer matrix, is connecting with the transfer matrix whose elements in each channal have a common divisor or not. Base on this relationship, a transfer matrix's decomposition algorithm is proposed in the paper. After developed this transfer matrix's decomposition algorithm, the minimal realization method proposed in this paper can be used to in the non-square processes.Lastly, discretization algorithms are researched and compared. With these algorithms, different kinds of discrete system madels (difference equation, pulse transfer function, discrete state equation) can be got.