tailieunhanh - Analysis and Control of Linear Systems - Chapter 4

Chapter 4 Structural Properties of Linear Systems công cụ cơ bản cho một phân tích cấu trúc của hệ thống Bất kỳ hệ thống vật lý có những hạn chế mặc dù các hành động kiểm soát có thể khác nhau có nghĩa là để cải thiện hành vi năng động của nó. Một số hạn chế về cấu trúc có thể xuất hiện rất sớm trong giai đoạn phân tích. Ví dụ sau đây minh họa tầm quan trọng của vị trí của số không đối với các giải pháp của một vấn đề điều khiển truyền thống mà là việc. | Chapter 4 Structural Properties of Linear Systems . Introduction basic tools for a structural analysis of systems Any physical system has limitations in spite of the various possible control actions meant to improve its dynamic behavior. Some structural constraints may appear very early during the analysis phases. The following example illustrates the importance of the location of zeros with respect to the solution of a traditional control problem which is the pursuit of model by dynamic pre-compensation. Being given a transfer procedure equal to t p p -1 p 1 3 is it possible to find a compensator c p so that the compensated procedure has a transfer equal to the one of the model previously fixed tm p It is well known that the model to pursue cannot be chosen entirely freely. Indeed the pursuit equation t p c p tm p imposes that the model must have the same unstable zero as the procedure otherwise the compensator will have to simplify it and hence an internal instability will occur. In addition the relative degree of the model the degree of difference between denominator and numerator we will refer to it later on as the infinite zero order cannot be lower than 2 otherwise the compensator will not be appropriate. Chapter written by Michel MALABRE. 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of numerous control problems. The plan is the following. After a brief description of certain main geometric and polynomial tools useful for a structural analysis of the systems section we will describe the Kronecker canonical form of a matrix pencil which when we particularize it to different pencils input-state state-output and input-state-output gives us directly but with a common perspective the controllable and observable canonical forms of Brunovsky and the canonical form of Morse section . The following section section illustrates the .